text:
Can Axis and Allies be played with two players, and does it require all countries to be picked?
I had just recently bought the game and I was wondering if we needed more than two players to control all the countries. We had already decided that I would take the UK and USA while he would take Germany and Japan. Do we need somebody to play as Russia or could we just play without Russia?

Axis and Allies only works well if all five countries are in play, on their correct teams.  If you have five players, this is easy to do.  If you have fewer than five, here are the recommended sets:
4 Players

Soviet Union, United States (Allied)
United Kingdom (Allied)
Germany (Axis)
Japan (Axis)

3 Players

Soviet Union, United Kingdom, United States (Allied)
Germany (Axis)
Japan (Axis)

2 Players

Soviet Union, United Kingdom, United States (Allied)
Germany, Japan (Axis)

If you insist on playing without one of the countries in the game, you'll be in for quite an unbalanced game.  Assuming that unplayed countries cannot be entered, here's some of what you're in for:
Soviet Union
With the Russians out, most of Germany's industry is freed up to:

attack Britain itself,
maraud the Atlantic,
and take out all of Britain's colonies in Africa, India, and further east

This would be a devastating game for the British player in particular and the Allies in general.
United States
Without the industrial might of the Americans, Britain would face Japan alone, leaving them no resources to throw against the Germans.  (This one I've actually tried -- it's a mess.)  The war tends to break into two separate wars: Britain vs. Japan in the east, Germany vs. Russia in the west.  Both of those wars are imbalanced in favor of the Axis Powers.
United Kingdom
This might be the closest to a balanced game with one power removed.  Taking Britain out of the game would remove the entire rim of the Indian Ocean: Africa, India, Australia, and all the various places in between.  The US would miss having a staging point in Great Britain, but they can use Morocco or Norway instead without too much difficulty.  Japan wouldn't have the British harassing their southern flank, but they also wouldn't have as many production points to gain in the south, either.
Germany & Japan
Removing either Axis Power completely unbalances the game.  Without Germany, Russia has nowhere to go but east into Japan's holdings.  Without Japan, Britain has no threat to their eastern territories and can easily focus all their firepower on Germany.

You always need all the countries.  With 2 players, one should be all the allies and one should be the axis powers.  So you will need to play Russia as well.


text:
Where is the Wizards of the Coast Offical Commander (General) banned list?
I just got destroyed in Commander (EDH).  Worst part of it is that the deck that killed me can do it over and over.  It has a guaranteed 4-5 turn win. (EVERY TIME)
It felt a bit broken to me, so I wanted to see if all the cards that were used to destroy me were legal for commander.
But the only site I can find is http://mtgcommander.net/rules.php.
Does Wizards let this external site dictate the banned cards for this format?

Out of curiosity, what was your opponent doing to guarantee a win? 4-5 turns is a lot of time to react!

mtgcommander.net is the authoritative source for EDH/Commander

"guaranteed" is also a pretty high bar, for seeing only ~13 cards out of a deck full of singletons.

@Jefromi With EDH's deep card pool, it's easy to stack a deck with tutors. Despite the banned list, there are a lot of effectively-one-card combos in the format (::cough:: Hermit Druid).

@AlexP I knew there were a lot of tutors just not that there were that many!

@Jefromi For example: here's a list with 18 tutors. (Here's a better version of that list, because you don't really need 18 tutors.)

The Commander format (née Elder Dragon Highlander) began with a bunch of judges entertaining themselves over the course of long, major tournaments, with cards that rarely saw play; Sheldon Menery in particular, who was at the time a level 5 judge although he has since retired from Magic judging.
As the format grew, the EDH Rules Committee formed, and they created "the" banlist -- while many groups customize the list to their own metas, and there is a different banlist designed for 1v1 play[1], the banlist maintained by the RC was the gold standard for EDH.
When Wizards wanted to get in on the action, they decided to let the RC maintain their autonomy, although they did need to brand the format, hence the name change to Commander instead of EDH. While commander is now a supported casual format, even to the point of being available for scheduling via the Wizards Event Reporter software, playable in Magic Online, and detailed in the Comprehensive Rules document, the rules of the format continue to be maintained by the RC.
The RC has synchronized their rules/banlist update schedule with that of Wizards, which helps to avoid confusion from mismatched information.
In short: The banlist posted on mtgcommander.net is the official banlist.

Notes

Duel Commander, occasionally called "French" EDH. The Duel Commander rules and banlist are maintained by a separate group from the Commander Rules committee, and Duel Commander is not supported by Wizards in the way normal Commander is.

Solid answer.  Thanks.  Also explains what French Commander is, which I had been wondering.

That list is correct. You can find the same list on Wizard's site here: https://www.wizards.com/Magic/TCG/Resources.aspx?x=magic/rules/100cardsingleton-commander.

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text:
Do commanders "die" if they go to the command zone instead?
If my commander would die and I opt to move it to the command zone instead of the graveyard, does it cause a "when a creature dies" ability trigger?
An example would be Fool's Demise. If my opponent puts that on my commander, and then does lethal damage to it, would they get my commander or could I put it in my command zone?
I'd love any answer, but my playgroup needs an actual rule. So I would love a supporting rule citation.

Yes, commanders can trigger “dies” triggers as they head to the command zone
This new rules change was announced on June 7, 2020 and became active in the Commander rules circa the release date of Core Set 2021. I'll explain the rules basis later, but to summarise the new rules:

If your commander would be put into the graveyard or exile, you can opt to send it to the command zone. If you do, it will hit your graveyard or exile and then be put into the command zone the next time state-based actions happen. Abilities will see that it died or got exiled, so your commander dying can trigger death triggers (its own or those of other cards).
If your commander would be put into your hand or library, you can opt to send it to the command zone. If you do, it goes there instead of your hand or library. It will never actually be put into your hand or library and cards will not see it enter those zones.

This means:

If Elenda, the Dusk Rose is your commander and dies, you can send her to the command zone, and her death trigger will still go on the stack to give you Vampire tokens.
Dark Prophecy will see your commander die, even if you send your commander to the command zone.
Kresh the Bloodbraided will see peoples' commanders die and will get +1/+1 counters equal to the power of that commander as it last existed on the battlefield.
Azorius Aethermage will not see your commander return to your hand if you opt to send your commander to the command zone.
If your commander dies and you send it to the command zone, many “dies” triggers that expect to see it in the graveyard will lose track of it. For example, Dread Slaver can't return a commander to the battlefield it killed if the commander's owners sent it to the command zone. This is because the commander is no longer in the graveyard, and Dread Slaver can't return creatures that are no longer there.

Note that you're only given the option to move your commander out of the graveyard/exile to the command zone once—the very next time state-based actions are checked. In simple terms, this will be immediately after the spell/ability that put them there resolves, or if they died from combat damage, immediately after things die from combat. In both cases, you'll do this before any triggered abilities go on the stack and before anyone has any opportunity to cast spells and activate abilities.
If you don't move your commander to the command zone then, they'll be stuck where they are until you find another way to move them. You won't have indefinite permission to move them out from then onwards.
The rules didn't always work this way. Prior to this date, if you wanted to send a commander to the command zone instead of graveyard or exile, it would never reach graveyard or exile first and nothing would see it die or get exiled. The rules for putting a commander into its owner's hand/library haven't changed though.
What's the rules basis for it working this way?
A commander being sent to your graveyard or exile is now handled by a state-based action instead of a replacement effect.
The new state-based action is as follows:

If a commander is in a graveyard or in exile and that card was put into that zone since the last time state-based actions were checked, its owner may put it into the command zone.

This means if your commander dies, you put it into the graveyard as normal. The next time state-based actions are checked, you can move it to the command zone. This state-based action will take place before any triggers go on the stack as a result of your commander dying. But those triggered abilities have already been triggered, and will still go on the stack the next time they have a chance to do so.
Your commander heading to your hand or library is still handled as a replacement effect:

If a commander would be put into its owner’s hand or library from anywhere, its owner may put it into the command zone instead. This replacement effect may apply more than once to the same event.

If you cast Rescue on your commander and choose to send them to the command zone, then because this is a replacement effect, Rescue functionally reads “Put target permanent you control into the command zone” — the “return to your hand” event is replaced and never happens.

For those interested, you can view the Commander rules both before and after the change on the Wayback machine: its content before this change was archived on June 18, and its content with the change was archived on August 18.

The word dies has a very specific meaning in mtg.

Dies used to be a keyword action in Magic similar to "destroy" and was
  reintroduced in Magic 2012 to replace the phrase "is put into a
  graveyard from the battlefield". "Dies" used to be a slang term for
  this occurrence before and is now officially used to signify triggers.
  It is exclusive to creatures while other card types still use the old
  phrasing.
700.4. The term dies means “is put into a graveyard from the battlefield.”

Although there is quiet a bit of slang usage of the term most of the slang usage out of a rules perspective is used incorrectly. There is a host of ways a creature can leave the battlefield and not die.
Things like exile, bounce and tuck effect will all remove the creature without it "die-ing"
SOURCE:

You would be able to put your commander back in the command zone.
This isn't because your commander didn't die, though when this question was originally asked that was how things happened. Instead what now happens is this:

Your commander, enchanted with Fool's Demise, is dealt lethal damage.
Your commander is put into the graveyard as a state based effect due to lethal damage. (this is a change from previous rules)
The trigger condition for Fools Demise is met, however since the last round of state based actions had an event, they are checked again.
Two state based actions happen in this round, the commander state based action from rule 704.6d and the aura state based action from rule 704.5m. The aura Fool's Demise is sent to your opponent's graveyard and you are given the choice to leave your commander in your graveyard or put it back in your command zone.
The second trigger condition on Fool's Demise triggers, but state based actions need to be checked again still.
State based actions are checked again and do nothing.
The two triggers from Fool's Demise are put on the stack, in the order your opponent chooses. Fool's Demise returns to their hand when the second ability resolves. If your commander is still in the graveyard, it is returned to the battlefield under your opponent's control.

Before, sending the commander back to the command zone was a replacement effect. It went to the command zone instead of going into exile or the graveyard. Now the commander does go to the graveyard or into exile, but then can be moved back to the command zone as a state based action under rule 704.6d:

704.6d In a Commander game, if a commander is in a graveyard or in exile and that object was put into that zone since the last time state-based actions were checked, its owner may put it into the command zone. See rule 903, “Commander.”

Dies in magic has a specific definition in the rules too:

700.4 The term dies means “is put into a graveyard from the battlefield.”

This means that, yes, your commander did die according to the rules, but you still have the chance to move it out of the graveyard before anything can interact with it there.

For completion's sake:

704.5m If an Aura is attached to an illegal object or player, or is not attached to an object or player, that Aura is put into its owner’s graveyard.

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text:
How often should I bluff in poker?
Obviously bluffing is an important element of poker, and bluffing too often, or not often enough will negatively affect your winnings, but is there a rule of thumb for how often you should bluff? For example, if I bluff once or twice an hour, is that too infrequent? If I bluff about once in a button cycle, is that too often? What's the optimum bluff frequency?
EDIT: I found these links:
http://en.wikipedia.org/wiki/Bluff_(poker)#Optimal_bluffing_frequency
http://en.wikipedia.org/wiki/Pot_odds#Bluffing_frequency

According to David Sklansky, game theory shows that a player should
  bluff a percentage of the time equal to his opponent's pot odds to
  call the bluff. For example, in the final betting round, if the pot is
  $30 and a player is contemplating a $30 bet (which will give his
  opponent 2-to-1 pot odds for the call), the player should bluff half
  as often as he would bet for value (one out of three times).

and

David Sklansky, in his book The Theory of Poker, states
  "Mathematically, the optimal bluffing strategy is to bluff in such a
  way that the chances against your bluffing are identical to the pot
  odds your opponent is getting."

So, if I generally bet half the pot, I should be bluffing 40% of the time; if I generally bet twice the pot, I should be bluffing 25% of the time. Sounds like a lot to me - how does this sit with everybody's experience?

What's a "button cycle"?

@ire_and_curses: A "button cycle" is a cycle in which the "button" (that determines the dealer and the blinds) has been around to each person once. It's actually the same number of games as the number of players at the table.

The normal term for that is "orbit". Measuring bluff frequency in terms of time is a bad idea, btw, since the speed of play will vary.

@KarlKnechtel: Another consideration is the "speed" of the GAME. Some games are "fast" with a lot of bluffing going on. In such cases, you should (almost) "always" have them when you bet--to catch bluffs and slow the game down. Other games are "slow" with few bluffs and few calls. In such cases, you should sometimes bet when you don't "have them" (bluff) to "steal" money and speed the game up.

A rough rule (from economics) is that you should bluff until the money you lose from getting caught approximates the money that you would forego from not bluffing. That is, you should equate the "marginal utilities" of the two activities.
If you "never" get caught, you aren't bluffing enough. That is, you are leaving money on the table with a number of bluffs that you could have "run" but didn't. You SHOULD get caught, partly for "advertising" purposes, and partly so that you "start" to lose money bluffing. Then bluff "a little more" and stop when you lose a little more. If you get caught "too often," you are losing more money than you're making with your last few or "marginal" bluffs.

One of the most important things in bluffing is the image you have on the table. If you generally play tight, your opponents will trust your bets more and your bluffs will be more effective.
Otherwise, if you are a loose player you could a lot more hands and your opponents will trust you less, and call your bets more often.
So, if you are a tight player, you should bluff more, because you will win pots with them more often, and if you're a loose player you should bluff a little less. Anyways, if you are loose and bluff often, they will trust you less and call more (as said above), and you can make profit from this when you actually have a strong hand.

How can there be a right answer to this question? You bluff for 2 reasons.
1 - To take a pot when you don't think you have the winning hand.
2 - To make people believe you are willing to bluff so you can sucker them in when you have a winning hand.
How often you can bluff totally depends on how well you've convinced others that you aren't doing one or the other of the above. That varies by night. That varies by the cards you've been getting. That varies by how well people know your style. That varies by how well you think the other players at the table can be bluffed. It varies by how often you think other players are bluffing. It varies by how often other players call versus fold. It varies by how other players have reacted to your bluffs. IOW, there is no way someone can say to bluff a certain percentage of the time since there are way too many variables. Besides, if you learn that someone bluffs say 2 times per hour then any decent player will use that knowledge to their advantage. And anybody bluffing 25%-40% of the time at tables I play at will lose their shirt night in and night out.
The rules of thumb that I use if I am going to bluff:

I believe that I am going to win with that bluff. (Notice that I didn't say hope)
I am playing for option 2 above; and then I ensure that I only lose minimal money.
The amount of money in the pot versus how much I need to put in has really good odds and there is still a prayer that I'll win outright.

You can't put a frequency on any of those options because it's all about feel and reading the other players.
Besides that, I think bluffing is far over-rated in poker anyways. In general, when you bluff you put up a relatively high amount of money, but you get relatively little in return since you are trying to get people to fold.  You are far better served learning when to play your cards and when to fold them and maximize your profits from that. People aren't stupid. You can make money bluffing in the short term, but eventually people catch on and set you up.

OK, so 25%-40% is too often. And obviously 0% is not often enough. Can you narrow that range any further? Is 20% still too often, or can you get say with that at certain tables? Is 5% still not often enough, or is that optimal at certain tables?

@gk-I think you are looking at it the wrong way by trying to put a % on it. If you play at a table where bluffing always works then bluffing 100% of the time is the proper percentage. If you play at a really loose table that people always call then bluffing 0% of the time is the proper percentage. The right number depends on you gaining experience to learn what works for you under various conditions. You also need to be unpredictable, so even if you play with the same people all the time, one night you might bluff 0 times and another you might bluff 50 times so you don't become predictable.

@gk-but like I said, IMO bluffing is only a short-term strategy. If you use it as your core strategy then you are destined to lose. You risk a lot of money and get relatively little in return. IOW, high risk, low reward. Rather than focusing on bluffing, focus on learning to properly play the cards you are dealt. In the long run you'll always be a winner since most people don't know how to properly play their cards.

I'm not focussing on it, but obviously bluffing is an important part of the game and bluffing 0% or 100% of the time is never optimal. I was just wondering what the average was, and if there was any way of calculating an optimal overall bluffing percentage.

It comes from game theory optimization (GTO)
The idea is the bluff rate is such that your opponent is stuck between call or fold.  Call or fold has the same EV.
You know you are beat.  Your opponent has a good hand but not the nuts. They will call every time with the nuts.
p is pot (before you bet)
b is your bet
f is your bluff rate
EV is expected value
EV = -b + f(p + 2b)
Set the EV to 0. Solve for f.
b = f(p + 2b)
f = b / (p + 2b)
So if p = b - you bet the pot you should bluff 1/3 of the time.
Note if you bet the pot you are giving your opponent 2:1.
Play three hands and you bluff once and have the nuts twice.
Your opponent is getting 2:1 to call and the pot has 100.
Your opponent folds all three:
0 + 0 + 0 = 0
Your opponent calls all three:
-100 - 100 + 200 = 0
To simplify set p = 1 and and fr just be the fraction of the pot you bet
bluff = fr / (1 + 2fr)
bluff   fraction
rate    pot
0.50    100.00
0.44      4.00
0.43      3.00
0.40      2.00
0.33      1.00
0.25       .50
0.20       .33
0.17       .25

Ironically you should bluff more with bigger bets.
You opponent also needs at least a bluff catcher to call.
Clearly you are going to get more bluffs through if a scare card hits on the river.  Don't try and bluff a naked 2 on the river if you have shown not strength.
Very important is that does not mean bluff the river 1/3 time period. 1 bluff for every 2 value bets.  If you get to the river against 1 then you are going to have the best hand about 1/2 the time and you are only going to be confident you have the best hand like 1/3.  So in 6 hands you would value bet 2 and bluff 1.
If you watch the pros some even bluff more.
If you never bluff then players know to lay down.  You have to bluff some to get paid off when you have it.
You can even do GTO on how often to call - assuming you have a bluff catcher.
Assume you put villain on GTO and bet the pot so you them on bluff 1/3
c = call rate
EV = c 2/3 (p + 2b) - c 1/3 0 - b
= c 2/3(3) - 1
= 2c - 1
c = 1/2
You should call back with a bluff catcher as often as you have hands that you would call back for value.

This is incoherent even to someone deeply familiar with poker, with mathematics, and with working out what is meant by poorly-written paragraphs about both. That's not helped by the absence of MathJax on BCG, but knowing the limitation, it should be accounted for.

@Nij I am sorry you could not follow

Cleaning up the comments here.  @Nij, you've made your point, thanks!

@PatLudwig I have the number on reputation on poker.stackexchange.com and yet a lot of down votes on this site for tag poker.  On math.stackexchange.com I have no poker tag with a negative vote.  Do you think it is me or the site?


text:
Resources for learning about good shape?
Shape is immensely important in Go, and you can read about the basics anywhere - don't make empty triangles, table and mouth shapes are good, etc.  Where can I find more advanced treatments of shape?

Charles Matthews wrote an excellent book on this topic, coincidentally called Shape Up!
It is available for free on the net, if you have a Gobase.org account simply grab it here, if not, Google should bring up something. To list a few of the ideas explained:
Part 1 of the book, "Principles of development", covers basic terminology (table shape etc.), wedge weakness, empty triangles, eye shape, tactical aspects of connections, one point jumps and compound shapes.
The second part "Principles of engagement" explains hane at the head of 2/3 stones, nose tesuji, bulges, the center of 3 stones, answers to attachments, open skirts and submarines.
Part 3 "Practical fighting" deals with all kinds of cuts, light play, keima, peeps, various pincers, caps and  sector lines.
In Part 4, "Vital points and shape in the opening", 2 and 3 point extensions and their invasions, 3rd and 4th line and enclosures are discussed.
The final part talks about "Theory", pretty advanced concepts like 3 instead of 1-2-3, miai, kikashi, probes and large distance jumps, haengma and sabaki.
Interestingly, this book can be understood by beginners (high DDK) and is still useful up to lower dan levels. All shapes explained are extremely common in actual play so studying this book is most rewarding. There are also several sets of tsumego to reflect on the chapters.
Sadly the amount of higher level books on advanced shape study is limited in the Western world. If you're capable of speaking Chinese, Japanese or Korean you'll find a vast amount of very high level books in Asian Go stores.
Apart from joseki study and Asian books, you're pretty much out of luck regards of lecture material. Of course there are still some high level (Western) books and lectures but they are rarely focused on the idea of shape itself, so you'll have to scrape together what you find.
As you grow beyond the point where the typical Western shape books are of much use, the study of joseki is the main way to learn. Joseki are carefully crafted by professionals over time, and the shapes they incorporate are often very advanced.
However, once study material has become difficult to get, you'll probably have connections to several sensei that will be able to help you out. Until then, let the basics become natural, and review your games to understand and learn from your shape mistakes.

Another good way to learn shape is to play shape game against a stronger player. Stronger player plays white you play black. To start with black places stones along the 1st lines, one space apart:
$$Wc Shape game
$$ +---------------------------------------+
$$ | . X . X . X . X . X . X . X . X . X . |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | X . . . . . . . . 1 . . . . . . . . X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | . X . X . X . X . X . X . X . X . X . |
$$ +---------------------------------------+

White starts the play, with the aim of making ONE living group in the center; black's aim is to not allow this to happen.  Playing this game is fun and teaches beginners about good and bad shapes naturally.

This game teaches specifically what are the good shapes to make eyes (and black learn the way to prevent them). But one should keep in mind that there are different kinds of good shapes.

I'd only offer a few more suggestions over those given so far.
The delightful book by Kageyama, Lessons In The Fundamentals Of Go. Besides being an excellent all round resource and pleasingly written, it has a chapter, ch8, on some fundamentals of shape. It may be too basic for your skill level, but it is a must read for any Go player in my opinion. Heres a link to the details for this book on Senseis Library.
http://senseis.xmp.net/?LessonsInTheFundamentalsOfGo
There is also the Rob van Zeijst, Richard Bozulich book Making Good Shape, which is volume 3 of their "Mastering the Basics" series. It is a shape problem book, and I find many of the problems to be challenging.
Finally, I would look at pro games, both new and old. They are full of examples of good shape, and exploits of bad shape. Both books above have pro games in them to review.
Hope that helps.


text:
What rules are used in international events
What rules are used during international events like the recent Samsung Cup?

There is no standardized international ruleset in Go.  Generally, a tournament will use the ruleset of the hosting country.
According to an article on Sensei's Library, at least in 2004 the Samsung Cup used Korean rules.
The Chunlan Cup is (again according to SL) the only international tournament played by Chinese rules.
The Ing Cup uses Ing rules.
I guess most other tournaments use Korean or Japanese (territory scoring) rules (?).


text:
Strategy for studying professional games?
I recently took A. Dinershtein's Go style test. It was useful to me, as the test is aimed at finding professional players who might think the way you do, for study purposes. It has definitely worked for me. But what should I bear in mind while studying professional games?

Dumb question, I took the test, but it didn't give me a list of professional players to study.  Where can I find such a list.  I got the "flexible" result.

A lot depends on your strength.  I find that memorizing them is useful for me.  I've also heard a lot of people suggest that you need to play them out on a real board.  It helps teach your fingers where the pro moves are :)
If you're not a dan-level player, you probably shouldn't focus too much on fighting sequences - you won't be able to understand all of the variations the players are considering.
It's a really good idea to look at each sequence or exchange in the game and try to tell what each player got out of it.  From an amateur perspective almost everything that happens in a pro game is an even trade, so you should look for sequences that don't seem even to you and try to figure out why they actually are.

"almost everything that happens in a pro game is an even trade." Unless one of the (pro) players (or a third pro) says it's not.

In which case, it is usually going to be close enough to even for the vast majority of amateurs. As Janice Kim one pointed out in a lecture: if an amateur played as well as the losing player in every pro game, they'd still be much stronger than most amateur players.

Most pro games are fairly even until a "turning point." This is when one player makes a mistake, as related by the author of the game commentary, usually a pro. Sometimes the commentator is one of the players, who says, "I made move X that lost the game, or "My opponent's move Y lost him the game."
Then the thing to do is to study the game up to the turning point, to see why it was even till then, and then after the turning point, to see why the winner had a clear advantage.
Some games are closely matched to the end, with White finally winning by less than the komi, or alternately, Black beating komi by say, one and a half points.
A model book in this regard is Kato's "Attack and Kill," about his winning streak of some 20-odd games, in which he points out his opponent's "losing moves." He is also self-critical, pointing out places where he made move X, which should have lost, but that the opponent's move Y was an even worse mistake, that resulted in a Kato victory.

I used to memorize games as a fairly large staple of my studies. Some general points:
1) The position at any point is approximately even.  A "losing move" to a professional–one that everyone agrees is bad–is still probably close enough to even for anyone but a high-level dan.  If you are at that point or getting close to it, be sure to look up the commentaries if there are in and read through them.
2) Take your time on each move.  Analyze how you would move, see how the professional moves, and analyze why the professional might have moved there.  It is oft repeated that you are about 3-4 stones stronger when you study, so take advantage of that and try to see as much as you can. Even if you are wrong, the process of thinking about it is very valuable.
3) Start with ten moves at a time and see if you can increase it over time.  So put down ten moves, then reset.  When I would do it I would go back to a blank board every ten moves and try to play back to the current point.
4) Replay your own games from memory immediately after you play them.  If you played a person at a club, see if you can get them to go with you.  Memorizing pro games is training your pattern memory, and replaying through your own games after you've played them is excellent practice here.
5) During the endgame try to count the value of each move.  This is an easy time to do that, and it is excellent practice.
Hope that helps!

Yuan Zhou just published a book on this topic. Check out Slate and Shell for sample pages. I am a big fan of Zhou's books and will certainly buy this one. He has a nice way of writing towards kyu level players.
Title: Learning from Pro Games
Author: Zhou, Yuan
Year: 2011
ISBN: 9781932001-57-0
Price: $20.00
http://www.slateandshell.com/SSYZ015.html

nice. i like yuan zhou too. i may have to check it out. hopefully schaak- en gowinkel het paard will have a copy.

I am a novice player, so take everything I might say cautiously.  But I have been working through "Invincible - The Games of Shusaku" by John Power and I think it has been helping me, even if there is a lot I don't understand yet.
It is mostly commentaries on games from Honinbo Shusaku, who is arguably one of the greatest Go players.  The one thing to keep in mind is that these games were played before Komi was invented, so generally black can be more defensive and white must be more aggressive then you would likely see in a modern competitive game.  Still, the general tactics should remain the same.

It's a fantastic book.

I learned the game's rule when I was 5 or 6 years old. However, I was really hooked after I read a go book in a small bookstore in Xian (西安) when I was eighteen. The book was written by Go Seigen (吳清源－名局細解).
The book explains every single detail in games between Go Seigen and other top Japanese Go players. It was so inspiring. It was like reading a great painting. It was just beautiful.
I'd say I fell in love with go because of the journal to Xian.
More than twenty years later, I have written a program on iPad to read the annotated games of great pro players. The first game to test the program with, is a game of Go Seigen XD
So, I'd say pro games, like great paintings, are art.


text:
Second line invasion of two-space extension
The two-space extension is a very common pattern and forms a base. I've found lots of material here, and here, and elsewhere on how it cannot be cut and how to defend against various invasions.
Nevertheless, in one of my games I was confronted with the following non-standard invasion:
$$cm1 Non-standard invasion of two-space extension
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . 1 . . . . Q X . . . . |
$$ | . . . . . B . O . . O . . Q X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Question 1: Ignoring the three marked stones, how would one usually defend this invasion? Is J17 correct here?
Considering the option for black to connect up to the left and the white wall at the right, I played H18, which resulted in utter chaos and a miserable result for white. Below is my failed attempt at defending against this invasion.
$$cm1 Failed defense
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 2 1 . 3 4 . Q X . . . . |
$$ | . . . . . B . O . 5 O 7 . Q X . . . . |
$$ | . . . , . . . . . 6 . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

With this, Black was able to connect to the right. I've been playing around with various options, but couldn't find anything useful.
Question 2: Is white 2 above already a horrible mistake? Or does there exist a follow-up after black 3 that kills the invading stones?
Question 3: How strong is the two-space extension? In the initial situation where black invades at 1, what is the best white can expect to get?
Question 4: I found myself at quite a lack of knowledge when it comes to defending such non-standard attacks, however, most resources (like SL) only cover the typical attacks. Is it worthwhile to invest a lot of time into learning how to deal with strange attacks? Or should one expect to get this simply by experience?

Question 4 is probably complex enough to warrant it's own post.

The 2 space extension is generally regarded as very hard to cut and thus solid, providing at least 1 eye with various options to gain a lot more eyespace easily.
However, invasions and attacks are still possible. The B1 move in your diagram is actually a standard invasion with the marked black stone around.
$$cm1 A possible invasion of two-space extension
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . 1 . . . . Q X . . . . |
$$ | . . . . . B . O . . O . . Q X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Influence
One usual aim of this move is to either create center influence like this:
$$cm1 Influence, part 1
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 2 1 . . . . . . . . . . |
$$ | . . . . . B 9 W 3 6 W . . . . . . . . |
$$ | . . . , . . . 5 4 8 . . . . . , . . . |
$$ | . . . . . . . . 7 . . . . . . . . . . |

.
$$Wcm1 Influence, part 2
$$ +---------------------------------------+
$$ | . . . . . . . . 5 . . . . . . . . . . |
$$ | . . . . . . 4 O X 3 . . . . . . . . . |
$$ | . . . . . B X W X O W . . . . . . . . |
$$ | . . . , . . 2 X O O . . . . . , . . . |
$$ | . . . . . . . 1 X . . . . . . . . . . |

(B9 and the atari may be different on certain boards.)
$$Wcm1 Influence, result
$$ +---------------------------------------+
$$ | . . . . . . . . O . . . . . . . . . . |
$$ | . . . . . . X O . O . . . . . . . . . |
$$ | . . . . . B X W . O W . . . . . . . . |
$$ | . . . , . . X X O O . . . . . , . . . |
$$ | . . . . . . . O X . . . . . . . . . . |

This can be good depending on the global situation. Of course, white gets super strong, so black should only consider this if there is no useful attack on the 2 space extension anyway and the center is important.
Base robbing
Another idea is to use this invasion to steal eyespace and gain some territory. It is usual if there is a black stone on either side of the extension.
$$cm1 Base robbing, simple variation
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . a 1 3 b . . . . . . . . |
$$ | . . . . . B . W 2 4 W . B . . . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

A and B are miai to connect the stones out, so black can consider an outside move to attack - or he can firmly link up his 2 stones to either side to rid white of any sente moves near the edge.
This way, white ends up with a solid, but eyeless group with good center access. Depending on the board, this can be good for either player.
$$cm1 Base robbing, white resistance
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 2 1 . . . . . . . . . . |
$$ | . . . . . B . W . . W . B . . . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

However, white may think about resisting like this. this move can be good, but usually black 1 is only played if black can follow up like this:
$$cm1 Base robbing, black counter
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . O X . 1 a . . . . . . . |
$$ | . . . . . B . W c b W . B . . . . . . |
$$ | . . . X . . . . . d . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

A and B are miai now, so the black stones are out and white has a weaker shape than by playing C to begin with. In some cases, black plays the B-D exchange before B1.
$$Bcm1 White resistance, another idea
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . 1 . . . . . . . . . . |
$$ | . . . X 2 . O . . O . X . . X . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . X . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Sometimes, white can try a kind-of-sente move instead of replying directly. If black answers the move, white can play more aggressively against the invasion stone. If black follows up the invasion, an exchange could take place. This should be considered carefully before invading at 1.
Depending on the board, white may dislike the invasion on the second line, and thus plays a tobi to strengthen her group:
$$Wcm1 Defend
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . e . . . . . . d . . . . . . |
$$ | . . . . . B . W . . W . B . . . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . a b c 1 . . . . . . . . |

Any of A, B, C are thinkable just as well, and in some cases a tsuke at D or E is reasonable, too. This requires some reading, as D and E tend to lead to a huge exchange.
By the way, keep in mind that base robbing can be beneficial to white on certain boards. That's one of the reasons white, instead of the second line invasion, an attack at black 1 or a is usual in this shape, too, as well as moves on top of B or C.
Actual game
In the actual game, white had some extra stones to the right, which changes the situation significantly.
$$cm1 Simple answer
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 3 1 4 . . . Q X . . . . |
$$ | . . . . . B 5 O 2 . O . . Q X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

White could simply answer at W2, connecting firmly. Black cannot play 3 at 4 because then white would play 3 and thanks to the white stones on the right, black dies inside.
Thus black has to connect out, allowing white to get a reasonable shape with the tiger mouth at 4 in sente. Black 5 is played on the third instead of the second line because it has far greater influence on the center and the strength of the white group.
$$cm1 Strong answer
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 2 1 . 5 . . Q X . . . . |
$$ | . . . . . B . O . 3 O 6 . Q X . . . . |
$$ | . . . , . . . . . 4 . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

White can also consider the strong-hand descend at 2, blocking the connection out. Black will play 3 and 5, to which white avoids the self-destructing reply to the right of 5 and instead simply nobis at 6. Black is now forced to find a way to connect out or live locally  - I'll leave the tsumego as an exercise for the reader.
Related joseki shape
$$cm1 Simple answer
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . 2 1 . . . O . . . |
$$ | . . . . . . . . B . O . . O 3 . X . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |

In this very common joseki shape white is supposed to have a very solid group with enough eyespace to be difficult to attack. However, with the marked black stone in place, the invasion of B1 is an astonishing threat. The details are too long to list here, but if white blocks at 2, black will play the tesuji of 3 and it is very hard for white to find an answer that doesn't lose half the group, base, and yose.
Answering your further questions

Question 3: How strong is the two-space extension? In the initial situation where black
  invades at 1, what is the best white can expect to get?

The 2 space extension is stable. It is not alive locally, it is not strong, but it is stable in the sense of being connected and thus difficult to fiendishly attack. Prefer this extension when you don't like the idea of being split.
$$Wcm1 Solid
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . . . . a 1 b . O . X . . . |
$$ | . . X , . . . . . c . . . . . , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |

For instance, in this shape, a wide extension to A would immediately be invaded at B. White could think about playing 1 at C, aiming for a light shape, but that offers a range of difficult to handle invasions that you need to be comfortable with.
Also, leep in mind that "killing" is not always the best answer to moves that are either unusual or bad. Sometimes letting the opponent live is the best punishment. Remember the idea of the sacrifice in the 'influence' section of this answer - in that case, maybe just go for center influence (connect instead of block) when the center is of more value.
And contrarily, you'll be astonished how much dan players hate living sometimes. I remember a high dan friend of mind talking about a game he played against a pro: "I lived everywhere by crawling on the second line. It was atrocious, I could not find a good way to die."

Question 4: I found myself at quite a lack of knowledge when it comes to defending
  such non-standard attacks, however, most resources (like SL) only cover the
  typical attacks. Is it worthwhile to invest a lot of time into learning how to deal
  with strange attacks? Or should one expect to get this simply by experience?

Midgame joseki as those presented in this answer are very useful. Either learn them by playing tons of games and remembering the best shapes, or look them up in books. I remember there was a pretty thorough discussion of the 2 space extension in "Shape up!" by  Charles Matthews. Eventually, as a dan player, you'll be forced to remember them from study though since (at least Western) books rarely cover deep variations for specific boards or new inventions.

Don't have any books available as reference right now sadly, so this is just from the top of my head - let me know if I made a mistake or if there's anything that should be further explained.

I feel horrible that I can only vote once. But then, I was only browsing 2 questions for "a couple" of minutes (goodbye, morning break!) :)

In Related joseki shape I would play M18 L18 N17

Although it can and often does provide territory, that is not the primary reason that you want to play the two-space extension on the third line; what you're looking for with this extension is a base which is very difficult to cut, one which you can use to fight and/or secure territory as the game progresses.  Unless black has support, white can easily connect in the face of any attack and either make life on the edge, or leap out into the centre, depending on the circumstances.  It's a very stable and efficient shape, and the flexibility is a major part of why it's so popular.
Maintaining the connection itself against black 1 is fairly simple:
$$Wcm2 The easiest solution: Connect
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . X . . . . O X . . . . |
$$ | . . . . . X . O 1 . O . . O X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Now the so-called invasion is little more than a reduction, which now looks quite lonely.  A continuation could look something like this:
$$Wcm2 Black's not-so-glorious retreat
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . 4 2 X 3 . a . Q X . . . . |
$$ | . . . . . X . O 1 . O . . Q X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Thanks to the marked stones white still has a very solid territory, even though black has "successfully" reduced it by a few points (in gote).  Black has traded a few points of territory for giving white a not-insignificant amount of influence toward the the centre; this is the type of move that's typically held off until the endgame after territory is more-or-less defined.  During the mid-game, black would usually be better off deferring the attack in favour of a big point elsewhere unless he has a good chance of profiting (e.g., by pressuring or outright killing the weakened group after reducing eyespace).
Even if the marked stones were absent, white could still comfortably jump out to the centre or secure an eye with a.
Playing white 2 at H18 isn't necessarily bad (depending on what's going on in the centre, I would probably avoid it), but it picks a fight you want to be sure that you can win, and that is actually worth winning; thinking that the best (or only) defence against any attack involves killing the offending stones is a common mistake.  If black can tip the balance in his favour by ten points now, you can still win if you tip it back later by twenty, and being overly aggressive is a good way to make things needlessly complicated.

Surely you mean that White makes life locally with M18, not N18?

Question 1: Ignoring the three marked stones, how would one usually defend this invasion? Is J17 correct here?

They really can't be ignored for a question like this. "This" invasion doesn't come out of nowhere (except vs. a belligerent beginner).

Question 2: Is white 2 above already a horrible mistake? Or does there exist a follow-up after black 3 that kills the invading stones?

4 at 7 seems to work. Black should not have enough space to live locally.

Question 3: How strong is the two-space extension? In the initial situation where black invades at 1, what is the best white can expect to get?

I wouldn't normally expect Black to accomplish anything positive without stones in the K15 area. The P17 wall may be troublesome, though. It also needs to be asked just how White got into this position in the first place. In particular, if J18 is worrisome, then defend first.

Question 4: I found myself at quite a lack of knowledge when it comes to defending such non-standard attacks, however, most resources (like SL) only cover the typical attacks. Is it worthwhile to invest a lot of time into learning how to deal with strange attacks? Or should one expect to get this simply by experience?

By definition, you won't see strange attacks often. There's no point in memorizing responses to them, at least until you get to the point where you've memorized everything more useful than that (which is probably pretty close to pro level). What you want to do is develop your tactics and your fighting strength. Studying shape is a good idea as well (it's a broader topic than many people give it credit for).

I played a little with 4 at 7, I don't think it actually works (though it's definitely better than 4 as is). I'll post a diagram when I get home from work.

I take it back, I'm not going to post it here. I started typing it up and there's more variations than I'd care to type, especially when it doesn't even answer the question. I'll side with @mafutrct's exercise left for the reader. But I don't think it's possible to completely kill the invasion.

I would play J17 and force Black to connect.
The way you played, Black got the optimal result; he broke up your extension and turned "your" area into a free-for-all fight.
Black's downside is that his "invasion" is on the second line. If you push against him on the third line, you've lost some territory, it's true, but you've more than made up for this in center facing influence.
Many players will trade influence for third line territory, but here Black is basically offering to trade influence for only second line territory. The trade would be all in your favor.
Besides, once you hane at K18, Black has to take gote with 5 (see the diagram to gold's answer). Then you should reduce Black's right side influence, perhaps with a move around N15.

I object: White simply building a wall on the third line here is not a great result in terms of "influence", because of the existing stones at F17 and P16. Walls that already face opposition at their endpoints - coming around the sides - are severely compromised. That said, White has probably played quite passively to get to a position like this in the first place.

@KarlKnechtel: I agree, white's position isn't great. But black's is worse, running on the second line, the "line of defeat." "It's all relative."


text:
Is this corner dead?
Played a game on KGS.  We are both 4K.  He was good at life and death, and I am rusty.
Was B1 sente?
$$ ------------|
$$ . X O 2 1 . |
$$ X . X O . . |
$$ . . X O . . |
$$ . . X O O . |
$$ . . X X O . |
$$ . . . O X . |
$$ . . . X . . |
$$ . . . . . . |

Since T14 allows a sente hane, the initial board effectively looks like this:
$$W
$$ ------------|
$$ . X O . . . |
$$ X . X O . . |
$$ . . X O . . |
$$ . . X O O . |
$$ . . X X O . |
$$ . . . O X 1 |
$$ . . . X 2 . |
$$ . . . . . . |

The usual attempt is to hane from the outside, then kill by playing at the vital point:
$$ ------------|
$$ . X O 4 3 . |
$$ X . X O 7 2 |
$$ . . X O . 6 |
$$ . . X O O 5 |
$$ . . X X O 1 |
$$ . . . O X 8 |
$$ . . . X . . |
$$ . . . . . . |

But after 8, play cannot play at 1 to remove the eye due to atari.
Let's try a vital point in the corner directly:
$$ ------------|
$$ . X O 6 . 8 |
$$ X . X O 4 1 |
$$ . . X O . 5 |
$$ . . X O O . |
$$ . . X X O 7 |
$$ . . . O X 2 |
$$ . . . X 3 . |
$$ . . . . . . |

After 8, the situation becomes a 2 step ko in b's favor.
Next, consider this sequence:
$$ ------------|
$$ . X O . 4 5 |
$$ X . X O 1 2 |
$$ . . X O . 3 |
$$ . . X O O . |
$$ . . X X O . |
$$ . . . O X . |
$$ . . . X . . |
$$ . . . . . . |

After B5, the position is a direct ko. Black wins the ko by playing at 2, creating a dead shape inside. The same position arises if B1 is at B3.
However, thanks to the marked stone, black should try this:
$$ ------------|
$$ . B O 6 5 . |
$$ X . X O 1 4 |
$$ . . X O 9 . |
$$ . . X O O 8 |
$$ . . X X O 7 |
$$ . . . O X 2 |
$$ . . . X 3 . |
$$ . . . . . . |

The shape is dead without ko.
In the original diagram, black can still aim for the same shape:
$$ ------------|
$$ . X O O X . |
$$ X . X O 1 . |
$$ . . X O 5 . |
$$ . . X O O . |
$$ . . X X O 4 |
$$ . . . O X 2 |
$$ . . . X 3 . |
$$ . . . . . . |

After B5, white is short of liberties and dies.


text:
4-4 pincer variant - not in joseki dictionary
I am 4K and played against 2K in handicap game (2-stones).
The point of B3 was to prevent a double-wing shape for white (along the right and bottom)
So W4 pincer leads us into this joseki variant.  Josekipedia suggests alternatives.
$$ ----------------
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . 4 . 8 6 . . |
$$ . 9 . . 1 7 . . |
$$ . . . 5 . . . . |
$$ . . . . . 2 . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . 3 . . . |
$$ . . . . . . . . |
$$

Josekipedia suggests playing this way:
$$Wm10
$$ ----------------
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . 1 O . O O . . |
$$ 2 X . . X X . . |
$$ . . . X . . . . |
$$ . . . . . O . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . X . . . |
$$ . . . . . . . . |
$$

Instead we played where I lost a large corner altogether with unstable shape outside.
$$Wm10
$$ ----------------
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . O 9 O O . . |
$$ . X 8 3 X X 1 . |
$$ . . . X 6 5 4 . |
$$ . . . . . O 7 . |
$$ . . . . 2 . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . X . . . |
$$ . . . . . . . . |
$$

For unrelated reasons, I won the game (SGF) against this 2K.
Was the pincer at 3 and kosumi at 5 the right choice? How could I have prevented the loss of the corner?

It is difficult to tell if the pincer at 3 was the right choice. Generally, such a wide pincer is good if you plan on a moyo on the right side. I'm assuming that W1 was in the upper left and B2 a hoshi in the lower right, as in this:
$$Wcm1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 1 . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 3 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . 4 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . 2 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------

On this board, B4 looks like a reasonable pincer. Typically, you'd expect something like this:
$$Bcm1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . 0 . 4 2 8 . |
$$ | . . . O . . . . . , . . . . 5 X 3 6 . |
$$ | . . . . . . . . . . . . . . . . 9 7 . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . 1 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------

Now the black right side has nice potential to grow big.
In the game, white chose the counter pincer instead, which is a good move (especially in handicap games). Your choice of the kosumi B5 was good, as it simplifies the game and leaves white less chances to start a complicated fight than other options (most notable the tsuke on top of W2.
White deviation from joseki was a mistake. Let's study why. First, one correct variation:
$$Wm1
$$ ----------------
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . O 3 O O 7 . |
$$ . X 2 1 X X 5 . |
$$ . . . X 4 a 6 . |
$$ . . . . . O . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . X . . . |
$$ . . . . . . . . |

Here, white first plays W1 to force black to play an empty triangle at 4. Next, white hanes at 5, and after W7, black would need to play at a to fix the shape. But that would leave black with a pretty heavy shape (too many stones used). This heavy shape is a direct result of the kosumi B5 in the original diagram, which often leads to shape troubles. This is still acceptable in handicap games, though.
Let's compare this with the game:
$$Wm1
$$ ----------------
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . O . O O 3 . |
$$ . X . a X X 1 . |
$$ . . . X . 4 2 . |
$$ . . . . . O . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . X . . . |
$$ . . . . . . . . |

In this variation black does hane at 2, followed by W3 and connect at 4. Note that white a does not threaten a cut anymore, because black already fixed at 4. Thus, black is less heavy, and the variation is a little bit worse for white than joseki.

When White hanes at 10, you need to play 11 at 13, then connect after he does. You cannot answer a contact move with a non-contact move in this situation (and most others).

You didn't lose the corner, you exchanged it for a position on the right side. That's how pincers work, so nothing wrong here. The high pincer combined with your move at 11 looks right here as it prevents a white moyo.
The sequence might not be optimal (see josekipedia/eidogo for the many variations), but the end result looks ok. Capturing at 13 is quite big for white, but its downside is that it gives black the initiative. You could have played 13 before 11, but then it would have given white the opportunity to play 14 somewhere else.


text:
life and death: 2 x 4 in the corner with defects
In a go game (with another 4K) I got a 2 x 4 region in the corner with lots of defects.
W1 almost surely will happen.  Can White get life or ko?
$$Wm1
$$ |------------
$$ | . . . . X .
$$ | . . O X . .
$$ | . . O O X .
$$ | . . O X . .
$$ | . 1 O X . .
$$ | . B X X . .
$$ | . . . . . .

I'm tempted to say its either ko or seki, black's choice.
$$Bm1
$$ |------------
$$ | . 2 1 . X .
$$ | . 3 O X . .
$$ | . . O O X .
$$ | . . O X . .
$$ | . O O X . .
$$ | . X X X . .
$$ | . . . . . .

W2 is the only move, and B3 enters the ko.
$$Bm1
$$ |------------
$$ | . 2 1 . X .
$$ | 3 . O X . .
$$ | . . O O X .
$$ | 4 . O X . .
$$ | . O O X . .
$$ | . X X X . .
$$ | . . . . . .

B3 fails, it ends in white life by W4.
$$Bm1
$$ |------------
$$ | 3 O X . X .
$$ | X 1 O X . .
$$ | 4 2 O O X .
$$ | O . O X . .
$$ | . O O X . .
$$ | . X X X . .
$$ | . . . . . .

Not even a ko. If B1 at 2, W1 is seki.
$$Bm1
$$ |------------
$$ | . O X . X .
$$ | 2 6 O X . .
$$ | 4 5 O O X .
$$ | 1 . O X . .
$$ | 3 O O X . .
$$ | . X X X . .
$$ | . . . . . .

1 is vital, but playing it directly doesn't work.
$$Bm1
$$ |------------
$$ | . O X a X .
$$ | 2 . O X . .
$$ | 1 . O O X .
$$ | 4 5 O X . .
$$ | 3 O O X . .
$$ | . X X X . .
$$ | . . . . . .

If 1 and 2, it becomes a ko (at a).
$$Bm1
$$ |------------
$$ | . O X . X .
$$ | . a O X . .
$$ | 1 b O O X .
$$ | 2 . O X . .
$$ | . O O X . .
$$ | . X X X . .
$$ | . . . . . .

White should instead answer B1 at 2, then a and b are miai for direct life.


text:
How does the example of rule 601.2h work?
I'm having trouble understanding the example of rule 602.1h in the Magic Comprehensive Rules.

601.2h The player pays the total cost in any order. Partial payments are not allowed. Unpayable costs can’t be paid.

Example: You cast Altar’s Reap, which costs {1}{B} and has an additional cost of sacrificing a creature. You sacrifice Thunderscape Familiar, whose effect makes your black spells cost {1} less to cast. Because a spell’s total cost is “locked in” before payments are actually made, you pay {B}, not {1}{B}, even though you’re sacrificing the Familiar.

If the costs are locked in before the sacrifice lowers them, why does it say only {B} is payed instead of {1}{B}? Should it not be the other way around?
The language ("even though...") also seems to suggest the costs were mistakenly exchanged.

When you say "costs are locked in before the sacrifice lowers them", it makes me think that you make have misunderstood some part of this scenario. Did you read both of the mentioned cards?

Seems the issue was "whose effect makes your black spells cost {1} less." I'd guess he thought "whose effect" was the effect cause by the sacrifice, instead of the effect cause by the card before it was sacrificed.

In other word, he read it as "You sacrifice Thunderscape Familiar, which has the effect of making your black spells cost {1} less to cast."

@GendoIkari Yes I hallucinated, surely like this :)

When it says that the spell's cost is "locked in" before payments are made, it means that you calculate the cost, including all modifiers, then you pay for it. This matches up with the steps described in the rules: you calculate the cost in step 601.2f, then pay the cost in step 601.2h.
So, when calculating the cost of that Altar's Reap, you take the base cost: {1}{B}, and apply any relevant cost reductions; in this case, you reduce the cost to {B} due to Thunderscape Familiar's effect. Then you pay the cost: you pay {B} and you sacrifice the Familiar. Since you do the sacrifice after you calculate the cost, the Familiar's cost reduction applies, even though it won't be on the battlefield when you're done casting the spell.
Note that sacrificing the Familiar is not what lowers the cost. The Familiar has a static ability that reduces the cost of black spells. Sacrificing it is, separately, part of the cost of casting Altar's Reap.


text:
Am I allowed to take a red 5 after reaching?
When I'm in riichi and draw a red 5 from the wall, am I allowed to exchange it with the non-red 5 in my hand?
I would argue it might be allowed, because it does not change the yaku, wait or hand structure in any way.
In case the above is correct, what happens in case there is an (isolated) 678 in my hand? Would I be allowed to discard the 8? Given the above rationale, the answer should be yes. However, this could be very complex in practice if the 678 were not isolated, or if there are were similar sequences in other colors, and I doubt this would be acceptable for the players to keep exact track of.
In comparison: I've learned earlier that a kan is allowed, when there are 3 equal tiles already present.

In general, no. There's very little tracking once you're in riichi, with the exception of concealed kans which are easily verifiable after. You take a tile and keep it separated from your hand. You then either discard that tile, form a concealed kan and take a new one, or declare a winning hand.

I think most "official" rules will not allow you to do this. (For reference, I looked up the Japanese Mahjong rules from the European Mahjong association here.)
In principle, I think swapping tiles that do not change the wait structure would be allowed, but it is impossible to verify. In your example of swapping the 5 for the 8, all that is visible is the discarded 8. From an outsider perspective, it is possible that you completed a different meld and simply discarded an 8 from 5-6-7-8 in hand.
It also appears that the hidden kan/kong is allowed, but only when the pung is isolated and cannot be interpreted as a different set of melds (e.g., you cannot draw and complete a kong if you have 1-1-1, 2-2-2, 3-3-3, because those tiles could be interpreted as 1-2-3, 1-2-3, 1-2-3).

This is not quite correct. Your hunch that it would not be allowed is correct. Once you declare riichi, all your draws must either complete your hand or be discarded. It is customary to keep your draws distinct from your hand for this reason (such as placing the drawn tile sideways on top of your hand). As for the concealed kan, you can only declare the kan if it does not change your waits. In the 111 222 333 example, you could declare the kan if the rest of your hand were 78 EE, but not if it were 45 EE. See the chombo rules here

@Teofrostus The rules you cited don't say that a hidden kan that doesn't change waits is allowed, only that a hidden kan that does change waits is penalized. The rules I linked to explicitly discussed when a concealed kong is allowed: "may declare a concealed kong if a tile is drawn that matches a concealed pung, if this does not change the waiting pattern and if the three tiles to be konged can only be interpreted as a pung in the original riichi hand. (In case of three consecutive pungs in the same suit, no kong may be declared, since the tiles can be interpreted as three identical chows)."

According to the Japanese Wikipedia article on riichi:

打牌の選択（手牌の入れ替え）ができない。つまり、和了する場合と後述の暗槓する場合を除いて、自摸した牌をそのまま捨てなければならない。

Translating, this means "You are no longer allowed to select your discards (switching the drawn tile with a tile in your hand). In other words, save for drawing your winning tile or calling a concealed kan as described below, you must discard each tile you draw."
That means if you draw a red five after calling riichi, it's either your winning tile and you're calling tsumo, you have three other fives of the same type and you're calling a concealed kan, or you're discarding it. You cannot simply switch a red five with a regular five, even if it wouldn't change your waits.

Refering to japanese rules seems a bit authorative. The answer isn't wrong (I don't know any rule variant that would allow this), but you should always consider your local rule variants and/or house rules with these things. The can sometimes deliberately contradict the japanese rules.

It was the best way to get a definitive answer. The wiki article also doesn't reference any rule variants re: how you select your discards (or don't) during riichi and I've found no other rules wikis/sites which suggest that riichi works in any other way except as described here. The main downside of riichi is that you can no longer choose your discards, meaning you may miss dora tiles or deal into other hands.

I don't actually think you can have a "definitive" answer as far as Mahjon goes. There are just too many rule variants, all equaly valid in their own regions. As such, one should always take care to consider the local variants first and foremost.

The whole point of stackexchange is to have definitive answers to concrete questions. =/

Japanese mahjong does not allow swapping tiles into the hand after riichi, as noted by so many.
Apocryphally, the European Mahjong Association did allow this between 2008 and 2012 (changed that year) because their community's comprehension of the rules as played elsewhere was incomplete and lacking, so they made stuff up to bridge the gaps. Now, EMA rules from 2016 onward are functionally the same to what people would consider to be modern Japanese mahjong, with variance only related to protocol and game etiquette, with a natural focus on a competitive style.
As for using Japanese wikipedia or a pro organization or a jansou chain as a source: it depends who, for what, and under what optics. Using a single source might not always work, but if they all conform to one or two clear options, then it does make sense. There are people who have their done their research on this and other topics already. Some things do have variance: this isn't one of them. House rules govern agreements between 4 players that have chosen to abide by them, but this does not make them normalized or "an equivalent option" because they simply are not common or relevant enough to make that distinction.

Could you provide a source for EMA allowing this? I have played for many years in Europe, and I was always told that the only three options when picking a tile after calling riichi were: tsumo, kan (with the caveats on not changing the ways the hand could be interpreted), discard.

No, and I will actively refuse to search this for you. Two reasons:

(Three. Limited edit time.)

Their source was literally one guy in the Netherlands playing nashi-nashi, around 1999-2000.
Integrating a tile in your hand post-riichi lets players cheat. I personally advocate against both the cheating aspect and the fact that no source we know does this. (Maybe some oddball jansou has allowed this, burden of proof is on them: even if there is, it isn't common enough to justify)
You have the information to find it in an internet archive. There is a reason the rule was changed: because it's a bad rule.

Other groups in Europe never allowed this.


text:
Komoku-Oogeima joseki order variation
In a game my opponent deviated from the joseki line I was familiar with.
$$W Actual game
$$ ------------
$$ -...........
$$ -.94........
$$ -.5128O.....
$$ -..X36...0,.
$$ -...7.......
$$ -...........
$$ -...........

Instead of B10, I expected this exchange first:
$$B Expected
$$ ------------
$$ -...........
$$ -.OX........
$$ -.OOXXO.....
$$ -..XOX1..3,.
$$ -...O.......
$$ -...........
$$ -...2.......

The result here appears to be even to me, white is a little better locally but she played first so it is to be expected.
Since black omitted the 1-2 exchange and played 3 directly, he seems to plan on letting the sole white stone die on a larger scale. Consequently it appears natural to use this stone to punish black's deviation.
I've got three basic ideas how to:

Tenuki and leave the bad aji. Omitting W2 as a securing move should be fine since black can't fight properly without swallowing the sole white stone first.
Play W2 regardless. Then black has 2 options: play B1 so it reverts to the known pattern, or tenuki - in that case white can move her stone out easily and fight, so black probably won't do that. However, since B3 is not joseki as far as I know, this would be too easy on black.
Move W2 out, splitting black's stones.

I'm thinking of either this attachment:
$$W Attachment and keima
$$ ------------
$$ -...........
$$ -.OX........
$$ -.OOXXO.....
$$ -..XOX..1X,.
$$ -...O....2..
$$ -.....3.....

or this shape:
$$W Attachment and sake bottle shape
$$ ------------
$$ -...........
$$ -.OX........
$$ -.OOXXO.12..
$$ -..XOX...X,.
$$ -...O..3....
$$ -...........

Option 3 seems to induce black to make white's left side group stronger, but at the same time, black's top stone gets stronger as well.
Is any of my ideas here reasonable? Or is black's "deviation" in fact a joseki, too?

I know this is ancient history, but is Oogeima a misspelling of Ogeima? Or is this an alternative romanisation? At any rate, Sensei does not have an article Oogeima! Also you write derived where you presumably mean deviated.

@PJTraill Thanks, fixed. As for Oogeima, I believe both are commonly seen. The Japanese word starts with "大" (large) which is read as "oo" here.

W1 seems like a good move to me. B can't get a rhythm to fight well even if he ignores it to make something happen. I may be wrong but B's deviation looks like a gross overplay to me. I can't see W playing a "solid be get better result" so starting a fight seems good for W.
The only other option I can think of, other than W1, is the 5th line shoulder hit which is worth thinking about. It's much harder to control and more easily ignored though.
$$W 5th line shoulder hit
$$ ------------
$$ -...........
$$ -.OX........
$$ -.OOXXO.....
$$ -..XOX...X,.
$$ -...O...1...
$$ -...........

The shoulder hit seems to lead to pretty complicated fighting and several semeai possibilities on the edge. Just as you said, really difficult to judge. I guess if black were to just push and connect by clamp it would be too submissive.

1 and 2 are "honte" moves. They result in solid positions as they remove all aji from the marked stones, but are not mandatory.
$$cm1
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X . . . . . . . . . . . . . . . . |
$$ | . O O X X Q . . . . . . . . . . . . . |
$$ | . . B O X 1 . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . . . . . . . . . . . |

If black has a strong position in the upper right, she'll welcome a fight that will allow to build while attacking.
$$cm1
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X . . . . . . . . . . . . . . . . |
$$ | . O O X X O . . . . . . . . . B . . . |
$$ | . . X O X . . . 1 . . . . . . . . . . |
$$ | . . . O 3 . . 2 . . . . . . . . B . . |
$$ | . . . 4 5 . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

So omitting F16 in this case seems reasonable, and white can't really punish black, at least not before reinforcing her own shape.
As often with joseki, it is difficult to analyze the moves here without seeing the context.
[Update] I browsed pro games that include this pattern, and it confirms that black doesn't need to play F16. Even after white plays D13 or D14, black might tenuki. If white doesn't reinforce the area, then later black might opt for a more aggressive move, like E14 or D13.
$$cm1
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X . . . . . . . . . . . . . . . . |
$$ | . O O X X O . . . . . . . . . . . . . |
$$ | . . X O X . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . a . . . . . . . . . . . . . . |
$$ | . . . b . . . . . . . . . . . . . . . |

The attachment is fine but B will resist in a different way, I guess (maybe pushing?).
$$W Attachment, black resists
$$ ------------
$$ -...........
$$ -.OX........
$$ -.OOXXO.....
$$ -..XOX..1X,.
$$ -...O2......
$$ -...34......
$$ -...........

In the (expected) variation move 2 shouldn't be a jump, rather a nobi (extension) to get a more solid shape, then I agree that W is better.
$$B Expected, stronger shape
$$ ------------
$$ -...........
$$ -.OX........
$$ -.OOXXO.....
$$ -..XOX1..3,.
$$ -...O.......
$$ -...2.......
$$ -...........


text:
What is a "dead hand"?
This book states that "If a claimed tile is not taken within the next two opponents’ turns, i.e. before another two discards has been made, the player has a dead hand."
What is a dead hand, and how does it affect the game?

It would help provide some context if you specify what 'This book' is.

"Dead hand" has a few different meanings. It's hard to tell just from that one sentence, but it sounds like the one you're describing is the case where somebody forgets to take a tile, so their hand ends up short tiles (it's also a dead hand if the player forgets to discard and thus has too many tiles). A dead hand cannot be used to win the round, but the player still takes their turns as normal until the round ends.
"Dead hand" also sometimes refers to a declared mahjong that turns out to be invalid (like above, that player cannot win anymore, and play continues), or a round where all tiles are drawn from the wall and nobody makes mahjong, but neither seems to be what you're referring to in this case

I think the statement in the question refers to the first situation in your answer. The player claims the tile, but doesn't pick it up to put in their hand, and the next two turns have gone by, so the player can no longer pick up the tile he/she claimed, therefore having a dead hand. I think that statement is allowing the player a window in which to grab his/her tile.

Yes, by now I understand it just like @kchau does.

Agreed -- player error has made it impossible for the player to win that round, but they must play out the round nonetheless. What's never been clear to me is if that player still has an obligation to play as if they were trying to win, or if they're allowed to play in a simply obstructive manner to minimize their losses...

The term "dead hand" is maybe ambiguous. The certainly most common use is for hands that may no further participate in the game due to a critical, usually accidental, mistake. This is related, but not identical to chombo (a usually intentional mistake by a player that ends the round and forces the offender to pay mangan).
The OP was referring to MCR rules. I am not very familiar with MCR, but to gain a basic understanding of the term, let me refer you to these (simplified) rules for dead hands in riichi mahjong:

The following actions result in a dead hand:

Looking at the tiles in an opponents hand or the dead wall.
Drawing a tile before the opponent before you has discarded, or drawing in any inappropriate way.
Making an invalid CHI, PON or KAN or declaring one invalidly. This includes KUIGAE.

A hand is dead immediately after any of the above conditions are noticed.
A player with a dead hand may not declare CHI PON KAN or a win.
A player with a dead hand is considered NOTEN, even if his hand is TENPAI.

I have found one other use of the term "dead hand", but I have never seen this elsewhere:

A hand in which no one completes a winning hand before all tiles except the Dead Wall have been drawn. The round ends then with no winner.

What I call a dead hand is one where there is no possibility of winning. The case I’m thinking of is a hand that was complete except it was missing one pair. All four of the needed tiles were out. Because it was for a pair and I didn’t have even one of the two, my hand was “dead”.
If I had one, I could claim a discarded one even though it was for a pair because you can call for the second tile in a pair if it’s for mah jong but I didn’t have any and the game was nearly over. I was taught that you can declare a dead hand and let the game continue three handed, without you. Is there a rule about this ?

Regarding your question, I think you should post it as a new question post. Asking a question in an answer doesn't really work well with a Q&A site.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/2.5/


text:
What does it mean to be furiten?
This book states that "a player who is furiten, is not allowed to win on a discard." What does furiten mean, and how does it affect the game?

Furiten is when you are unable to win on a tile due to certain circumstances. There are about 3 different circumstances.
One type of furiten is when you previously discarded a tile that you needed to complete your hand. Let's say if you go for a hand without honors, 1s or 9s(a hand called 'tanyao', worth 1 han), and you have a double wait of 3 or 5 circles to win. If you have previously thrown 3 circles, even if it was taken by someone when they did a chi/pong/kong, you are unable to take the tile if someone else discards it. You are, however able to take it from the wall yourself and win with it.
The second type is when you ignore a tile needed to complete your winning hand. Similiar to the previous situation, but this time you are waiting for a 1 or 4 circles to win. You have neither thrown the 1 or 4 circles previously. Let's say someone throws the 1. If 'tanyao' is your only yaku, you obviously are unable to win it. So you pass on it. However, this puts you in a state of temporary furiten. If within the same turn(before you get to take another tile), someone throws the 4, you are unable to claim the tile for your win. If someone does a pong/kong, you will remain in furiten until your turn comes again.
The third type is when you declare 'riichi', and ignore a winning tile. Since riichi is already a yaku, you are able to win even without any other yaku. Let's say you are waiting for a 1 or 4 circles(again). You have neither thrown either tile previously. Someone throws   the 1. If you don't claim it, you will be declared furiten for the REST OF THE ROUND. Same goes if you draw a 1 and discard it. In other words, your hand will be permanently declared invalid til the next round.
source: i love mahjong~ :D

Nice answer! Could you clarify what "rest of the round" means? (Until someone wins the current stage and the wall is rebuilt, or until its your turn again after supposedly 3 turns by the other players?)

thanks for the welcome. and the rest of the round means til someone wins or the tiles run out. after the wall is rebuilt, and you take your tiles, that is when a new round starts, even if the round still remains the same due to the dealer winning or waiting for a last tile(tenpai).

This explanation is not completely correct for the riichi rules currently used in Europe. In these, any player declaring chi, pon or kang will interrupt the turn, thus removing a temporary furiten.

According to the mahjong wiki:

Furiten in riichi mahjong is a state in which a player has discarded a tile that would have otherwise completed his hand. A player who is furiten cannot win on an opponent's discard, but can only win by self-drawing the needed tile. This rule is the crux of riichi mahjong. This is why all discards and melded sets are organized to show ownership the tiles discarded.

It's not just in Riichi...

@aramis Riichi is the only variant I know of that has such complex furiten rules. Most other varieties of mahjong either have no rule or something like "You may not claim a win on a tile identical to your most recent discard, or which has already been discarded by another player after your most recent discard." Furiten is a lot more complicated than that.

Furiten is often referred to Sacred Discard in other types of mahjong such as Chinese Mahjong. I like to think about as a "Locked Discard" that prevents you from winning.
What is Furiten?:

...A Locked Discard (Furiten) prevents a player from declaring a win (Ron) on another player's discard if they have previously discarded any tile they need to complete their hand. This rule ensures that players cannot capitalize on mistakes they’ve already made by discarding crucial tiles.

Types of Furiten:

Permanent Furiten: This occurs when you discards any of the necessary
tiles needed to complete your ready hand. Your discards locks you out
of winning on any future identical tiles discarded by opponents AND
any other waits you my have.
Temporary Furiten: This happens when you
ignore a winning opportunity (calling mahjong or Ron) from a player's
discard. You are now temporarily locked out of a win which lasts
until you draw and discard a tile again. Exception: When you are in
Riichi, you must claim any winning opportunity otherwise you will end
up in Permanent Furiten.

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text:
Advanced heuristics in Pentomino
The game of Pentomino is a tiling puzzle game played on a grid. A Pentomino piece is a shape of five non-diagonally connected tiles. There are 12 unique pieces (ignoring rotation/reflection). The goal of the game is to fill the board with the available pieces without overlapping.

I'm interested in which strategies I can use to find good pathes to a solution faster. So far I primarily researched non-rectangular boards, possibly with 'holes' inside, that have exactly one solution. Later, I want to also try boards with multiple solutions.
I've identified a few ideas that were quite helpful:

Do not search where to place a piece, but search the grid for connected spaces. In other words: instead of asking "where can I put this piece?", ask "what piece could be put here?".
This search should start in cells with few options (i.e. narrow alleys). This often leads to long, forced sequences, which is good.
If unclear, assume that two cells are separated (not part of the same piece). Then try to refute this assumption by showing that the board cannot be solved anymore. This means they must be connected. Rinse and repeat.
If a subspace is created (that is not connected to other open areas), check if its number of cells is a multiple of 5. If not, it is impossible to solve.
Point symmetric subspaces of 10 cells cannot be solved.
(Some others that are more complex)

These came to my mind while just playing the game for many hours (I was a test subject in a study about Pentomino). Are there any resources, links, books, etc where I can learn about more advanced strategies?

Focusing on narrow spaces, checking if any piece goes and stopping if any gap isn't a multiple of five are the strategies that I use too.

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text:
Element, wind melds worth it to reach minimum han requirement?
Just wanting to confirm whether I'm understanding these rules correctly. The rule set from which I'm deriving most of my (Rīchi-)Mahjong knowledge only has this short paragraph about tiles being worth han:

三元牌、圏風牌、門風牌を飜牌とし、その刻子、槓子組ごとに一飜とする。
  連風牌はニ飜とする。

Which I translate to:

Elements tiles, prevailing wind tiles and player wind tiles are han tiles, with each triple or quad meld of them being worth one han.
  Double wind tile melds are worth two han.

In a game with a one-han minimum requirement, does this mean if I have any element meld or a meld of any of the two relevant wind types, I can complete my hand? Meaning, it may be worth it to make a call for these tiles and opening my hand, even if the rest of my hand is not really worth much?

Just to clarify, standard riichi mahjong has a one-yaku minimum to go out, not a one-han minimum.  The difference between yaku and han is subtle, but important (dora and ura-dora provide han, but they are not yaku).

@gold That may be a difference in translation. The above rule set uses the term "han pai" and that these are worth one/two han. I also think the rule that specifies the minimum requirement also says han. I couldn't say whether this rule set is typical or necessarily the best though. :)

Your understanding is correct.

Yakuhai (役牌), also known as Fanpai (飜牌), is a 1-han yaku consisting of a pon/kan of any of the following:

Dragons (elements)
Your current seat wind
The current round wind (typically east or south)

As it is a yaku, it will net you the 1-yaku minimum required to complete your hand.  It doesn't matter if the hand remains open or closed, so calling a discarded tile to complete the set is perfectly legal.
Whether it is the best choice in any circumstance is highly dependent on the rest of your hand; the point value of an open set is only half that of a closed set, and there are many other potential yaku which are unavailable when a hand is opened.  In particular, you lose out on the ability to call riichi, which would also provide the 1-yaku minimum and give you a chance for ura-dora as well.

Is this quoted from somewhere? If so, could you link to the source?

@ire_and_curses: It's not a quote, I just used the notation for aesthetics so it would stand out


text:
How far can you safely extend from your own wall?
When extending into what is basically open territory, how far can you extend to increase your influence/moyo, without inviting an invasion?

Choosing the right distance for an extension basically depends on your goal in extending as well as the relative strength of stones in that area. Also, we need to differentiate between extensions to just explore open areas and extensions from existing walls.
Extensions from a wall
Let's start with the basics first. There is a well known rule of thumb, called the "wall plus one" rule. If you got a wall of height n, extend n + 1 spaces.
Assuming your wall has a height of 2. Consequently, the basic distance for an extension should be 3 spaces.
$$Wcm1 Wall of 2, extend 3
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . O . X . . . |
$$ | . . . . . . . . . W . . . O X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

For a "wall" of height 1 (that is, a single stone), the safe distance is 2 spaces.
$$Wcm1 Wall of 1, extend 2
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . X . . W . . O . . X . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

"Safe" means that is is difficult to invade and split your stones. The reason why it is safe is that you can either capture an invading stone, or at least connect your stones so you're not left with two weak groups. There are several midgame joseki that revolve around this, and the details will become more apparent as your reading grows stronger.
$$Bcm1 Safe distance: Difficult to invade, white can choose from A or B to kill or cover the invading stone
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . a b . O . . . , . . . |
$$ | . . . . . . . O . 1 . O . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

Extending further than wall-plus-one distance means your position is more open to invasion and typically leads to bad shape (it's difficult to fix the invasion point without becoming overconcentrated). On the other hand, extending less wide leads to immediate overconcentration. Neither is desirable, so especially beginners should heed the wall-plus-one rule.
$$Bcm1 Unnecessarily difficult: Two wide extensions are far easier to invade.
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . 3 . . . . . . . . . |
$$ | . . . , . . . 2 . , . O . . . , . . . |
$$ | . . . . . . O . 1 . . O . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

Extensions to explore open areas
Sometimes, you simply want to extend along a side without having any kind of wall. In that case, the usual idea is to simply play in the center of the stones on that side (no matter whom they belong to).
$$Bcm1 Simple extension along the side
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . 1 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

This means that, since you intentionally ignored the wall-plus-one rule, your opponent will be able to invade and split you. However, since you played right in the center, you can simply extend to get a base (this leads to the concept of miai), while your opponent will be left with a single stone stuck between two relatively safe groups of yours.
$$Bcm1 Invasion is possible, but we can handle it
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . 3 . . 1 . 2 . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

Occasionally, you want to adjust the distance slightly, but this dives into the realms of tactics already.
Relative strength adjustment
The stronger you are, the further you should go, and the stronger the opponent, the more tight and defensive should you be. What does this mean in practice?
If your opponent is strong around, sometimes the wall-plus-one rule should be changed to wall-plus-zero, i.e. a tight extension. This means, in the classic sense of the word, overconcentration, but it makes for more safety which might be more important. Typically, this is chosen if the opponent already has a checking extension that interferes with your extension.
$$Wcm1 It's a good idea to hold back sometimes.
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . O . X . . . |
$$ | . . . . . . . X . . 1 . . O X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

Extending further may provoke an invasion.
$$Wcm1 After B6, black can connect on either 'a' or 'b' and white has cuts.
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . X . . . . . . . . 5 . . . . . . . |
$$ | . . . , . . . . . , 3 4 . O O . X . . |
$$ | . . . X . . . X . 1 . 2 . O X X . . . |
$$ | . . . . . . . . . b . 6 . a . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

White can try to dodge, but is left without a base while black got extra points.
$$Wcm1 No base, no points.
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . 7 5 3 . O O . X . . |
$$ | . . . X . . . X . 1 4 2 . O X X . . . |
$$ | . . . . . . . . 8 6 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

Compare to when there is no extra stone on the lower side.
$$Wcm1 The invasion does not work that well: Black can't escape, the invasion failed.
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . X . . . . . . . . 5 6 . . . . . . |
$$ | . . . , . . . . . , 3 4 7 O O . X . . |
$$ | . . . X . . . . . 1 . 2 . O X X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

On the other hand, if you're really strong somewhere, the correct distance is "as far as possible"; ignore the vast space and go right to your opponent's corner. If he dares to invade and split your extension stone, attack him and make him suffer by using your thickness.
$$Bcm1 Wide extension is desirable
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . O . . . . . . . . . . X X O O . . |
$$ | . . . , . . . . . , . . X . . X O . . |
$$ | . . . O . 1 . . . . . . X . . X O . . |
$$ | . . . . . . . . . . . . . X X O O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------

Can you expand on the "no base, no points" comment on the third last diagram? To me, it seems like white can easily extend to the wall and live with a least a little territory. Do you just mean that it's not enough territory to justify the stones?

@naught101 Black stole the edge area from white, so white cannot make eyes there anymore - which sucks, because making eyes in the center is much more difficult (it simply takes more stones to do so). Accordingly, white cannot expect to make many points with this group (because she will probably be busy to keep them alive). I'm not saying  the white stones are weak, but they are weaker than they should be, without any gain in exchange - it is simply a poor trade, and white should try to avoid it if possible. In this case, it is relatively simply to avoid without major losses, so why not!

There's an excellent and detailed answer already, but I want to throw in some other thoughts. I attended a workshop with Guo Juan (5P) where someone asked about the wall+1 rule and she explained that it's a nice mnemonic that works in some common situations (2-space jump between single stones, 3-space jump from 2 stones), but isn't much of a good rule past that. The point of a wall (a real wall, not a small 2-stone wall) is to attack!
If you have a big wall, you shouldn't try to make territory next to it, rather you should invite an invasion by making a moyo that threatens to become a massive territory if not invaded. Then, when your opponent invades, you attack. Even if you can't kill, you should make profit in a chase and come out ahead.
In your question, you ask about "increasing your influence/moyo without inviting an invasion." Without an invasion possibility, what you have is territory. Influence/moyo is invade-able, otherwise it would just be territory. What you really want to know (and  @mafutrct's answer addresses very well) is how far to extend to make an invasion to your advantage.
The Sensei's Library page on this topic cites the wall+1 rule, but if you follow the link to the page about four-space extensions the biggest comment is about how rare they are, and no mention of a 3-stone wall is made.