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What is this pattern/tile board game?
It has blocks in different arrangements- L shaped joined, three-in-a-line joined, single. Colours were red, blue and black. The objective of the game as I remember it was to put the tiles/ blocks together in different ways to make a pattern shown in a book that comes in the set, the over-all pattern usually contained in a square outline. Levels range from easy to hard, definitely a game that adults can attempt too. Someone said Tetris but it's nothing like that, although the blocks are similarly structured. Got this as a present when I was younger but I can't for the life of me remember what it's called.
edit: Comments below say it's a variation of Tangram and pentominoes and I think that sounds about right! Hopefully this image will help identify the name.

This sounds like a Tangram, but you describe shapes that are not in the basic one. Maybe a variant of it?

It very much reminds me of a pentomino puzzle. Square board where you try to build certain shapes. I believe Tangram is a pentomino puzzle variant. Linked is an example of what I'm talking about (pieces are made of wood but you get the idea).
https://www.amazon.com/Square-Root-00012-Pentominoes/dp/B00000IZUL
Good luck finding your game!

It looks similar to the
Kaleidoscope Classic board game. One side is red and black, the other side is yellow, blue and black.


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Is it okay / does it make sense for another player to join a running game of Munchkin?
In a "just for fun" session of the card game Munchkin, would it be okay to join a game in progress? Of course the joining person would be in a disadvantage.
Arguments against this, as far as I can think of for now:

The current order of the players is disturbed by adding another player.

Is this the board or card game version?

Munchkin is about the least serious game you can play.  It also has ridiculous catch up mechanisms so if you're going to add someone mid-game, Munchkin is the game to do it in.

I've played plenty of games where someone has joined mid-game, and it has worked very well them just starting as if from scratch (i.e. at level 1 and drawing the starting hand of 4 treasure, 4 doors).
In my experience, what tends to happen is the established players have no problem with helping them to fight monsters they can't beat, meaning they'll level up and get loot just fine without needing a level boost.
In terms of changing the play order, I have a feeling there's a card which influences turn order in one of the early expansion sets, something along the lines of "Player is now fighting this monster, and play continues as though this were the player's turn", effectively skipping everyone in between - although I can't find the card name or text with a cursory search. Also, I wouldn't have said Munchkin is a game which particularly relied on the turn order, so I don't really see how this could be a problem.
In my opinion, if someone gets upset over a new player joining mid-campaign in casual play, they're probably taking Munchkin too seriously.

I'm accepting this answer, but I had trouble deciding between so many good answers! Thank you everyone! :)

There is if I remember (though I haven't payed a game of munchkin in years) a bunch of to the left or to the right, IO know some of the bookmarks get given like that if used, though I;d have to find my munchkin bookmarks.

Regarding your third paragraph, the basic Munchkin game has the Transferral Potion which works kind of like that, but it explicitly says that "the original player then resumes his turn" after the combat ends (although it's kind of easy to forget this, especially if it's a long combat).

That might be the one, so no turn-order change then. I may have been confusing it as I normally try to use the Transferral Potion as a winning gambit, so in an ideal world (for me!) there's no turn after it

This answer would profit from adding that player characters can (and often do) die, losing everything and starting from level 1. This is almost indistinguishable from a new player joining.

@vsz I'm afraid that's incorrect. Normal death means you only lose equipment, your character comes back looking exactly the same (class, race, curses, and levels are preserved). The only way you go back to level 1 is through suffering the Bad Stuff(TM) of one particular monster, which again escapes my recollection (I think it might be the Wight Brothers but I can't find any card text online to support this)

If it's "just for fun" and everyone is still having fun, then sure. If someone finds their fun level jeopardized by, for example, the disruption of the play order, then either you should delay the introduction of the new player or change the mind(s) of the opposed player(s).

Does it make sense: That depends on how long the game has been running. If you've only been around the table 1-3 times the disadvantage isn't so massive that the player has no real chance of catching up, more than that it doesn't make much sense to join games already in progress.
Is it okay: That's up to the people playing the game. There's no major difference from adding a player, some things would have been different if the game had started out with 4 people instead of 3, but those are made up for by the disadvantage the new player faces by coming in late. The turn order is disrupted, but the new player gets none of the benefits or detriments of having been in turn order until now. The best place to add a new player to the game is immediately after the current player, so they get into the game and start their catch-up immediately.

Would it be okay to join a game in progress? If everyone at the table is okay with it, of course. I have played dozens of games where someone or multiple people have joined late, I would restrict new players only if the end-game was clearly in sight.
Some arguments against:

Player order. If someone believes mixing up the player order is a game breaker, they leave too much up to chance rather than strategy. It is just as likely they will be positively or neutrally affected by the new player order as negatively.
New player will ally with a particular player. I've had people invite their friends part way through and this I was apprehensive, assuming they would just assist their friend to victory. Often they are even more competitive with their friend and if they are a good player will be persuaded by good arguments for coordination rather than blatantly helping their friend.
End-game is in sight and new player has no chance. I have joined very late and still won games. But if the end is only a few turns away, the new player will only be able to throw their weight for or against one of the contenders. This leaves a sour taste in the loser's mind, even if they may have ultimately lost anyhow.
New player needs to be taught the game. I am fine teaching new players at the start of the game, having a new player come partway through upsets the flow and may detract from other's fun. Best to wait until next game.

Good point about new players needing to be taught the game.  I'd generally come down on the side of being nice and letting people just insert themselves into the game, but a new player doing either 3 or 4 is just obnoxious!

As a counter to point 4 - having someone join a few turns in after watching experienced players is a great way to learn a new game - but that's a game played with that goal to teach in mind from the start and a player joining in late is expected from the start.

Inserting a new player into the turn order is far less consequential than the change in balance of power that a new player introduces.  Most games of Munchkin I've played come to a series of showdowns in which one player tries to win and the other players try to stop that player.  Players too far behind have a much higher risk of kingmaking to end the game rather than trying to win.
Given that, the question is whether a new player added at that point in the game has a reasonable chance of winning.  You may want to have them start at a level higher than one (such as the lowest level any other player is), and possibly draw a few random pieces of equipment if the game is reasonably far along.

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What happens if you roll doubles 3 times then land on "Go to jail?"
Do you have to serve two jail sentences? For example, you go to jail the first time and use your "Get out of jail free" card, and then go right back to jail for another sentence without rolling the dice.

Highly related/duplicate: https://boardgames.stackexchange.com/q/38845

Although this question has already been answered correctly, if you want to have some fun with this I suggest that it is in the scope of the rules to pretend like you didn't remember this is your third roll of doubles, start moving, then land on "go to jail" and exclaim, "OH NO! I LANDED ON GO TO JAIL!" as you move your token to the jail.  This would work especially well if some of the other players catch you on it being your third roll of doubles and are trying to explain it to you while you ignore them and move your token anyway.

@Jan I agree that these are about the same thing, but neither is a good duplicate candidate for the other.  I've tried to create a canonical question to merge the two: https://boardgames.stackexchange.com/q/45706/9999

You go to jail directly on rolling the third double, so there’s no opportunity to land on “go to jail”.
From the Official Monopoly Rules (Hasbro)

If you throw doubles, you move your token as usual, the sum of the
  two dice, and are subject to any privileges or penalties pertaining to
  the space on which you land. Retaining the dice, throw again and move
  your token as before. If you throw doubles three times in succession,
  move your token immediately to the space marked "In Jail" (see JAIL).

This answer, as well as the other answer given later on, addresses the game mechanics. It is explicitly stated in the rules that property cannot be purchased, and it sort of follows that rent cannot be collected, either. I don't think I have ever tried moving my piece according to the dice value before going to jail when rolling doubles a third time in a row.

@Iktys "and it sort of follows that rent cannot be collected" No it doesn't. That's one of the most often debunked myths.

@Joseph, I believe what Iktys meant is that if your third doubles would cause you to land on someone else’s property, the other player doesn’t get to collect that rent before you go to jail.

I mean, at the space you would have landed on with the third doubles, you don't pay rent.

There's no such thing as "the space you would have landed on with the third doubles."  When you roll the third set of doubles, you go immediately to jail.  There's no point in counting spaces to see where you "would have landed."

@Kyralessa I believe that was the point he was making. He's saying that since it doesn't say that rent is collected after the third doubles, it can be assumed that rent CANNOT be collected, thus proving that you don't land on the space at all, indicating that you don't move, you simply go to jail immediately when you roll the doubles.

@CollinB There's no rent to be collected because for rent to be collected, you have to land on someone else's property.  After the third throw of doubles, the only place you land is in jail.  It only confuses matters to talk about "the space you would have landed on."  There's no such space when you roll doubles three times.  There's only the space you do land on: Jail.

This same misconception is in the original question.  The original question implies that after rolling doubles three times, you could land on the Go to Jail space.  This isn't true.  Upon the third roll, you go directly to Jail.  You don't "land" anywhere except Jail.  There's no point in counting off the spaces for your third roll.  It doesn't matter how many spaces it is to the Jail; that's the only place you're going.

@Kyralessa That is...... exactly what I just said......

@CollinB You said a lot of things that don't have any relevance.  It's not necessary to reason one's way 'round from "It doesn't say rent can be collected" to "You go to jail immediately."  It could scarcely be more clear: "If you throw doubles three times in succession, move your token immediately to the space marked 'In Jail' ".  It's obvious that if you move directly to jail, then you don't land on any other space and don't take actions associated with any other space.

@Kyralessa I'll point out that it is clearly not obvious to everybody, hence this question's existence. It was someone else's separate way of reasoning that you have chosen to disagree with because it was "unnecessary," but as long as it might help the person who asked the question, I see no reason to disregard any path of logic, no matter how convoluted you may think it is.

I'll grant that the Monopoly rules do leave quite a bit of ambiguity in some cases, but this is not one of them.

You're thinking about this too much in terms of real-life prison sentences, and too little as game mechanics. "Jail" is simply a location on the board, associated with a few specific rules, but none of those rules suggest that there would be "Jail Time" stacking up. Instead, you are either in Jail, or not.
Furthermore, upon rolling doubles a third time, you are directly placed in Jail without executing your movement anyway:

When doubles are rolled, the player resolves the roll as normal (including purchase, renting or passing "GO"), but rolls the dice again for another turn (you have to keep going). The player moves forward as directed by the dice, and if this is also doubles, rolls again. If the third dice roll is doubles, the player cannot buy property, and is instead moved directly to jail. [source]

" "Jail" is simply a location on the board, associated with a few specific rules," Ooooooh... suddenly a lot of things regarding life and politics are more clear to me.

Where is your quotation from?

@EleventhDoctor I hadn't realized I forgot the source link - added!

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Phase 10 Going Out - Do you keep picking up?
I've just picked up a copy of Phase 10 to play with my kids. I'm a little confused about the 'Going Out' part. Once you get a phase and place it on the table, you can place any appropriate cards on your own and your opponents' phases, or the discard pile. The object is to get rid of your hand. Do you still just carry on picking cards up and discarding them until you happen to be able to get rid of them all (or your opponent does)? Or do you just discard one at a time?
EDIT: I think I've just realised that you can 'Hit' a phase at any point, so you could pick up a card, Hit it on to a phase, and discard a card into the discard pile. Is that right?

Before making your phase, your turn structure is like this:

You MUST draw a card from the deck or discard pile.
You MAY make your phase and put it on the table.
You MUST discard a card onto the discard pile.

When making your phase you MAY immediately add any number of your own cards to other phases on the table. Afterwards, you MUST discard a card to end your turn.
Then after making your phase, your turn structure is like this:

You MUST draw a card from the deck or discard pile.
You MAY add any number of cards from your hand to the phases on the table.
You MUST discard a card onto the discard pile.

The round ends immediately when a player gets rid of their last card.


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Using an omen card, can you kill yourself?
Let's say I have Sanity 3, the last Sanity step on my character sheet, and I choose to use the omen card Mask. I roll a 4+, which means I can put on the mask to gain 2 Knowledge and lose 2 Sanity. Did I just kill myself when I have only one Sanity step left? Does my Sanity level drop to a minimum? Or does it drop to 0, killing me? Can I decide after rolling 4+ that I don't want to use the mask?

Why would you ever bother rolling if you know that you would choose to not use the mask even if you succeed?

I checked my characters sanity only after doing the roll.

Fair enough. I know for sure any group of people I'd be likely to play with would have no issue just letting you ignore the roll if you explained that you didn't notice that your sanity was that low, even if the rules didn't technically allow you to ignore it because of the "can" wording.

The text on the Mask omen 4+ roll reads "You can put on or take off the mask.", keyword here I think being "can". If you attempt the roll and get the 4+, read as written you can choose not to put the mask on.
That being said, if losing 2 sanity would cause you to go lower than the lowest sanity level on your character, yes, putting the mask on would cause your character to "go insane" and your character would die and drop the Mask.
The one stipulation to this being that your character cannot die before the haunt has begun, so this only applies post-haunt beginning. That rule is on page 8 under "Making an Attack".

Thank you! Yes the word can gives there a lot of meaning. If there would be must, I would have to take on or off the mask. Here I can put on or of the mask but I dont need to do anything with it if I choose to.  :)

Betrayal is notorious for loose & inconsistent wording. It says "can put on or take off the mask" - I read it as you have the option to either put it on or take it off, depending on whether it is currently on or not. If you don't want the mask on, you just don't make roll.

@KenHerbert, Definitely true. I love the game to death but a lot of the rules come down to personal interpretation, in this case it being whether the emphasis is on the word "can" or the word "or".  Either way you're right, you should just avoid the roll all together if succeeding will kill you, since a 0-3 has no effect at all.

I checked my characters sanity only after doing the roll.

I think an important part of this answer is the part about the haunt having started or not.


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How do Wounds, Damage, Saving Throws and Invulnerable Saves interact with each other?
I have read the freely available Battle Primer, which explains the core rules. However, I am still a bit confused regarding how exactly to resolve damage.

Imagine a unit of Space Marines gets 10 shots at a unit of Orks. The weapons of the Space Marines have an Armour Penetration value of -2, and a Damage Value of 2 as well.
Out of those ten shots, six shots hit. Of those six hits, four of them wound.
The next step would require me to allocate "Wounds". How many Wounds did I generate? Is it 4, because 4 shots hit and passed the Wound roll? Or is it 8, because each shot would deal 2 damage?
The Ork player would then have to allocate the wounds and roll Saving Throws. Let's assume his Orks have a saving throw of 4+. Does this mean he has to roll 4 individual Saving Throws (one per shot) or 8 individual Saving Throws (one per damage).
Imagine one Ork had the ability to roll Invulnerability Saves. Are those Save rolls per-shot, or per-damage?

Here's a step-by-step breakdown of the procedure. This is basically the same regardless of whether it's in Close Combat or Shooting.

Select an Eligible Unit.
Declare targets for all weapons before making any hit rolls (important in units with mixed weaponry)
Pick one weapon type (in some situations you may need to attack with each weapon one at a time, but usually you can save time by rolling groups at once) and make your to hit rolls.
For every Hit make a wound roll. Again sometimes you'll need to roll the wound rolls one at a time, but usually you can group them.
For every wound your opponent needs to pick a model and make a save. If the AP (Armour Penetration) of your weapon makes their regular save worse than their Invulnerable save they'll use the Invulnerable. For a unit w/ multi-wound models, if a model already has a wound it must be picked first for this step. If the damage of the weapon is greater than the wounds of the picked model and that model fails the save it is removed and a new model is chosen for the next wound. Keep going until all the wounds are applied.
Sometimes a unit will have an effect (often from another unit, or a psychic power) that lets it ignore damage (such as Disgustingly Resilient). Often this will be referred to as "Feel No Pain" as there was a universal rule with that name in previous editions. If so, for each point of damage it takes from failed wounds (or Mortal Wounds) it gets to make a FNP roll. If successful that damage is ignore. However note that a roll is made for each point of damage. So if a 2 wound model failed its save from a 3 Damage wound, it would need to make at least 2 of its FNP rolls to avoid dying.

If you've got mixed save units w/ FNP and multi-damage damage wounds you'll need to go through the process one at a time as things can get complicated. Once you've played a few games you'll figure out when and where you can speed things up by rolling multiple saves/FNP at once.
Note that mortal wounds ignore saves (regular and invulnerable) completely but don't usually ignore Feel No Pain type effects...
In the specific example of 8 hits > 4 wounds, the orks would make 4 saving throws (needing 6s). If you had a single ork with an invulnerable save, you could choose to roll against its Invulnerable, but if it fails that ork in particular would die. Since they're all single wound models, the extra damage is wasted.


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Can you use one card on multiple obstacles?
I'm just started playing shadowrun crossfire prime runner, and I had a question about if you can play one black market card on two or more obstacles. Like if a black market card has a face damage and mana damage it it's damage category in the top left. Can I use the face on one obstacle, and the mana on another obstacle? Thanks

Black Market cards work in much the same way as the basic cards, unless they have an ability which lets them damage multiple obstacles, they will deal all of their damage to a single obstacle.


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How many possible starting moves are there in Abalone?
I have not found a listing or reference to the initial number of moves.
I believe there are 44, but I'm not sure if this list is complete: https://github.com/void4/pyabalone/blob/master/allinitmoves.txt
https://en.wikipedia.org/wiki/Abalone_(board_game)

I agree with 44.  Here's my break down:
Diagonal X2 (once for each diagonal direction):

6 moves with a single marble
5 in-line moves with 2 marbles
4 broadside moves with 2 marbles
3 in-line moves with 3 marbles
1 broadside move with 3 marbles

Horizontal

2 moves with a single marble
2 in-line moves with 2 marbles
2 in-line moves with 3 marbles

(6 + 5 + 4 + 3 + 1) * 2 + (2 + 2 + 2) = 44.


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Does Magic the Gathering need an independent arbiter for reliable detection of cheating?
In complete information games like chess, a player can always be certain about if and when an opponent cheats only given their own observations of the past and present state of the game because the decisions all players make (where to move a piece), and the board state are always fully public.
But Magic the Gathering has a lot of hidden state/information through zones like the library and hand, and mechanics like upside-down morph cards, which are only revealed later.
Do the game rules ensure that, at the very least when the game ends, each player knows for certain that the rules have been followed correctly - that no opponent cheated?
Which I could imagine happening through them manipulating hidden information in a way that is against the game's/cards' rules. Such as retrieving a card from their library that does not match the tutor's specifications (the tutors seem to require revealing the retrieved cards however, probably for this reason), or retroactively changing a decision to their advantage when it is revealed to the other player(s) (which might be prevented by making the player provably commit to it by writing their decision down)?
Do such situations actually exist which necessitate that an independent arbiter observes/tracks the game as well, so that evidence of the cheating does not get lost, and the matter of whether or not someone has cheated is adjudicated correctly?
If so, does the arbiter have to watch the entire game from both/all sides and note down every decision, or does the game ensure that they can always correctly reconstruct decisions once a player detects an incongruity, not using past observations?

It would be great if the people downvoting this question explained why they did so

If I had to guess, the question was asked a little paradoxically and conflates some concepts. No amount of rules will help against cheating because the very definition of cheating includes breaking the rules. And if the rules or certain cards knowingly left such a loophole open, it's not exactly cheating to use that to your advantage. That being said, the core question of "does Magic need an arbiter" is quite basic but valid, so I chose to answer it.

I intend it to be about the reliable detection of cheating. With hidden information, there exists the possibility of the game (accidentally) giving players choices that are unverifiable by opponents, so cheating may have occurred, but not provably

If you play a game of chess and your opponent illegally (but plausibly) moves a piece while you're not looking, how can you prove that cheating has occurred? Let's say they move a rook, you look away, and while you're looking away they move the rook another square in the same direction?

@Hackworth I'm assuming perfect observation

@2080 perfect observation is an unrealistic assumption

@Andrew Then let it be unrealistic - I'm interested in the theory of the game. I'm aware that the practice is much different. Assume a player recording everything with a camera from their point of view, seeing (only) what they see themselves, and opponents not being overtly obstrusive.

@2080 every competitive game could benefit from having a team of people watching every part of the game from every angle to ensure everything happens above board, the reason they don't isn't because they couldn't benefit from it (and benefit is different from need) but because of the logistical and realistic issues. There's not a single competitive game that wouldn't be in the abstract made better/more fair under such conditions, the conditions are just not possible.

FYI, the vast majority of cheating in chess involves getting outside assistance with making moves, rather than simply making an illegal move when nobody is looking. Such cheating used to require an accomplice, but in modern times usually involves plugging the current board state into a computer program and having the computer program suggest a strong move. For one of the most recent scandals, see https://en.wikipedia.org/wiki/Carlsen%E2%80%93Niemann_controversy

@Andrew: That’s missing the point of OP’s question: There’s a clear theoretical difference of whether or not there’s enough public information to verify that the rules are being followed.

"No amount of rules will help against cheating because the very definition of cheating includes breaking the rules."
That doesn't make sense. The question makes it quite clear how rules can help against cheating. For instance, requiring cards found with tutors to be revealed makes it harder to tutor an ineligible card.

Your logic (which you fail to make explicit) seems to be that if someone is willing to break one rule, then adding another rule is pointless, since they would be also willing to break that rule. But the point isn't that people will follow the additional rules out of honesty, but out of necessity. If your opponent is paying attention, no amount of willingness to not reveal a card is going to allow you to get away with not revealing it.

"And if the rules or certain cards knowingly left such a loophole open, it's not exactly cheating to use that to your advantage."
Of course it is. If there were a card that said "Deal X damage to target creature, where X is the number of creature cards in your hand", it absolutely would be cheating to lie about how many creature cards are in your hand.

I don't think this is quite the direction you were going for with the question, but I'll point out that the existence of card mechanics like Richard Turner suggest that even with a trained expert observing the shuffling of cards, you're still struggling to catch up.

@CortAmmon This could still be theoretically fairly mitigated without an arbiter by giving every player the opportunity to re-shuffle for anyone else after every instance of them shuffling, right?

@CortAmmon Hmm, I guess not only after shuffling but also choosing a random card(s) for them when a card effect requires this.

Yes, but only to verify deck legality
During play, all printed cards (un-sets excluded, along with online-only cards) are worded in such a way that their effects can be verified by other players. Hackworth's answer goes into more detail here. It's very difficult to prove a negative, but I've never seen a card which was not designed this way.
However, that only guarantees that cards are resolved correctly. The game does not allow players to inspect their opponents deck to ensure that the deck itself is legal. There are several kinds of illegal deck (some could be more easily hidden than others):

A deck with more than 4 copies of a vital card.

See this question for discussion of how this might be caught.

A deck with fewer than the required number of cards (e.g. a 59-card deck in a 60-card format)

The number of cards in hidden zones is not hidden, so theoretically their opponent could ask them to count the cards in their library at the start of the game, which would expose the cheating.

In constructed tournaments, players are required to use the same deck and sideboard for all games in the tournament, however, the lists are not revealed to their opponent. A player who swaps a few cards out (for example, someone who talks to their opponent's previous opponent to find out what kind of deck they're up against and then makes a few sideboard swaps before game 1) cannot be caught except by a judge.

Similarly running too few cards for the format isn't particularly noticeable, especially given that different ways of sleeving a deck will mean different per card thicknesses

@Caleth - While it's true that it wouldn't usually be caught, the number of cards remaining in the other player's library is public information. A player can ask their opponent "how many cards are left in your library" and their opponent must either count or allow them to count.

you'd have to count all zones, i.e. suspect they were short on cards

I am no expert player, but it seems to me that many of these issues could be solved by making the decks and sideboard lists public after the tournament is over. Is this not common practice?

@FedericoPoloni It is for at least important tournaments, but at that point it's way too late. How would you prove a few days later that your opponent played a sideboard card in game 1? Keeping exact score sheets like in Chess is enormously impractical in Magic.

Can't you pile shuffle your opponent's deck at the beginning of games to count it?

Some games, like Yugioh, aren't designed this way. Yugioh has a whole bunch of cases where the game depends on players being honest about private knowledge. This is at least in part because so many game elements were invented ad-hoc to make an interesting manga, instead of to make a practical card game.

Under the parameters of the question, why would this need an arbitrator after the game is over? Couldn't both players check each other's deck for validity after the game has been played?

@trlkly They could, but nothing in MTG's rules requires it, which is what the question is asking about.

@trlkly - Additionally, in a tournament setting, multiple games are played in a row with the same decks (with a few cards swapped from the sideboard). If deck inspection is allowed after each game, that would reveal previously hidden information before sideboarding to the next game. If deck inspection isn't allowed until after all games are complete, then it would be possible to run an illegal deck in game 1.

Aren't there cards that require your opponent to reveal cards from their hand if they are correctly named, too?

@Brondahl - No. The way those cards are written: you name a card, then your opponent reveals their entire hand, then they take some action (such as discarding or exiling) any cards which match the named card. I can think of one online only card which requires the opponent to only partially reveal their hand (only "nonland, noncreature" cards, I think), but that card has never been printed in paper because it would be unverifiable.

Within the rules, the game does not need an arbiter. Cheating is another matter.
The rules of the game, together with the card designs, make sure that cards whose abilities affect the game state or have to fulfill certain criteria will at some point be visible to all players, if only at the end of the game. Some casual (not tournament-legal) game variants that put more emphasis on the social aspect of Magic might have exceptions, such as the Un-sets or certain multiplayer variants, but these are not discussed in the Comprehensive Rules that describe typical tournament formats.
For example, when a tutor effect allows you to search your library for a creature card and put it in your hand, you will always be required to reveal that card before you do that.
For another example, if you play a card as a 2/2 morph creature and that creature survives until the end of the game, it has to be revealed as the game ends to make sure you were allowed to play it as a morph.

708.9. If a face-down permanent or a face-down component of a merged permanent moves from the battlefield to any other zone, its owner must reveal it to all players as they move it. If a face-down spell moves from the stack to any zone other than the battlefield, its owner must reveal it to all players as they move it. If a player leaves the game, all face-down permanents, face-down components of merged permanents, and face-down spells owned by that player must be revealed to all players. At the end of each game, all face-down permanents, face-down components of merged permanents, and face-down spells must be revealed to all players.

That being said, rules violations both intentional and not do happen, of course. For that reason, each official tournament is required to have a Head Judge, an WotC-accredited person with sufficient knowledge of the game rules and tournament organization. The Head Judge assists players and ensure the orderly conduct of the tournament, including checking allegations of cheating, as described in the Magic Tournament Rules (MTR). The MTR further define the types of information in a game of Magic and how players are required to keep track of them.
This Head Judge requirement, however, is not part of the Comprehensive Rules that govern an individual game of Magic. Any game of Magic can correctly finish without any outside supervision at all. If cheating occurs, then the rules are not to blame, because by definition, they have been broken by the cheater.

I will add that MTG judges don't exactly fill the "independent arbiter" role as the question describes it. Judges do not watch any single game continuously, so they generally have less information about the game state than either player has.

"The rules of the game, together with card designs, make sure that cards whose abilities affect the game state or have to fulfill certain criteria will at some point be visible to all players, if only at the end of the game." While I believe this is true for each individual card, I also believe there are some multi-card interactions (perhaps most famously Brainstorm + Sylvan Library) where this isn't true. I know how that specific interaction plays out in tournament settings, but I wouldn't know for every possible interaction.

@PhilipKendall What exactly is the issue with Brainstorm + SL? If it's about clearly marking which card was drawn how, then that's a failure to follow card instructions that can be immediately noticed by opponent. If the game asks about whether or not a card has been drawn this turn, then the implication is that it's a piece of info the game (and thus the players) keep track of.

It can't necessarily be noticed by the opponent because the player is (generally) at liberty to shuffle their hand at any point, and generally will do when resolving Brainstorm to avoid revealing whether the cards they put back are cards they drew this turn. But if you do that with a Sylvan Library trigger on the stack, the opponent can no longer verify that the cards put back with SL were in fact drawn this turn. It plays out differently in paper, where the interaction is very slighty nerfed, as opposed to MTGO where there is an independent arbiter.

@PhilipKendall Yes, "generally" they are at liberty to shuffle their hands, when it doesn't matter for the game state. If a card such as Sylvan Library needs to know which cards they've drawn this turn, then they're not at liberty.

Technically, it is possible to resolve a Brainstorm during your upkeep without knowing that you will need to handle a Sylvan Library trigger. For example, with Leyline of Anticipation, you could resolve the Brainstorm, then resolve a different draw spell, then cast Sylvan Library all during your upkeep. However, I believe the standard resolution for a situation like that is that when resolving the Sylvan Library trigger, you are only allowed to put back cards you kept separate to establish that you drew them that turn.

@murgatroid99 Arguably, if your deck allows for such a scenario, you are obliged to keep track of the cards drawn at all times since it might matter in a future game state., and thus, the game state. But if that's too far out and you're not obliged to account for non-deterministic future game states, then an arbiter could not help either because the information does not exist.

The point is that Sylvan Library doesn't actually create an obligation to track every card you drew that turn, it just restricts you to putting back cards that you drew that turn. It's perfectly consistent to not track those cards at all, and not put anything back.

@murgatroid99 How about we move this to chat? I'd like to ask you to clarify what you're saying here

@Hackworth An opponent might also find a way to gift and make the player play the second card, thus forcing everyone to keep track of this information at all times, (also so they can share it with the opponent when if they take control)?

@murgatroid99 At the lowest level of the "judge iceberg" there are a couple interactions that cannot be resolved without an independent arbiter.  It's just Sylvan Library/Brainstorm examples are by far the most common since both cards see tournament play.  A list of current examples might be an interesting separate question.

@PhilipKendall can you make this an answer so it can be upvoted, none of the answers explicitly mention this kind of case?

Magic the Gathering has Judges, I'm one of them. No we don't watch the whole of every game, that would mean one judge for every two players and is just not possible when you have hundreds or thousands in some events. At later games in the finals when there are only a handful of tables left, then yes judges will watch games more closely. Usually we get called in when a player sees something they think is questionable.
There is a lot more that a judge can tell about what happened in a game than a lot of players think just by looking at game state and asking questions. Most of the time you can count cards and turns to see if any extra cards were drawn, can count game state on lands, and so many other things to verify a legal game state. Though we can look at your examples:

Retrieving a card from their library that does not match the tutor's specifications (the tutors seem to require revealing the retrieved cards however, probably for this reason)

Correct. Every single tutor that has any kind of restrictions on it either puts the card found into play (where it will be public, and thus revealed) or requires the player reveal the card they found before putting it in their hand or on top of their library to prove that it matches the restrictions. The only tutors that don't require revealing the card are ones like Demonic Tutor where there is no restrictions, so every card will be legal to find.

retroactively changing a decision to their advantage when it is revealed to the other player(s) (which might be prevented by making the player provably commit to it by writing their decision down)?

Magic does tend to avoid simultaneous decisions as much as it can to avoid scenarios like this, but when they do, yes, usually players make these decisions in some concrete way, for example with wheel of misfortune players often write their number down or choose it with hidden dice that they will reveal so it's hard to change when revealing.
Will this prevent every case of cheating, no, in a game of imperfect information it's pretty much impossible to prevent everything, even if someone is always watching. The game and tournament rules are set up as they are to try and limit cheating as much as possible, from your opponent always cutting your deck after shuffles, to the examples discussed. Independent arbiters for each just aren't feasible, most of the time between the rules structures and judges, it's not perfect but it's the best we really can have.

I think you're answering the wrong question here. The question isn't "is it possible for an independent arbiter to determine if a player was cheating?", but "are there situations by which an independent arbiter would be required in order to determine if a player was cheating?" The OP wants to know if there's a way by which a player could cheat through actions taken purely in hidden zones or with hidden information while all visible actions or information were precisely in line with the Comp Rules, or if the Comp Rules as-is are structured in such a way that that would be impossible.

First of all, as mentioned, it's worth noting that one aspect of cheating (that is actually seen in chess tournaments) is whether there is any outside help, such as from an AI.
Ignoring that, then I believe the question is really whether or not someone can completely observe the game play to determine if there was any cheating.
In MtG, this is not initially the case, because there is information in the deck of cards that is hidden (such as number of cards, specific cards, etc..), but also allows for cheating by a clever card manipulator (such as not dealing from the top of the deck, etc.., improperly shuffling).
You could allow players to shuffle each other's decks to ensure they haven't "stacked" their deck in a specific way.  That solves one possibility of cheating.
You can also solve the issue of deck construction and still have the contents of the deck initially unknown to the opposing player by using a cryptographic hash - i.e., once the deck is shuffled you come up with a text list of all the cards in order, then you come up with a public cryptographic hash of that list which can be known at the start of the game (without revealing the cards themselves).  At the end of the game the players must reveal their private key for the cryptographic hash and then the card identity and order in the game can be confirmed.
Unfortunately the second technique conflicts with the first, unless you have an arbiter of some sort that can track the deck (and then you wouldn't need a hash).  Of course - this arbiter could be automated, something that scans the deck after it's been shuffled and then this would be able to handle ensuring deck ordering in play (as well as construction).
But there's another form of cheating that you can't really discover by simply looking at the game play afterwards, and that's peeking.  If the player is able to peek at their down cards (or yours) then that won't show up in the final game play.
There's certainly techniques you can use to minimize this type of cheating, but delve into magic (as in "tricks" instead of "the gathering") and you will be shocked with what is possible, including having rfid encoded cards that can be read by a palm reader/ring.
So, to answer your question in the end, MtG is not something where all forms of cheating can be determined by simply looking at the game play afterwards.
Though this is not fully true of chess anyways.


text:
Cheapest unstoppable, mandatory infinite loops in Magic the Gathering
Like expanded on in the Cheapest mandatory loop answers, there exist game states induced by combos where card effects trigger off each other indefinitely without any further action required by the player(s).
By CR 729.4.

If a loop contains only mandatory actions, the game is a draw. (See rules 104.4b and 104.4f.)

But usually, interaction, breaking the loop and preventing the draw is still usually possible, because all players gain priority from triggers being placed on the stack.
Are there examples of infinite combos that not just do not require any actions to maintain them but are actually unstoppable/uninterruptible (by (all) opponents or all players) once initiated, because they do not allow any interaction (at all, or one(s) that would lead to a different outcome), and thus force a draw?
Perhaps by, in some way, not using the stack and instead recurring state based checks that cannot be responded to?

No, I mention this in the first paragraph of this question

The animate dead / worldgorger dragon loop in the linked question describes how to make it unstoppable

@Caleth But it still puts triggered abilities on the stack, allowing any player to respond to (and potentially interrupt) it while it is running (?)

If you allow for arbitrary board states of opponents I don't think there are any unbreakable loops, because of End the Turn effects

@Caleth I can shut down most of that by giving both players Teferi, Time Raveler.

@PhilipKendall is there a Time Raveler equivalent for activating (non-mana) abilities?

@Caleth Grand Abolisher and Myrel, Shield of Argive come to mind but I'm not sure if they cover all possibilities

City of Solitude covers a few more cases than Myrel. I hope there's not a Time Raveler equivalent for abilities because Teferi already makes for really uninteresting play patterns.

@PhilipKendall starting with City would be enough to make Worldgorger / Animate Dead unstoppable, assuming you've removed any on-board replacement effects that would disrupt it

The question I linked has answers has answers that answer this question

I know of two truly unstoppable mandatory loops that don't need any extra pieces to be unstoppable: the Lich's Mirror loop and the Enduring Scalelord loop. Of those, I think the Enduring Scalelord loop is probably cheaper to assemble and trigger: I found a way to do it for 8 mana. I disagree that the other question addresses this. Neither answer there addresses making the loop impossible to stop.

@murgatroid99 how do you make Enduring Scalelord a mandatory loop? it's a may ability

I meant to refer to Scalelord Reckoner. That one can create an actual mandatory loop.

I know of two mandatory loops that allow no interaction once the loop starts, one using Scalelord Reckoner and another using Lich's Mirror.
Scalelord Reckoner (7+ mana)
Scalelord Reckoner has the ability

Whenever a Dragon you control becomes the target of a spell or ability an opponent controls, destroy target nonland permanent that player controls.

The loop it creates is described in one of the official rulings on the card:

If the only nonland permanents on the battlefield are Scalelord Reckoners and Dragons controlled by players who control Scalelord Reckoners, any spell or ability that targets one of those Dragons will cause an infinite loop of triggered abilities and the game will immediately end in a draw.

This is a loop of putting triggered abilities on the stack, which triggers other abilities. No player gains priority during this process, so there is no way to stop it.
This can be set up by one player if there are not already any non-Dragon nonland permanents on the battlefield for 7 mana as follows:

Play Scalelord Reckoner for 5 mana.
Play Mystic Reflection targeting Scalelord Reckoner for 2 mana.
Play Forbidden Orchard and activate its ability to give an opponent a Spirit token, which enters as a copy of Scalelord Recokoner due to Mystic Reflection's ability.
Play any 0-mana effect that targets a creature, such as Smoldering Spires.

If there are other nonland non-Dragon permanents, some amount of additional mana could be required to set up the loop. The amount will vary depending on what permanents there are.
Lich's Mirror (9-12 mana)
Lich's Mirror has the ability

If you would lose the game, instead shuffle your hand, your graveyard, and all permanents you own into your library, then draw seven cards and your life total becomes 20.

The loop it creates is described in two of the official rulings on the card (I refomatted the first one for this site):

As part of Lich's Mirror's effect, it typically shuffles itself into your library. If it does, that means that if you'd lose the game again immediately after its effect is finished, it can't help you a second time. This can occur in a few different ways. For example:

You have ten or more poison counters. Lich's Mirror doesn't remove poison counters. If you'd lose the game this way, you'll do what Lich's Mirror says, then you'll lose the game the next time state-based actions are checked.
Your life total is 0 or less and an effect says that you can't gain life. Since your life total can't be raised, it stays at whatever it is rather than becoming 20, and you'll lose the game the next time state-based actions are checked.
The number of nontoken permanents you own plus the number of cards in your hand, graveyard, and library is less than seven. When you try to draw seven cards as part of Lich's Mirror's effect, you'll be unable to complete at least one of those draws and you'll lose the game the next time state-based actions are checked.
You control but don't own a permanent such as Immortal Coil with a triggered ability that causes you to lose the game when a certain game state happens (also known as a "state trigger"), and the condition that causes the "lose the game" ability to trigger hasn't changed. If you owned the permanent, Lich's Mirror would shuffle it into your library. In this case, however, it remains on the battlefield and its ability will trigger again.

If you control but don't own Lich's Mirror, Lich's Mirror itself will still be on the battlefield after its effect is finished. If you would lose the game again for any of the reasons above, Lich's Mirror has its effect again . . . and again . . . and again. An involuntary infinite loop will be created, and the game will end in a draw. (In the case of the triggered ability example given last in the list above, it's possible that a player could cause the loop to end while the ability is on the stack. None of the loops caused by state-based actions can be stopped at all.)

As the ruling says, the loops caused by state-based actions cannot be stopped, because no player gains priority between successive evaluations of state-based actions.
The cost to set this up is 5 mana for Lich's Mirror itself, 3 mana to donate the mirror with Harmless Offering, and some amount more mana to put the opponent in the state that causes the loop. The simplest way to do that is probably by giving them 10 poison counters. This could cost 1 mana to play a Glistener Elf and then attack 10 times, or 3 mana to play the Glistener Elf, give it +4/+4 with Groundswell after playing a land, and double its power with Berserk and then attack with it once.

Mystic Reflection can achieve the same result as Cytoshape, but costs 1 less

That's a good point. Edited

Grindstone (4–6 mana)
Grindstone's ability is: {3}, {T}: Target player mills two cards. If two cards that share a color were milled this way, repeat this process.
If all the cards in the player's library share a color, and they include at least two Progenitus (If Progenitus would be put into a graveyard from anywhere, reveal Progenitus and shuffle it into its owner’s library instead.), then Grindstone's ability keeps going, forever. This all happens within a single resolving activated ability, so players do not get priority while it is happening.
With a deck that naturally meets the condition of all cards sharing a color (which can be made somewhat practical using MDFC lands), this takes 4 mana in total. Otherwise, we can use the well-known combo, adding Painter's Servant to make the cards share a color, for a total of 6 mana.
Grist, the Hunger Tide (5 mana)
Grist, the Hunger Tide also has a similar repeating-mill ability: +1: Create a 1/1 black and green Insect creature token, then mill a card. If an Insect card was milled this way, put a loyalty counter on Grist and repeat this process.
A cheap way to arrange for this to repeat forever is: Begin the game with Leyline of Transformation on the battlefield for free, choosing Insect; Demonic Consultation, naming a card not in the deck, to exile the whole library; Pull from Eternity to get Progenitus back into the library.

Upvoted, but I think this answer would be improved by adding an explanation of what "Then repeat this process" means on an ability (specifically, that they don't use the stack). That rule is non-obvious to me and I only know it from playing Arena.

Your Grindstone effect would work better against a players library having two Worldspine Wurms.

Grindstone would not create an infinite loop with Worldspine Wurm because Worldspine Wurm's ability is a triggered ability. It specifically creates an infinite loop with Progenitus because Progenitus's ability is a replacement effect.

Sphinx's Tutelage does the same thing as Grindstone but for three mana, not four, right?

@PatrickStevens It's similar, but the "nonland" condition stops it from working with Painter's Servant, and the restriction to "target opponent" makes it generally less plausible.


text:
When using Talix's power in a two player game, do you return one or both cards to the turn deck?
Talix's, available on Aeon's End: The New Age, power reads:

Destroy two sparks in hand. If you do, shuffle your turn order card into the turn order deck. OR Gravehold gains 5 life.

If you are playing a 2 player game, each player has two turn order cards. Then, if you use his first power on your second turn that round (meaning both your turn order cards are in the discard pile) do you place both your turn order cards into the pile or just one?
While the wording on the power seems to indicate it is a single one, it also reads like you just have one "your turn order card". In a two-player game, you have two, so it might make sense to move both back? Is there an official answer?

As far as I know, there is no official answer on this, nonetheless, it's the last turn order card, as in, the active one. You've got a similar ability with Lash, he only gets one card. If you're playing a 3 player game, and got the wildcard to trigger your turn, I'd say you must put this one in the turn order, with no forced play on draw.


text:
Whose are the cards played through Mesmerize considered to be?
The Malkavian player has two related cards:
Chaos

You may choose to take 1 or more of your Deployed cards at this Location back into your hand, including this one. For each card you take back, Steal 1 blood from each Rival.

Mesmerize

Choose a Rival. Play all of the cards remaining in their hand on your Position at this Location, face up.

Can the Malkavian player return cards played through Mesmerize to their hand and steal blood with them through Chaos? Or the your modifier on Chaos explicitly means your own clan cards only?

The cards played via Mesmerize are treated as the Malkavian's deployed cards. You can take them into your hand via Chaos.
See the publisher's answer in this thread on BGG:

Mesmerized card on the table goes back to the original owner's hand at the end of the round. But I don't know what would happen if I try taking that card into my hand by playing Chaos. Is mesmerized card MY card so that I can use Chaos or Mindless Assault etc. on that card?

Yes indeed, the Mesmerized cards are considered as part of your Clan deck in regard of any effect, but you'll have to give them back at the end of the round of course.


text:
Can the Malkavian player use Chaos twice?
The Malkavian player has two related cards:
Chaos

You may choose to take 1 or more of your Deployed cards at this Location back into your hand, including this one. For each card you take back, Steal 1 blood from each Rival.

Madness Network

Play all of the cards remaining in your hand at this Location, face up.

Both of these cards are on the "Preparation (sun)" stage.
Can the Malkavian:

Use Chaos, taking Chaos + all cards back to their hand but leaving Madness Network.
Use Madness Network to deploy all cards again.
Use Chaos again, taking all cards back

And thus steal a ton of blood in the process?
Rules seem to support a yes for this question, which is what we went with, but we wondered if there's anything that says no.

5.3 Preparation:
Players resolve the effects of their Preparation cards.
Starting with the player with the Ambition
token and proceeding clockwise, apply
the effects of each Preparation card you
have at the current Location. If you have
more than one card at this Location that
triggers during this step, you may decide
the order in which you activate them.
Each card must be entirely resolved
before activating the next.

Contradicting Rules?
This is a game about rule-breaking. As such, there will be times where cards seem to
contradict each other, or this rulebook! Here’s how to resolve these inevitable disputes:

The text on the cards always prevails over the rulebook.
In case of timing issues between cards (i.e., two cards have the same symbol), they are resolved in turn order, starting with the player holding the Ambition token and proceeding clockwise (i.e., card(s) played by the player holding the Ambition token take effect first, then cards by the next player in turn order take effect, etc.).
Remember that ties are always resolved in turn order.
If a single player has multiple cards that trigger at the same time, they choose the order in which they are resolved.

The publisher clarifies (errata?) this on this thread on BGG:

Chaos (or any other cards) doesn't get activated again once it's played through Madness Network,

Let's say, for simplicity, each card ability only get activated once regardless of how many times it get played.

and also note that this restriction is "per location" (although that doesn't affect your case). From that same thread:

Each card activate once PER LOCATION so to speak,


text:
When purchasing the 13th technology, can you use its power right after doing so?
The 13th technology on the manual reads:

After resolving one or more powerups gained from performing a Main action, you may pay 1 cocoa to gain an additional power-up (same Action Board)

While the main action part on the manual reads:

Pay the cost in gold as shown on the selected tile and place one
  of your Technology markers (wooden discs) on it to mark that
  you have acquired this Technology. Refer to the Appendix for an
  explanation of the ongoing benefit of each Technology tile.
After placing the Technology marker, advance once on one
  temple, depending on which column the selected Technology
  belongs to: for the left column, for the centre column,
   for the right column
Afterwards, power up one of your workers on the Alchemy (5)
  Action Board, unless you used the 3rd option when selecting the
  tile (you used a single power 4 or 5 worker to place your marker
  on a second-row Technology).

Therefore, you get the power-up after you have already received the technology, and advanced on a temple. Does this mean that when powering-up your die, can you immediately pay one cocoa to gain an additional power-up?
TLDR: Can you use the technology 13 power on the same die power-up you get from purchasing the technology?

No you can not.
From the FAQ file on BGG here the following Q and A is included.

Q: When do Technology benefits trigger? A: Each Technology triggers at
  most once during your turn. Most Technologies trigger after performing
  the Main action on the board (or boards) listed at the bottom of each
  Technology tile. No Technology will trigger during the turn when it
  was acquired.

I've tried to find evidence to back this up in the rules printed though and could not.


text:
Can Accelerated Rot deal 9 damage if you meet elemental requirements?
The major power, Accelerated Rot, shown below:

Has "+5 Damage. Remove 1 blight" if you meet the elements. Does this total to 9 damage or just 5, 2 fear and remove a blight? It seems to very clearly indicate it deals 9 total damage, but that seems very powerful.
The only relevant section in the manual, on page 17 says:

Elemental Thresholds: Optional effects which may only be used if the Spirit has gained certain Elements this turn. The requirement Elements are not "used up"; the threshold is simply a check to see if they are in play. [...] You may always resolve a Power as if you had fewer elements than you actually do. If you meet more than one threshold under a Power, do each of them in order, from top to bottom.
  Exception: If a threshold says "Instead", it replaces the effects of previous levels.

Since this doesn't say instead, it does seem to support it deals 9 damage - so we went with that. Can someone confirm for sure that's the right interpretation?

9 damage is quite strong, but 1) It's limited to targeting jungle or wetland, and 2) it's not easy to hit that threshold.

@GendoIkari Yup! It was much more clear to us after playing a few games, but in the first one did have that question while playing it :)

Yes, major powers are very strong when you hit their thresholds.  I don't have a rules citation beyond what you list there, and I don't see anything explicitly in the FAQ about it, but the lack of "instead" and the plus sign both indicate that the power does 9 damage and removes a blight when played and you hit the threshold.
Compare to Pillar of Living Flame (3 fear, 5 damage, add blight if target land is jungle/wetland), which by the other interpretation would get worse at the threshold (+2 fear, +5 damage).


text:
How to adjucate the interaction between Blue Velvet location and Mass Manipulation
Blue Velvet location card reads:

To Withdraw from here, you must Spend 2 blood

The rulebook is fairly explicit in saying you can't willingly send yourself into Frenzy, so we always play that you can't withdraw if you have 2 or less blood.
However, Mass Manipulation says:

During the Withdraw Step at this Location, each Rival must either Withdraw or let you Steal 2 blood from them to Stay.

This presents players with sort of a paradox. If they have 2 blood, they can't let the Ventrue Steal 2 blood for them to Stay, so they have to retreat. But if they retreat they must Spend 2 blood, so they can't retreat either.
What we've been playing with is: in this scenario, the player is forced to Retreat by Blue Velvet, Spends 2 blood and Frenzies. Should that be the case? In this scenario, does the Ventrue player get 1 Influence Point for making that player Frenzy?


text:
Haunt 42 - How does the traitor attack the [spoiler]?
The rules don't seem to say what are defense traits for the

 statue

and they don't seem to say what the traitor attacks with?

The Traitor's tome intentionally doesn't cover the [spoiler]
That's up for the Heroes to let the traitor know. The Secret's of survival book has all the rules for

 attacking the statue.

Here's the relevant bits from the Secrets of Survival book:

 Once the Statue animates, it remains in whatever state it transformed into for the rest of the game. When the Statue has been animated, tell the traitor what form it has taken.
 If the traitor attacks the Statue and defeats it, it isn’t stunned. Instead, the Statue can’t lower an ability during its next turn. The Statue can still be moved to follow the traitor.

So this is how it works:

 The traitor can attack the Statue normally, and the heroes should let the traitor know so when it animates. The traitor attacks with the default might, and the statue defends with might, as normal in any combat - unless an item says differently (like The Ring allows you to attack with Sanity). The Statue's attributes are 8 for everything (Speed, Might, Sanity and Knowledge) and it defends with the appropriate attribute for the attack.


text:
Can a worker leave a territory controlled by an enemy mech?
I have already unlocked the +1 movement mech upgrade. I take one of my workers inside my mech, I use one of my movements for move this mech with the worker inside to a place where already are an enemy mech. I know my mech cant move more, cant use this +1 movement upgrade, need stay there and resolve the fight. But the question is, I have still one more movement for whatever other of my units before resolve that, so can I (with this other second movement) move this worker that was "inside my mech" out from this spot to other spot?

No. The worker cannot leave a territory controlled by an enemy Mech. The rulebook says:

If your character or mech move into a territory
controlled by an opponent’s character and/or mechs,
its movement ends (even if you have a mech ability
that would allow it to move further). The opponent
still temporarily controls that territory. After you’ve
completed all Move actions, if any of your mechs or
your character share a territory with an opponent’s
character or mechs, combat happens (see Combat
section, pages 22-23).

Your workers cannot move by themselves into or out
of territories controlled by opponent characters and/
or mechs.


text:
What is the name of this pyramid game?
I used to have this game, not any more. It must be at least 10-15 years old, but possibly older. I don't remember the rules, only that you had to follow a certain path with your pyramids, and that they could be stacked in a way (perhaps blocking off others?). Searching on the internet, I have found pictures of the game, however I can't seem to trace it back to a name. One of the pictures I found shows the board clearly:

It is called Pyramidis (at least the dutch version). I found one last year in a thrift store. Fun little game.
To move, take a stack of pyramids of which the top color is yours and put these one by one in the next few spots, covering other pyramids. You need to get five of your eigh pyramids into your start area. Or (which is the harder option) cover all other users pyramids so they can't move and lose the game.

Useless trivia, the game Ramses II uses the same pyramids.

Awesome, thanks! Fun little fact indeed, I noticed it when searching on BGG, as I encountered Ramses 2 as well. Too bad querying 'pyramids' was not enough though.

I hope you find the game. There are possibly some for trade on BGG.

I will definitely take a look! Let's see if stacking the pyramids still sounds the same as in my recollection.

You could probably get away with using Icehouse pieces for this as well - those are likely to be much easier to find as they're used in many different games.


text:
Duplicate Bridge
Can the Dummy ever play a card without direction from Declarer?
What if an Ace is led by the defense and there are 1 or more cards in the same suit in Dummy?
What if a card is led by a Defender and Dummy cannot take the trick with a card in that suit or with a Trump card?
What if a card is let by a Defender and Dummy has no cards in that suit and no Trump cards?

It happens often that dummies play small cards when the declarer would probably tell the dummy to do so if they didn't. Many partners are okay with that. Also fun fact: if the declarer tells the dummy "meh, choose one", a rule states the opponents get to choose.

The dummy can't decide what card to play, ever.
Of course, practically there are some shortcuts when the dummy has only one card in a suit, or all remaining cards in the suit are for instance 'seven-eight-nine', or the dummy has a long run of al the high cards in a suit which can't be trumped anymore (either by playing NT or because the trumps are out already) and the declarer simply states "play 'm from the top". The last example is a 'direction from Declarer' for several tricks
The dummy can never just throw a small card under a leading ace without direction. There are situations that the declarer would like to get rid of another card in the dummy to prevent locking up later on.


text:
Is it possible to cast 2x Final Payment while sacrificing just one creature?
Situation:

Player A controls 2 creatures.
Player B controls 1 creature.
Player B plays 1x Final Payment and declares his creature as additional cost.
Before resolving the spell, Player B plays another Final Payment, once again declaring his creature as additional cost.

What happens here?

Option 1: Only the second Final Payment is executed since the additional costs for the previously casted spell aren't paid.
Option 2: Both creatures of Player A are destroyed while Player B only sacrificed one creature.

I suppose it's option 1 but we had a draft the other day where my opponent claimed that option 2 would be correct.

Step 4. is not possible; sacrificing the creature is part of the cost of the spell, so it is done while the spell is cast, not when it resolves. Player B just cannot play the second Final Payment and the card stays in his/her hand; only the first Final Payment is executed.

117.8. Some spells and abilities have additional costs. An additional cost is a cost listed in a spell's rules text, or applied to a spell or ability from another effect, that its controller must pay at the same time they pay the spell's mana cost or the ability's activation cost. Note that some additional costs are listed in keywords; see rule 702.

601.2. To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. Casting a spell includes proposal of the spell (rules 601.2a-d) and determination and payment of costs (rules 601.2f-h). To cast a spell, a player follows the steps listed below, in order. A player must be legally allowed to cast the spell to begin this process (see rule 601.3). If, at any point during the casting of a spell, a player is unable to comply with any of the steps listed below, the casting of the spell is illegal; the game returns to the moment before the casting of that spell was proposed (see rule 721, "Handling Illegal Actions").

thanks for the fast and profound answer. Just to clarify: Would player A be able to destroy the creature of player B with, let's say Cast Down in response to Final Payment, making it have no legal target? I guess not since you have to pay the additional costs at the time of casting final payment, or am I wrong here?

As soon as Player B has priority, they can announce Final Payment, and it's too late to cast Cast Down.

It might be helpful to contrast with situations where the sacrifice isn't "an additional cost to cast", like "Accursed Centaur"

601.2. To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs, so that it will
  eventually resolve and have its effect. Casting a spell includes
  proposal of the spell (rules 601.2a-d) and determination and payment
  of costs (rules 601.2f-h). To cast a spell, a player follows the steps
  listed below, in order. A player must be legally allowed to cast the
  spell to begin this process (see rule 601.3). If, at any point during
  the casting of a spell, a player is unable to comply with any of the
  steps listed below, the casting of the spell is illegal; the game
  returns to the moment before the casting of that spell was proposed
  (see rule 721, "Handling Illegal Actions").

As per the rules, do you ever cast a spell and wait for it to resolve before you tap your mana? or does the spell only go on the stack when you pay for the mana?
The rules clearly say that you need to meet all of the casting costs, so if you want to cast Final Payment you need to have all of the costs to cast it, this means, if your life is at 4 an you control no creatures you are  unable to cast it, even if your opponent was to take over your turn (by the means of cards like emrakul, the promised end or such) and tried to cast Final Payment to for you to lose the game, they would be unable to unless your life was at 5 or you controlled a creature.
There is no time between announcing that you want to cast a spell and paying for the spell costs.*
This is also the reason why if you cast Final Payment and while it is on the stack you cast the expansion side of  Expansion // Explosion you would copy Final Payment without having to pay the additional cost, this is because the card is already on the stack and all casting costs have been met, and copying it is the same as copying any other such spells.
This is the same for any other copy effects.
*There is a window of time there, to activate mana abilities, this is what allows you to use Llanowar elves ability without having to do it before announcing that you want to cast the spell and to tap lands. This is usually disregarded as nothing can be done in this time, but there was a deck that abused this fact in modern not to long ago so I thought I'd mention it.


text:
How are colored mana symbols ordered?
Yesterday when I organized a part of my collection I noticed something odd. I especially looked at Flying Crane Technique and Ruhan of the Fomori.
Note how Flying Crane Technique's mana cost are {3}{U}{R}{W} and Ruhan of the Fomori has {1}{R}{W}{U}. In the oracle box of Ruhan the mana costs are already different to what the printed card shows and thus match the pattern of Flying Crane Technique.
Are colored mana costs of cards in any specific order? Was this not the case but they changed it after a specific set?

Both of your links show {U}{R}{W} for me.  I'm guessing your cards are just an older version?

Did you look at the printed version or at the oracle box? The printed version has a different order.

The general rules for mana costs are to order them in sequence around the WUBRG circle, with white also following after green, with adjacent pairs having equal gaps in the clockwise direction, and minimizing the size of those gaps.
For two-color cards, this means that you order the pair so that you move the shortest distance in the clockwise order. So, white and blue will be WU, and white and green will be GW.
Four-color cards are also pretty simple, you write them going clockwise around the circle with no gaps. So a non-black card will have the order RGWU.
Five color cards are the simplest of all: they always have the order WUBRG.
Three-color combinations are the most complicated. There are two kinds of three-color combinations: shards and wedges. Shards are combinations with three adjacent colors, and they are just written with the colors adjacent in clockwise order. So, a white/blue/black card will have the order WUB, and a white/blue/green card will have the order GWU. Wedges are combinations with two adjacent colors and one opposite both of them. They are written with the two adjacent colors on the outside, and the opposing color in the middle. This creates a gap of size 2 between each adjacent pair of colors in the cost.
The cards in the question are examples of wedges: blue and white are the adjacent colors, and red is the opposing color. The order you see is the one that obeys the listed rules. The previous rule, as you can see on Ruhan of the Fomori, was to put the opposing color first.
According to this reddit thread, the color order for wedges was changed in Khans of Tarkir, the set Flying Crane Technique was printed in, and it has not changed again since then.

Stuff like this is what makes MTG so special, always overcomplicating things.

@bautista It's not overcomplicating at all, the way I see it. They can choose between having a set order, and not having a set order. If you want a set order, then you're going to have to make up the rules. Going clockwise around the circle that's printed on every single cardback ever makes a lot of sense. Going the shortest possible distance around that circle makes a lot of sense. All that remains is to decide on where to start with the wedges and the full five-colours. It may take a paragraph or two to explain, but it is, in essence, quite simple and intuitive.

Somewhat weird that all the other cases prefer showing adjacent colors adjacent, but in this case, they do exactly the opposite and break the neighboring pair.

The "opposing color in the middle" order creates a symmetry you wouldn't get otherwise: the gaps between adjacent colors in the cost may not be minimized, but they are consistent.

@Arthur the rule could have been "they appear in the order WUBRG, always". It's still clockwise, it still uses the handy reference, and it takes no paragraphs to explain.

@hobbs Sure. That is also a rule they could've chosen. I still don't think the current rule is overcomplicating. Guess they wanted some symmetry.

How is hybrid mana ordered?

Hybrid mana symbols complicate things further. Iluna, Apex of Wishes has a mutate cost of 3{R/G}UU. The adjacent pair comes before the opposite color in this case. Nethrol, Apex of Death has a mutate cost of {G/W}BB. Same thing.

The rules for ordering mana symbols has changed over the years. The current ordering scheme has been established with Khans of Tarkir (2014) and formalized with the Dominaria Oracle update (2018)
Apart from Ruhan of the Fomori, there is also Numot, the Devastator and Lightning Angel with a URW mana cost but with the old RWU ordering. All 3 of them were printed before Khans of Tarkir.
According to this Ask Wizards, which specifically mentions Lightning Angel, there had already been 3 ordering systems by 2004. The ordering on 3-color mana costs with "color plus both its enemy colors" like on Lightning Angel (nowadays known as wegdes) was internally consistent, but essentially an arbitrary decision by one designer.

"Then came the Apocalypse 'wedge' cards. Our system breaks down when you're trying to order two friendly colors and their common enemy, and Apocalypse has five rares with mana costs that fall into that category. For Lightning Angel's mana cost, 1RWU and 1WUR are equally valid options. In the end, I decided to put the enemy color pair first.

Khans of Tarkir (2014) officially named color wedges, which made URW the Jeskai wedge. The ordering of mana symbols was formalized in the Dominaria Oracle Changes update:

With Khans of Tarkir, we changed the order of mana symbols when one color meets its two enemies.
Up until then, the color facing its enemies came first, followed by its enemies in the standard two-color order. For example, Lightning Angel's cost was 1RWU.
Khans of Tarkir reordered these by putting the solitary color in the middle, paired up with its enemies in standard two-color order. For example, Jeskai Ascendancy's cost is URW.

In the color wheel, the colors next to each other are called allies, while ones separated by another color are enemies. To sort the symbols in a mana cost, it’s considered aesthetically pleasing and helpful for Limited gameplay to arrange them in such a way that either all pairs of neighboring symbols are allies, or all are enemies, and that they always go around the color wheel in the same direction. This rule results in unique orderings of combinations of up to three colors. For four or five, both options are possible, it was decided to prefer allied chains.
If you’d like to sort a mana cost the way Wizards do, look at the image below and find a sequence that includes the necessary colors and no others, following either the pentagon (allied colors) or the star (enemies). The clockwise direction will tell you the ordering.
The effect on gameplay is mostly when drafting a set with a high quantity of three-color cards. In a set with “shard” combinations (e. g. WUB, two allied pairs and one enemy pair) the two-color cards will tend to favor allied pairs, while “wedges” (e. g. URW, two pairs of enemies and an allied one) will be found in sets with enemy-colored two-color cards. Wizards prefer to design sets this way so three-color cards are compatible with a greater portion of other cards in the set. The arrangement of colors in the mana cost helps identify such compatibility at a glance (e. g. a deck with GUR cards will also contain GU and UR cards but not RG, so it makes sense to arrange the GUR symbols in a way that emphasizes the GU and UR subsets).


text:
How to get the best value out of gold and gems in MTG Arena?
I'm grinding MTG Arena pretty hard and managed to get my hands on 2-3 top tier decks by now (while still holding some wildcards).
Up to now i just played Ranked Games to get the daily challenges done. Once I have 5k Gold I play drafts. Traditional drafts seem pretty risky to me since you have to pay a lot of gems while getting a low base-value (3 boosters)
But I haven't figured out yet if it would be better to solely play Constructed events and then buy packs with the acquired gold.
What is the best approach to get the largest cardbase with no in-game purchases assuming a winrate of 50% across all event-types?

Play during a new set's release
This is only anecdotal, but I've noticed greater success in Draft and Sealed during the first week or so of a new set's release.  Thinking logically, this makes sense - Releases are popular, and the time when the most players will be playing.  So the percentage of players who play infrequently is higher, and you're more likely to play against inexperienced players.

This will also only work at the beginning of a new season. Since your limited-rank depends on how many games you play (and of course your win/lose ratio), you will get matched with similarly skilled players.


text:
How many cards can I gain in a buy phase with a single buy?
I was playing dominion this afternoon and I gained 4 cards during my buy phase with a single buy1, this was pretty impressive, however this got me wondering:  What is the theoretical limit to how many cards can be gained with a single buy?
Some ground rules to further clarify what I mean:

Only cards gained during the buy phase count.
As suggested by Joe W and GendoIkari only cards gained after you purchase something count.  (for example using loans to discard tunnels doesn't count as gaining)
You may only use one buy even if you have more.
We only count cards that are kept until the end of the turn. If a card is gained but trashed it does not count.
We care about only what is theoretically possible, not what is reasonable, so you can dictate:

What other players choose to do
Shuffling outcomes or any other source of randomness

But the result must still be possible, meaning that there must be some path through proper play that arrives at the turn and all moves in the turn must be legal.
You may choose to play with any number of players.
To keep the scope a little small I would also like to ignore black market.

Just thinking about this on my own I came up with a way to gain 75 cards now 141 cards in a single buy which I posted as an answer to get the ball rolling.  I had a lot of fun coming up with it but I'm sure someone who knows the newer sets can come up with something way better.

1: I bought border village, which allowed me to gain cache which gave be two additional coppers (which I ended up turning to silvers with my trader)

I can’t easily prove it off-hand, but I suspect that the answer is infinite, or bounded only by the total number of cards in the game.

@GendoIkari It would be nice to see an engine that can pick up arbitrary cards if you can find it.  Even then making the engine smaller will improve your gains since you will have more cards to pick up.

I know for sure that there exist engines to go infinite; even emptying the entire supply on the first turn. It just isn’t all the result of a single buy.

One example: http://forum.dominionstrategy.com/index.php?topic=17909.0

Also http://forum.dominionstrategy.com/index.php?topic=17800.0

“If a card is gained but trashed it does not count.” Good restriction. This will probably be key to prevent the answer from being infinite.

I’m not sure of the best wording; but you probably need to exclude simply buying Villa and then gaining a bunch of cards by playing actions afterwards. This is technically after your buy. The gains should all be the result of resolving on-buy and on-gain events.

@GendoIkari I'm not sure how much of a problem villa is since only cards gained during the buy phase count the action portion of the villa can't contribute to the count directly.

You can gain over 200 extra cards without using extra buys.  The limit to the number of buys will come from component limits rather than anything inherent in the game, the most important number being the number of each treasure card you play with (as there are at baseline only 136 cards to gain).  Ignoring that, the number of types of kingdom cards and the number of each kingdom card in play is also a substantial limitation as you can only pick a subset of the following abilities to use together in an actual game.
Mechanisms of gaining extra cards
There are four distinct ways to gain extra cards during the buy phase.

Extra buys.  This is the normal way, and so is not what we're considering here.  Via action chaining and action replication, the limit on extra buys you can get comes purely from component limits.
Action hacks.  The Innovation project lets you play an action card during your buy phase, and there are a bunch of actions that let you gain cards.
Triggered abilities that cause you to gain cards.
Free cards.  Treasure Chest gives you an extra card every buy phase.

All of this assumes arbitrary setup and that you are going to buy a King's Court for maximum action hacking.
Action Hacks (260 extra cards*)
Have the following in your hand:

9 King's Courts
10 Throne Rooms
9 Thieves
9 Beggars
9 Remakes
9 Develops

Now when you buy a King's Court, you use that to play an extensive tree of King's Courts and Throne Rooms, which will letting you then play a bunch of other action cards that will happen many times.  I believe the optimal way to play it is Throne Rooms first and King's Courts second, giving you ability to play 18 actions 3x each and 11 actions 2x each.
If we rig the game (let's say everyone is playing big money with massive decks) and it's 6 player, Thief will gain you five cards every time, so that's one of the one we want to use on the 3x actions.  Beggar gives the second most (3 cards per shot), so this is what we want to use the rest of the 3x actions on.  This is already 216 cards*.  We can then use the remaining 2x actions on Develop/Remake (2 cards per shot) for another 44 cards.
* This number may be lower in practice depending on how many coppers (and silver if you use Trader) are in the supply.
Triggered Abilities (100+ extra cards)
The cards in this category I know of that work with the action hack above are:

Haggler
Cache
Border Village
Death Cart
Market Square
Catacombs
Hunting Grounds
Skulk

(Hoard and Port aren't going to work because they only trigger off of buying a certain type of card.)
Taking component limits into account, we're only going to be able to use 10 of each of the triggered ability cards.  The cards listed above let you gain over 100 extra cards (given we have some way to trash cards during the buy phase).
Maximum without projects (50 extra cards)
Without using the Innovation project, the limit here is going to be the most triggers we can chain off of one buy.
In this case, I believe the optimal move is to play 10x Hagglers, 10x Hoards, and then buy a Province.  This will let you get 20 extra cards, 10 of which can be Border Villages, which can in turn let you get 10 Caches or Death Cards, which will give you 20 more cards.  This gives you a total of 50 extra cards.

With innovation I was able to get 356 (only bounded by number of cards)
4p game (opponents aren't buying anything)
Using the following cards:
12 Colonies
12 Providences
12 Duchies
12 Estates (Est for short)
10 Platinum
30 Gold
40 Silver
32 Copper (C for short)
30 Curses
30 Ruins
9 King's Court (KC for short)
8 Overlord
9 Watchtower
10 Lurkers
10 Feasts
10 Pillage
8 Inventors
10 Death carts
10 Young witches
10 Tournaments
10 Druids (swamps gift is one of the choices)
15 Spoils
12 Will-o-wisps
5 Prizes
Innovation (you have a cube on it)
Pathfinding (+card on overlord)
Your deck is:
2 platinums
7 c
3 est
1 kc
2 inventors
2 overlords
1 watchtower
Your hand is:
2 platinums
1 kc
1 inventor
1 overlords
Next cards are:
Watchtower
Overlord
Inventor

Play platinum. Buy kc. Play it with innovation.
Play kc
Play inventor 3x (gain some cards)
Play overlord as  feast (gain a card) then lurker (gaining itself and topdecking using watchtower) then kc. (+3 cards from pf)
Play inventor 3x (now all cards are 5 or less)
6 . Repeat step 4 until all cards in supply are gained.
Before all pillages are gained do step 4 but play overlord as pillage rather than feast. (Do this 8x to gain all spoils)
All cards will be in your hand since you are drawing 3 cards for every one card you gain.
Use your kc and overlords to play druids and tournaments to gain prizes and will o wisps.

What do "kc" and "cool" stand for? Could you expand on the card names in full at least the first time you mention them, for those of us less familiar with the cards?

@doppelgreener Based on context, KC = King's Court, Cool = Colony

This doesn't work.  Innovation does not let you use extra actions gained during your buy phase (which is a key assumption of this answer)


text:
Can you trash fortress indefinitely with donate?
So the two cards* in question here are Fortress, which reads:

+1 Card
+1 Action

When you trash this put it into your hand

and Donate which reads:

After this turn, put all cards from your deck and discard pile into your hand, trash any number, shuffle your hand into your deck, then draw 5 cards.

And the question is whether after a Fortress returns to your hand can you trash it again with the same Donate, and thus trash the same Fortress a potentially unbounded number of times.
This question actually matters since the landmark Tomb grants a player +1 point for every card they trash, thus this scheme could potentially net an unlimited number of points if Tomb is active.

No, because you trash all cards simultaneously.
From the Dark Ages rulebook:

When two or more cards are trashed at the same time, such as due to Count, first trash them all, then pick an order to resolve things that happen due to trashing them.

So with Donate, you must trash all of the cards you want to trash at the same time; and only then do any trashed Fortresses trigger and return to your hand.
There is also a ruling for Chapel, which uses basically the same wording:

You choose all the cards you want to trash, and then trash them at the same time; you don't trash them one-by-one. This matters for interactions with Dark Ages cards with on-trash abilities.


text:
What exactly "triggers an additional time" in the interaction between Afterlife and Teysa Karlov?
I'm pretty new to MTG and just have built my first commander deck around Teysa Karlov. One of her passive abilities is:

If a creature dying causes a triggered ability of a permanent you control to trigger, that ability triggers an additional time.

My deck features a lot of cards with death triggers, such as:

Afterlife N. (When this creature dies, create N 1/1 white and black Spirit creature tokens with flying.)

Let's say Teysa is on the battlefield and a creature of mine that has "Afterlife 2" dies, such as Ministrant of Obligation: what exactly gets triggered an additional time?
I see two options:

"Afterlife" triggers an additional time, so Afterlife 2 becomes Afterlife 3
"Afterlife 2" triggers an additional time, so 2x Afterlife 2

Which interpretation is correct and why?

Even if you're treating Afterlife 2 as being two triggers of Afterlife 1, each of those triggers is doubled by Teysa Karlov, so you get 4 white and black Spirit creature tokens with flying either way.

@Acccumulation Note that her ability states it triggers an additional time, not that it doubles the triggers.

I think it amounts to the same thing. Suppose Ministrant of Obligation instead said "When this creature dies, create a 1/1 creature, then creature another 1/1 creature." You would have two triggers, and each of those triggers would cause Teysa Karlov to trigger.

@Acccumulation Ah, now I get it. Thanks for clearing that up!

Option 2, you will get 2x Afterlife 2.
The thing that triggers an additional time is "that ability", based on the wording of Teysa Karlov. And "that ability" in this case is "Afterlife 2". So "Afterlife 2" triggers an additional time, meaning that on the stack you get both "Afterlife 2" and "Afterlife 2".
The first interpretation would require seeing Afterlife 2 as an ability that triggers twice, and then triggering 3 times instead. But nothing about Afterlife 2 is an ability that triggers twice. It is an ability that triggers once, and just happens to have an effect that involves the number 2.
This hinges on the definition of a triggered ability:

603.1. Triggered abilities have a trigger condition and an effect. They are written as “[When/Whenever/At] [trigger condition or event], [effect]. [Instructions (if any).]”

Whatever the number "afterlife" is; afterlife itself is a triggered ability:

702.134. Afterlife

702.134a Afterlife is a triggered ability. “Afterlife N” means “When this permanent is put into a graveyard from the battlefield, create N 1/1 white and black Spirit creature tokens with flying.”

From the wording on the Afterlife rules, you can see that under normal circumstances, when a creature with Afterlife 2 dies, only 1 ability would trigger and be put on the stack. That ability would cause 2 tokens to be created when it resolves.
Teysa Karlov makes this 1 ability trigger an additional time (triggering twice instead of once). So you get 2 separate instances of "create 2 tokens" on the stack, instead of the normal 1. You would choose the order that they are placed on the stack, though because they are identical to each other, the order is meaningless. Then each of them would resolve independently.

Thanks a lot! Could you also please add the ruling (of where I could find it) that supports your claim?

@Lainathiel There doesn't seem to be a specific ruling or comprehensive rule to point to here; it's more an issue of what a triggered ability is... I will edit to include the rules for that bit. But I would actaully recommend not accepting the answer just yet; others may come along with an even better response that includes a helpful rule I overlooked.

I think the important rule here is in fact 702.134a that you already quoted. It specifically says that Afterlife N is a single triggered ability that creates multiple spirits.


text:
What are the mechanical differences between Adapt and Monstrosity?
If we compare Incubation Druid with Ill-Tempered Cyclops, we see respectively:

Adapt 3. (If this creature has no +1/+1 counters on it, put three +1/+1 counters on it.)

Monstrosity 3. (If this creature isn't monstrous, put three +1/+1 counters on it and it becomes monstrous.)

Now I'm curious about the mechanical differences between the two abilities.
I can think of one difference: Monstrosity has more flexible prerequisites than Adapt: A non-monstrous creature could have other counters on it already (from a different source) and still become monstrous, while a non-adapted creature couldn't become adapted if it already has a counter on it.
Are there more mechanical differences between Adapt and Monstrosity?

Other than the one you mentioned, Monstrosity is actually less flexible in many circumstances; There are many cards that add -1/-1 counters which would cancel out with +1/+1 counters, removing both, such as Archfiend of Ifnir or Baleful Ammit, or otherwise use +1/+1 counters as a cost for abilities such as Bolrac-Clan Crusher. If a creature with Adapt loses all its +1/+1 counters it can Adapt again, whereas a creature with Monstrosity can not become non-monstrous again, so can only benefit from this ability once:

Once a creature becomes monstrous, it can’t become monstrous again. If the creature is already monstrous when the monstrosity ability resolves, nothing happens.
Monstrous isn’t an ability that a creature has. It’s just something true about that creature. If the creature stops being a creature or loses its abilities, it will continue to be monstrous.

In practice, there is little difference between Adapt on Monstrosity, but there are minor differences.
As you already pointed out, Monstrosity and counters are independent. You can make a creature monstrous even if it already has +1/+1 counters on it, whereas you can't adapt a creature that already has +1/+1 counters on it.
On the flip side, many monstrous creatures (such as Stormbreath Dragon) have a triggered ability that triggers when it becomes monstrous. Since an object can only become monstrous once, you can get that trigger at most once per object. Some adapt creatures (such as Growth-Chamber Guardian) have a triggered ability that triggers whenever +1/+1 counters are placed on it. This can happen any number of times: most commonly once through the adapt ability, but also through any other means of putting a +1/+1 counter on that creature.

I'd argue that the difference is actually pretty significant. I've abused proliferate and Sharktocrab to tap an opponent's entire board before, which you couldn't possibly do using Monstrosity. And being able to turn on an Incubation Druid without having to spend 5 mana is incredible.

@ArcanistLupus On the other hand, I remember playing a monogreen devotion deck that let me make 20 20/20 Hydra tokens by making Hydra Broodmaster go Monstrous, and it doesn't look like any of the Adapt creatures do anything close to that.