text:
What happens if The Grand Calcutron leaves the battlefield after players hand cards have already become programs?

When The Grand Calcutron enters the battlefield, each player's hand becomes a program (an ordered row of revealed cards).
Players can only play the first card of their program.
If a card would be put into a player's hand from anywhere, that player reveals it and places it anywhere within his or her program instead.
At the beginning of each player's end step, if that player's program has fewer then five cards, he or she draws cards equal to the difference.

Assuming The Grand Calcutron enters the battlefield, it's first ability triggers and eventually resolves, and later in the game, it leaves the battlefield again - what happens to the cards in a player's program? Where will cards be put from this moment forward that would be put in a player's hand? Are there any other special interactions?

Superseding my previous answer, and due to the lack of detail and accuracy in the post quoted by this answer, I decided to rewrite it and hopefully clarify the exact functionings of this card.
What is a program?
A "program" is not much more than a descriptor for a hand revealed with The Grand Calcutron. As stated by the release notes (a.k.a. Unstable FAQAWASLFAQPAFTIDAWABIAJTBT):

Your program is still your hand, [...]

So what happens when The Grand Calcutron leaves the battlefield?
The release notes further mention something that isn't reflected on the card itself:

[If The Grand Calcutron leaves the battlefield,] the players pick their cards up and put them back in their hand. They are no longer public and no longer have to follow the rules of The Grand Calcutron.

A lot of technical details and interactions past this one are rather ambiguous, but in general, everything that interacts with a hand interacts with programs as well, in the same manner.

What if The Grand Calcutron is destroyed in response to it's last ability?
The ability itself is independent of the source and will resolve as normal.
When Grand Calcutron was still on the battlefield, those cards would be put in the program and revealed in the process, but now they're just drawn as normal and won't be visible to the other players.
Are there any even weirder interactions? How should they be handled?
There are a few weird interactions that happen if you look at the exact ways the rules work, and the way The Grand Calcutron is templated. For example, if you counter the first ability, players won't have programs and therefore would be prevented from casting anything.
In that kind of situation, assuming this wasn't deliberately done because it fit one player's strategy, you should probably go with common sense over rules and ignore everything but Grand Calcutron's fourth ability. As suggested by doppelgreener:

With the Un-iverse intention that "The point of Unstable is to lean towards the fun side of the spectrum", the idea probably would be: if your hands don't actually become programs, then you just use your hand as normal. The abilities on [The Grand Calcutron] apply to how we use our programs, not how we use our hands.

As with everything else in Un-sets, it's probably best to solve problems like this within your playgroup.

Mark Rosewater, the Un-set rules manager, has answered this question directly:

What happens to a program without the Grand Calcutron? Does it returns to hand? Can I play cards from it? Do I still need to follow the order?
If The Grand Calcutron every leaves play, the cards in the program return to your hand.

I'm very curious about the release notes now, as nothing on TGC suggests that this is happening. Still, coming from MaRo, I suppose this is as official as it gets.

This answer makes no sense to me, despite coming from an official source. Rainbolt’s answer explains why.

Rosewater also said that "your hands are the program", so my interpretation is that the word "program" only actually means something while The Grand Calcutron is in play, and once it leaves, the effect generated by its ETB effect no longer means anything.

@murgatroid99: I'd guess it's just a poorly templated card that that wasn't thought about as in-depth as we now have and as a result have some weird rulings to deal with that don't make a lot of sense otherwise. In any case, this seems to be a reason to bring back R&D's Secret Lair, whichever answer below you may favor :D

This isn't errata though, it's a ruling. In any case, this set was in development for close to a decade; I'm sure they put a great deal of thought into the cards. They probably chose the wording that they thought best conveys the effect they wanted.

@GendoIkari I've seen Rosewater admit on camera that some of his fantastic ideas were shot down by the rules team, suggesting that he may not be the most intimately familiar with the rules. I think he does a good job ruling in the "spirit" of the card.

@murgatroid99 The wording that would be best though would be :
When The Grand Calcutron enters the battlefield, each player's hand becomes a program (an ordered row of revealed cards) until The Grand Calcutron leaves the battlefield. [Triggered with end trigger like Banishing Light]
OR
Each player's hand is a program (an ordered row of revealed cards) [Static]

I think you would need the triggered ability variant. because there are actions associated with the hand "becoming" a program, specifically that you choose the order, which you can't change later. Rosewater has also ruled that if another Grand Calcutron enters the battlefield, you get to choose the order of your program again.

When The Grand Calcutron leaves the battlefield, whatever cards you had in your hand at that exact moment remain a program until you play them, any new cards you draw will be hidden (like normal), and you are no longer obligated to play only the first card.
The continuous effect created by The Grand Calcutron's first triggered ability is independent of Calcutron itself (CR 112.7a). It also has no stated expiration date. Therefore, any cards you had in your hand remain revealed and ordered indefinitely. It doesn't matter much that they are ordered anymore (unless someone plays another Calcutron), but they are ordered nonetheless.

112.7a Once activated or triggered, an ability exists on the stack independently of its source. [...]

However, The Grand Calcutron's second ability is a static ability. Static abilities only apply while the object they are printed on remains on the battlefield.

112.3d Static abilities are written as statements. They’re simply true. Static abilities create continuous effects which are active while the permanent with the ability is on the battlefield and has the ability, or while the object with the ability is in the appropriate zone. [...]

Therefore, when Calcultron leaves the battlefield, you can play any card in your program (as opposed to only the first card). Any new cards you draw will not be revealed, because Calcutron's second ability isn't around to make them part of the program.
The third and fourth abilities won't trigger any longer, because they are triggered abilities.


text:
In a multiplayer game, if a player is controlling another player's turn, may they reveal that player's hand?
With cards like Mindslaver and Emrakul, the Promised End, a player can take control of another player's turn. The controlling player can make most decisions for the controlled player, but they may not, for example, concede the game for that player, or look at their sideboard. Mindslaver's Gatherer rulings even provide a very general explanation:

You can’t make any decisions that aren’t called for or allowed by the game rules, or by any cards, permanents, spells, abilities, and so on.

Now, since when controlling a player, you also gain access to their hidden information, such as their hand cards. In a two-player game, this usually means that until the end of the turn, one player has access to all hidden information in the game, since they see both their own as well as their opponent's information - in a multiplayer game, however, there will be other players not permitted to see this information.
All the Comprehensive Rules have to say about it seems to be:

402.3. A player may (...) look at [his or her hand] as much as he or she wishes. A player can’t look at the cards in another player’s hand but may count those cards at any time.

The Tournament Rules elaborate on a player being allowed to reveal hidden information available to them:

3.12 Hidden Information
(...) players may choose to reveal their hands or any other hidden information available to them, unless specifically prohibited by the rules. (...)

This is a dilemma, because even if the above-quoted Gatherer ruling prevented the controlling player to decide that the the controlled player reveals their hand, the controlling player themself has access to this hidden information, so they could always state exactly what was in that player's hand. The point of bluffing aside, this effectively is the same difference.
Now, the entire hidden information rule is part of the tournament rules, and while it's sensible to assume a player may just as well reveal their hand in a casual game, I do wonder if it's a difference in this example.
Questions

Is a player allowed to decide that the player they control reveals their hand?
In case they aren't, are they allowed to share the knowledge they themselves gained, therefore achieving about the same?
May the controlled player still decide to reveal their hidden information?

All of those questions would be interesting to hear about whether it makes a difference if played in a casual environment vs. in a sanctioned event, or in other words, whether the applicability of the Tournament Rules changes things (knowing that there aren't any actual multiplayer formats with more than two teams.
Concerns
These aren't really part of the question, but may help understand why I think it's a relevant question.
If the answer to either 1 or 2 is yes, that would make an effect like this surprisingly strong in multiplayer games, seeing as you're not only getting the already strong effect of taking over someone's turn, but you're also gaining a lot of diplomatic power from revealing certain cards, or not doing so.
Furthermore, if the answer to 1 is no, but to 2 is yes, this means a player may rightfully state that they're not allowed to reveal the cards, but could state what they can do. Since it's not forbidden to misrepresent hidden information, they could effectively bluff that any given card is in that player's hand.
Both of these points aren't game-breaking on their own, but are promoting to decide games not by skill or the contained amount of randomness in Magic, but instead by skill of diplomacy, deceit or other traits that aren't suited for tournament matches, and could spoil casual or social matches just as well.

I see revealing one's hand to be much like talking. Sure, it's allowed, but it's not a game decision.

The controlling player cannot reveal the controlled player's hand. Rule 718.5b says

The controller of another player can’t make choices or decisions for that player that aren’t called for by the rules or by any objects. The controller also can’t make any choices or decisions for the player that would be called for by the tournament rules.

Revealing your own hand in accordance with tournament rule 3.12 is a decision that would be called for by the tournament rules, so the controlling player is not allowed to make that decision. By that same logic, the controlled player would be allowed to make that decision.

I don't have a solid ruling for this part, but my interpretation is that the controlling player can verbally name the cards in the controlled player's hand. Revealing your hand is a game action that involves game objects, so it is covered by the game rules. However, there are very few rules about players' verbal communication, and there are none that govern statements that players make about hidden information. In other words, there is no rule against naming those cards, and there is no rule against lying about them.

I think "revealing" a card means more than just physically turning it around so the other players can see it. It's about giving out any kind of hidden information in whatever physical way, be it showing, naming the card, sign language, a drawing, or whatever else. It would be quite pointless to prohibit showing another player's hand card but allowing to name it or reveal it any other way. That's why the tournament rule 3.2 mentions revealing "information", which is as broad as it gets, rather than just (physical) cards.

According to rule 701.14a, revealing a card is exactly "physically turning it around so the other players can see it." It's a keyword action; it has a very specific meaning. And the important difference, as I see it, is that you can lie about cards you've seen, but you can't lie with a revealed card.

This is a surpisingly satisfying answer, can't belief I missed the quoted rule when searching for this myself (in fact, I had no idea whatsoever that there was a section about controlled players in the CR).

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text:
Will countering a spell that left the stack still trigger abilities?
Situation
I control Baral, Chief of Compliance, a sufficient amount of mana, and have Mystic Confluence in hand. My opponent casts Grizzly Bears, to which I cast Mystic Confluence in response, choosing the first mode three times, each targetting the Grizzly Bears.
Question
If my opponent chooses to pay for the effect all three times, obviously, the spell won't be countered and Baral won't trigger.
However, if they do pay no mana and therefore having the spell countered, how often will Baral trigger?
In other words, will an effect that attempts to counter a spell still counter it if the spell isn't on the stack to be countered anymore?
Rules Background
I looked at the following rules, trying to determine what would happen. First...

608. Resolving Spells and Abilities
608.2b. If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it was in when it was targeted is illegal. Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed or an effect may have changed the text of the spell. If the source of an ability has left the zone it was in, its last known information is used during this process. The spell or ability is countered if all its targets, for every instance of the word “target,” are now illegal. If the spell or ability is not countered, it will resolve normally. Illegal targets, if any, won’t be affected by parts of a resolving spell’s effect for which they’re illegal. Other parts of the effect for which those targets are not illegal may still affect them. If the spell or ability creates any continuous effects that affect game rules (see rule 613.10), those effects don’t apply to illegal targets. If part of the effect requires information about an illegal target, it fails to determine any such information. Any part of the effect that requires that information won’t happen.

Those rules clearly relate to determining whether the spell would resolve. Since in the example given, Mystic Confluence's targets are all legal, the spell isn't countered and will resolve normally, handling all three modes one after another, even though for the second and third time, the targetted spell will already be illegal and therefore the ability might do nothing.
To determine that, I looked at the keyword action's rules:

701.5. Counter
701.5a. To counter a spell or ability means to cancel it, removing it from the stack. It doesn’t resolve and none of its effects occur. A countered spell is put into its owner’s graveyard.

I noticed that there's no qualifier that states whether the countering will still occur, regardless of the spell still being legal - likely due to the fact that normally, a spell like Counterspell would be countered on resolution if that were to occur.
As a possibly noteworthy mention, other keyword abilities do have equivalents to such a qualifier, such as the rules about tapping an untapping stating that permanents that are already (un)tapped may not be (un)tapped again, clarifying whether abilities on cards like Reckless Racer would trigger.

Baral will trigger once. You cannot counter the same spell more than once.
As you already quoted the relevant rule 701.5a, countering a spell or ability means to remove it from the stack:

701.5. Counter
701.5a To counter a spell or ability means to cancel it, removing it from the stack. It doesn’t resolve and none of its effects occur. A countered spell is put into its owner’s graveyard.

Since spells can only exist on the stack, a countered spell will stop being a spell, and will no longer be a valid target for counter effects.

111.1. A spell is a card on the stack. As the first step of being cast (see rule 601, “Casting Spells”), the card becomes a spell and is moved to the top of the stack from the zone it was in, which is usually its owner’s hand. (See rule 405, “Stack.”) A spell remains on the stack as a spell until it resolves (see rule 608, “Resolving Spells and Abilities”), is countered (see rule 701.5), or otherwise leaves the stack. For more information, see section 6, “Spells, Abilities, and Effects.”

If you choose the counter option of Mystic Confluence three times, Mystic Confluence effectively reads:

Counter target spell unless its controller pays 3.
Counter target spell unless its controller pays 3.
Counter target spell unless its controller pays 3.

When Mystic Confluence resolves and the first ability already counters the targeted spell, that spell will immediately be removed from the stack and Baral will trigger. The second and third part of Mystic Confluence lack a valid target, and will not do anything.

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Can poison action card destroy Warbot?
In the Smash Up game, Ninjas have a poison action card. Will it have any effect on Warbot, who is a minion which cannot be destroyed?

Poison - Play on a minion. Destroy any number of actions on it. Ongoing: This minion has -4 power. (Minions have minimum power of 0.)
Warbot - power 4 - Ongoing: This minion cannot be destroyed.

No, it can't destroy Warbot, but that's because it can't destroy minions in general. It can only destroy actions attached to a minion, and Warbot doesn't prevent that.
Poison affects Warbot as any other minion because Warbot's ability has no effect on Poison's ability.

Poison doesn't destroy minions.
Warbot's ability doesn't prevent actions from being played.
Warbot's ability doesn't prevent actions attached to the Warbot from being destroyed.
Warbot's ability doesn't prevent the Warbot's power from being reduced.

The Poison card does not destroy Warbot.
The Poison card does not destroy any minion directly. Reducing a minions power to 0 does not destroy it.  It hangs around until an effect destroys it or the base that it is on scores.

In the Smash Up game, Ninjas have a poison action card. Will it have any effect on Warbot, who is a minion which cannot be destroyed?

Will it have any effect. Yes. The effect will be to reduce the power to 0. However poison doesn't destoy the minion merely reduces it's power. To the Warbot will be a minon of 0 power. While most of the time this is an academic point there are cards that are affected by minion prescence. For instance

Count how many minions you have on a base. Destroy a minion with that power less than or equal to that number.

In this instance, the Warbot though it does not give any power, would still count as a minion. Plus the poison action can be removed restoring the Warbot to full power or the Warbot can have other actions placed on it that increase it's power to again.


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Forester and Copse in Agricola
Looking at some links that show statistics of the most used occupations and minor improvements from winning players, I've noticed that the Forester and Copse do not rank nearly as high as I thought they wood (haha, "wood", get it).
When my friends and I play, if someone gets one of those two cards it seems that person wins quite often. The ability to not need to pick wood first and not being starved for wood appears quite powerful. Being able to expand rooms as well as building fences to get that first pool of sheep seems pretty powerful.
However, statistics from 2000 winning games seems hard to ignore. Do you think  the Forester and Copse as good as I feel they are? Perhaps our strategy is just sub-par?  :)
EDIT: Here is the link I was looking at. Follow the accepted answer's links.

To me, the benefits of these cards have always seemed limited for several reasons:

Initial outlay. You need to invest a number of wood into the card to begin with.
Delayed gratification. The first harvest after you sow the forester/copse, you simply get back your initial investment, therefore it is two harvests before you get any benefit at all. This is particularly negative when we are talking about wood, which is most useful early in the game.
Needing to sow. Sow spaces are often at a premium, particularly in games with 4/5 players. You aren't going to want to waste a whole action just to sow your copse, so it's only really valuable if you are going to be sowing grain anyway.

For these reasons, an occupation like the Wood Collector seems preferable. On the surface it might seem like a poor alternative, since the total amount of wood that you get is potentially less: 5 versus 12 if you were to use the Forester to its full potential. But compare them over time, if both were played as early as possible:

On round four, the Wood Collector is already up by 3 wood, whereas the Forester is DOWN by three wood.
On round six, the Wood Collector is up by 5 wood and the Forester is drawing even.
It's not till round 10 that the Forester is actually ahead by 1 wood over the Wood Collector (6 vs 5).
By round 14, the Forester has gained 9 wood compared to the WC's 5. There is an extra three to come, but it is only useful if you have the Joinery/Sawmill.

And that's all if the Forester is used perfectly. If you don't get the chance to sow before the first harvest (which requires having picked up three wood and used the "Sow/bake bread" spot) then your return is much poorer.

Being able to expand rooms as well as building fences to get that first pool of sheep seems pretty powerful.

From this, I wonder if you have misinterpreted the cards in some way. You should be taking one wood from the top of each stack during the field phase of each harvest and putting it into your supply. The wood on the card is not available for you to use to pay for anything until you have harvested it. For that reason, you don't get ANY benefit from the Forester/Copse until Round 8 at the earliest (the first harvest is just recouping your initial investment), so to use it to get the first pool of sheep seems implausible.

Interesting. I interpret from the card instructions that it behaves as a field where wood can be "sown" instead of grain. AND, 3 pieces of wood can be sown on it. So every harvest, a total of 9 wood is collected from the card for an initial investment of 3.  Is that not the official ruling?

Thank you for taking the time to write such a complete answer. And for reading between the lines to fix my understanding of the cards!

@Jeff.Clark - No problem! From your first comment, you were definitely misinterpreting the rules, but do I take it from your second comment that you now get what the mistake was?

Yep, have it figured out!  Just downloaded that rule compendium, it is pretty nice.


text:
Respected Citizen rewards
In Encounter 2 of the Respected Citizen quest of the Shadow of Nerekhall campaign the rewards include:

If Bertram is present during the quest and not defeated, during the next Shopping step of the Campaign Phase, the heroes reveal one additional Shop Item card per hero.
If Bertram is defeated, the overlord receives “The Scoundrel,” Corrupt Citizen card.

The setup for Encounter 2 includes:

If the heroes won Encounter 1, they place a villager token in an empty space adjacent to a hero figure. This is Bertram.

The heroes win Encounter 1 “if Bertram is knocked out”. Otherwise the overlord wins by moving him off the map.
Questions

Do the heroes get their Bertram reward if the overlord wins Encounter 1?
If the overlord wins Encounter 1, can ze not get zir Bertram reward?

Under the Victory section of Encounter 1 it reads:

If the overlord wins, he immediately receives “The Scoundrel” Corrupt Citizen card.

So the answer to the second question is no. If he won Encounter 1 he already has it.
The answer to the first question: they probably meant encounter rather than quest; otherwise your interpretation is correct and the “If” is redundant.

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text:
How does Unstable set's "The Grand Calcutron" work with cards that interact with a player's hand?
The upcoming Unstable set features a card called The Grand Calcutron:

A particular part of the card seems to make it so that players no longer have hands, along with changing how draws work.

When The Grand Calcutron enters the battlefield, each player's hand becomes a program (an ordered row of revealed cards).
Players can only play the first card of their program.
If a card would be put into a player's hand from anywhere, that player reveals it and places it anywhere within his or her program instead.
At the beginning of each player's end step, if that player's program has fewer then five cards, he or she draws cards equal to the difference.

The way that it is written it seems like players will no longer have a "hand". I am wondering how this card will change interactions with other cards that look at, or modify, player's hands in some way.
Specifically I am wondering about:

Discard effects, (eg: Duress, or Thoughtseize)
Effects that modify a player's handsize (eg. Locust Miser)
Effects that ask you to make selections from someones hand (eg. Agonizing Memories)
Effects that try to count how many cards a player has in their hand (eg. Adamaro, First to Desire)

Note: As this is a card from an Unset, Official Rulings from Mark Rosewater would be word of God, failing that well reasoned answers that draw on existing card rulings or game rules are perfectly acceptable.

The program is your hand, and effects that affect or care about the contents of your hand affect or care about the program while The Grand Calcutron is on the battlefield.
Mark Rosewater answered this question specifically regarding discarding as follows:

What happens if an effect forces you to discard a card while The Grand Calcutron is in play? Do you discard from your program?
You discard a card from the program. With Grand Calcutron on the battlefield, your hands are the program so things that affect your hand affect the program.

Presumably, "things that affect your hand" includes the rule instructing you to discard to hand size in the cleanup step, so an effect that modifies your maximum hand size would affect the program the same way they would affect a regular hand.
Similarly, an effect that requires selecting a card from a hand would have you select from the program instead, and anything that wants to count the cards in the hand would count the cards in the program.

This answer has since been refuted by a statement from the Un-set rules manager.
I'm pretty sure this works by introducing a new "Program" zone (or exiles those cards with special rules attached to it, similar to how Imprint works), which in no way other than functionally replaces the Hand zone, or even gets rid of it. Players will still have hands, but The Grand Calcutron will prevent any cards from being put there from anywhere with its third ability. After all, if players didn't have Hand zones anymore, nothing could be put there in the first place, meaning that ability would never have anything to replace.
From there, the answers to your questions are rather straightforward:

Discard effects, unless explicitly stating otherwise, make players discard cards from their hand. Just like any other time when a player's hand is empty, they will simply do nothing.
Hand size doesn't matter for the "Program" zone, and unless some other card was already modifying hand sizes, even with The Grand Calcutron in play, a player's hand size would be their starting hand size. The Grand Calcutron itself doesn't modify hand size.
Just like discarding, selecting a card from a player with no cards in hand will simply do nothing.
With The Grand Calcutron in play, Adamaro, First to Desire would be a 0/0 creature by itself, because the highest amount of hand cards would necessarily be 0.

This was my take on how the card would work as well. I think it is a pretty reasonable way to handle it and will probably be how I will play it, barring any conflicting ruling from Mark Rosewater.

@Malco Well we're still waiting on rulings for these cards in general, which we'll get near their release.

@doppelgreener I have been keeping an eye on blogatog, one ruling is kind of concerning to me but is unrelated to calcutron... but I will swap over to chat now

So, brainstorm, becomes ancestral recall with Calcutron in play...


text:
More four-player Quoridor shenanigans
As a followup to this question, what happens in the following two scenarios? In each, the turn order is Green -> Red -> Blue -> Yellow, and no pictured player has any fences left.
1) Is Red allowed to play the purple fence? If so, what happens over the next two moves?

2) Is Red allowed to move their pawn downward? If so, what happens over the next two moves?

In both scenarios, it seems like if you allow the move in question, Blue is forced to move downward as the next move, and then Yellow has no legal moves. The options I see are:

Escape both scenarios through increasingly tortured readings of the existing rules. For example, in scenario 1 say that the fence placement is somehow banned by the fences-can't-completely-block-people rule (even though in a different turn order it would be ok), and in scenario 2 say that Red and Blue can move down and then Yellow can somehow use the diagonal jump rule to move to Red's former location (even though that rule only applies if there's a fence in the way, not a player).
Accept that the current rules aren't quite sufficient and change them. My vote would be for "In the rare event that a player has no legal move, their turn is skipped."

My design principle behind my objection to banning either of Red's moves: finding all good moves should be hard, but finding all legal moves should be easy. You shouldn't have to look multiple turns in advance to figure out your move is illegal.

It’s another interesting problems that you submit here
For the First one,
you're right, in this situation yellow must skip his turn, the rules with all the differents explanations implied that.
For the second case,
It’s quite easy when you refers to the rules and it’s not a tortured reading of the rules you just have to follow the legal move in the Fig 10 (fig who show the legal move in a case of a jump with two pawn in front of you )
Yellow can escape in jumping in the upper square of the red pawn.

I'm happy to accept both parts of this answer as Word of God rulings, but I do think they're missing from the printed rules. For part 1, the rules imply that yellow has no legal moves, but then don't say what to do about it - skipping their turn is quite reasonable, but many other games resolve it differently e.g. by declaring the game a draw. For part 2, you mention the "legal move in Fig 10", but Fig 10 shows just one illegal move and no legal ones at all? Has this been changed since the Oct '03 rulebook we've been looking at?

Is Red allowed to play the purple fence?

Yes. There's still a path from each player to their goal.

If so, what happens over the next two moves?

Blue moves down, then you get into a situation where Yellow has no legal moves, so the game can't legally proceed. This question is a duplicate of an earlier question.

Is Red allowed to move their pawn downward?

Yes. It's one square away along an orthogonal axis, it's unoccupied, and there are no intervening boards.

If so, what happens over the next two moves?

After Red moves down, Blue must move down, and then Yellow must take over Red's current location. Fig 8 of these rules[1].

While it's not explicitly stated in the rules that a jump blocked by the borders of the board or by other pawns allows one to take a diagonal jump, this seems obvious like an obvious omission.


text:
How does casting a Storm spell on Zada, Hedron Grinder work?
Related Question: How does each copy of a spell cast to Zada, Hedron Grinder count towards Storm abilities?
If I cast a storm spell that targets only Zada, Hedron Grinder (like Astral Steel) then I will have a copy of it for each of my creatures. However, If spells had already been cast this turn, then I will have more than one copy of the Storm Spell, a nd I could have each copy target Zada. Would the additional copies of the storm spell also trigger Zada's ability, thus giving me more than one copy of the spell per creature?

Zada only makes copies of the original Storm spell, not the copies that it makes.
Zada has the text

Whenever you cast an instant or sorcery spell that targets only Zada, Hedron Grinder, copy that spell for each other creature you control that the spell could target. Each copy targets a different one of those creatures.

And the definition of Storm says

Storm is a triggered ability that functions on the stack. “Storm” means “When you cast this spell, put a copy of it onto the stack for each other spell that was cast before it this turn. If the spell has any targets, you may choose new targets for any of the copies.”

The copies of the spell that storm creates are put onto the stack, not cast, so Zada's ability does not trigger when that happens. So, Zada only makes copies of the original spell that you cast.


text:
Village/Smithy strategy
I am very newbie to Dominion. Looking at
Smithy Village strategy
which has the following buying script

$8 or more to spend: Province (if you have 5 or more Smithies)
$5: Duchy (if there are 3 or less Provinces left)
$2: Estate (if there are 2 or less Provinces left)
$6: Gold (max 2)
$5: Market (max 5)
$4: Remodel (1), otherwise Militia (1), otherwise Village (if you have
less Villages than terminal actions), otherwise Smithy
$3: Village $2: Cellar (max 2)

what does it mean if you have 5 or more Smithies? Does it mean 5 Smithies in my discard pile?).
Similarly when it says if there are 3/2 or less Provinces left are these in the supply pile? And max 2 or max 5 means 2/5 in the discard pile?
And if you have less Villages than terminal actions  means in the discard pile?
Finally this is a buy strategy. What should the strategy be as far as which actions to play?

"If you have 5 or more Smithies" means if you have 5 total Smithies in your deck (your deck being all cards you have; between your draw pile, discard pile, hand, in play, etc).
"If there are 3 or less Provinces left" means that the rule will only be followed when the Province pile is down to 0, 1, 2, or 3 Provinces. If there are still 4 or more Provinces in the Province pile, Duchies will not be bought.
Max 2 is like the first question; it means that once 2 Cellars have been bought total, no more will be bought.
The strategy for which actions to play is in this case programmed into the simulator. For the most part, it is trivial, though there are sometimes tricky decisions to make. For example, if you have some actions that give +1 action when played, and others that don't, you play the ones that give +1 action first. (If you play Smithy first, you can't play any other actions). If you have Market and Village, the order is irrelevant.
Occasionally, you would have to decide between playing a Smithy, a Militia, and a Remodel. Which is the best play would depend on a lot of factors including how late in the game it is, what else is in your hand, what is left in your draw pile, etc.
The simulator has a list of cards programmed that are considered "junk" cards that will be discarded when Cellar is played. I believe these include any victory cards, as well as Curses and Coppers. This is because any cards you draw in place of those will, on average, be better to have.
Welcome to Dominion!


text:
Thorncaster Sliver and Venom Sliver vs. Priority or Lack Thereof
I have been gone from MtG for some time now and recently played a couple games with some of my old friends. Midgame the same thing happened that always happens when I play with that group. A fight.
Long story short, it happened like this:
My opponent had a Thorncaster Sliver, Venom Sliver as well as several other slivers out; while I currently had a Master Transmuter, several artifact creatures out and a Ethersworn Shieldmage in my hand.
My opponent declared their attack step and then proceeded to deal damage to my Master Transmuter. In response I played my Ethersworn Shieldmage, he then dealt damage to that with another creature and then damaged my Master Transmuter again with another one of his attacking slivers. I tried explaining to him that although I messed up and played my response a little too early, he could not damage something and kill it before I responded to the damage.
Eventually after fighting for a couple minutes, I just gave in and had him kill all my creatures, and gave him the game.
He has been hounding me now for weeks about the actions and still telling me I am wrong. Looking for some answers to prove my point to him, I decided to research a previous inquiry here:
Do Thorncaster Sliver's triggered abilities go on the stack?
However it did not provide all of the information I needed.
Now here is the real question (again been away from MtG for a while, so I might be wrong), am I right or wrong in the following train of thought. Using the previous thread as an example, however inserting our previously stated creatures into the equation.

As in the example let's say he attacks with 5 slivers, one being a Thorncaster Sliver and a Venom Sliver.
Using the previous thread as an example he moves straight to step 3, while skipping over step 2. Basically trying to resolve damage before he declared all of it. I tried to tell him that all of his creatures attack at the same time, thus he would have to declare the damage at the same time BEFORE he can pass me priority (during the game I kind messed this up by playing my Shieldmage when he first applied the damage and waited for my response). Is this correct?
That being said the damage that he declares cannot be resolved UNTIL I have priority, correct? Meaning that he would have to pass me priority after he declares all of who he wants to damage, but before it is applied or that (if in the case he does not pass priority) the damage carries over until the declare blockers step (CR 112.3c) when I would have priority, correct?
As I said during the game I kind messed things up by playing my Shieldmage when he first applied the damage and waited for my response; however his ability still goes onto the stack and he cannot damage it or other creatures until he resolves, correct? Meaning that any creature damaged before he comes into play would be destroyed via Venom Sliver's Deathtouch ability, however after he comes into play all creatures I had in play would not receive damaged. So technically it doesn't matter when I play him because once he resolves it nullifies anything before he was on the stack and after (especially if I played him during the example thread's step 2, like I was trying to do), because the damage would have to resolve and he can't be dealt damage before he comes into play.

That being said, am I right or wrong in this? I'm trying to understand "Priority" and how it would relate to the above scenario. I believe that I'm right, but I could be just as wrong in this...

Isn't this really a duplicate of: https://boardgames.stackexchange.com/questions/12652/in-plain-english-how-does-casting-spells-and-using-creature-abilities-work-with ?

The simple answer is that your opponent cannot use any of the abilities from Thorncaster Sliver to deal damage to Ethersworn Shieldmage, and Ethersworn Shieldmage can protect all of your artifact creatures from all of the damage.
This is the exact sequence of events for how your example should play out:

Your opponent declares 5 Slivers as attackers, with both Thorncaster Sliver and Venom Sliver on the battlefield.
For each attacking Sliver, your opponent puts their triggered ability from Thorncaster Sliver on the stack. This is part 508.2 of the Declare Attackers step. At this time, your opponent declares which creature each ability is targeting (see rule 603.3d and rule 601.2c).
Your opponent gains priority (rule 508.3). From how you described your example, they choose to do nothing and pass priority.
You gain priority. At this time, you cast Ethersworn Shieldmage.
You gain priority again, but you have nothing else to do here so you pass priority.
Your opponent gains priority. They have an opportunity to act here, but they can't do anything with the abilities from Thorncaster Sliver, because those are already on the stack. Once you do nothing and pass priority, Ethersworn Shieldmage resolves and enters the battlefield. At this time, the Shieldmage's ability triggers, and goes on the stack.
Your opponent has another chance to act, but they still can't do anything with the abilities from Thorncaster Sliver. They pass priority, and so do you.
Ethersworn Shieldmage's ability resolves. For the rest of the turn, any damage that would be dealt to any artifact creature is prevented.
The abilities from Thorncaster Sliver resolve. All of the damage that they would do to artifact creatures is prevented.

Your opponent did one major thing incorrectly: they tried to deal damage to the Master Transmuter in response to you casting Ethersworn Shieldmage. You didn't have an opportunity to cast Ethersworn Shieldmage until after all of those abilities were on the stack, so there is nothing they could have done to make one of those ablities resolve before Ethersworn Shieldmage.
However, since you revealed the Ethersworn Shieldmage out of turn, it would have been reasonable for your opponent to choose non-artifact creatures as the targets for any abilities that they had not yet declared targets for.

Thank you! Yeah, what he was trying to do was declare damage and resolve it at a one for one basis (effectively skipping steps 2-7 in your example) trying to kill my creatures one at a time without actually declaring all of his targets.

Actually, the order of steps 5 and 6 is somewhat reversed. After casting a spell, the spell's controller gains priority again, see rule 601.2i. This might be a rules change since 2016 though, I don't know much about previous rules.

You're right, I had those switched. I've corrected the answer.

As I think you noted, your play itself was in fact invalid - but you're correct in the general thrust of your argument.  The keys are that the ability granted to slivers by Thorncaster Sliver is a triggered ability, and that all attackers must be declared at once.  This is how things should have gone:
1) Your opponent declares the slivers that they're attacking with as the very first thing in the Declare Attackers step during combat.  This action doesn't use the stack, and it can't be responded to - they just indicate what creatures they're attacking with.
2) Abilities triggered by the attack declaration go on the stack - in particular, the triggered abilities of your opponent's slivers go on the stack here.  Your opponent can choose what order to put those abilities on the stack in, but he must choose targets for all the abilities as he puts them on the stack.  Note that all of this happens before either of you are allowed to play spells or abilities.
3) Once all of the triggered abilities have been put on the stack, your opponent gets an opportunity to put any other spells or abilities on the stack; after he passes, you're allowed to put any spells or abilities (for instance, Master Transmuter's ability) onto the stack.
4) Once both of you have put on the stack whatever spells or abilities you wish, you start to resolve the stack.  (After each item on the stack 'pops' you both have the opportunity to put additional spells or abilities, but that's mostly moot here.)  Damage from the triggered abilities won't happen until those triggered abilities are resolved here during the popping of the stack.
The key rules to understand here are rule 405 (governing how the stack works) and rule 508 (which explains the declare attackers step; 508.1 and 508.2 are about declaring attackers themselves and triggering all relevant abilities).

Thank you! Ok. So from what I gather, what I'm trying to tell him is correct. He can distribute all the damage in the world to anything he wants, but until I have priority (whether he gives it to me or I receive it during the declare blockers step), the damage cannot resolve? And since they are all attacking at the same time I cannot have priority BEFORE he distributes (but before it resolves) all of the triggered damage.

That's basically so, except that he's not 'distributing' damage; he's just choosing targets for his abilities.  The damage will be dealt as part of the resolution of those abilities.  (Distributing damage used to be used for combat damage - and note that this isn't combat damage! - and is used to describe spells like Rolling Thunder or Arc Lightning where one source is dealing damage to several targets, which also isn't the case here.)

Ok. Thank you. Yeah, maybe my old school (or learned through card shops) language is confusing him (and rightfully so) a bit. I have the basic premise down and how it's supposed to proceed, just not the right words (triggered ability instead of damage, distributing damage instead of declaring targets, ect) for it. =)

My opponent declared their attack step and then proceeded to deal
  damage to my Master Transmuter. In response I played my Ethersworn
  Shieldmage, he then dealt damage to that with another creature and
  then damaged my Master Transmuter again with another one of his
  attacking slivers. I tried explaining to him that although I messed up
  and played my response a little too early, he could not damage
  something and kill it before I responded to the damage.

Yes that is not how it works. You declare all your attackers at the same time. Then your opponent would have a trigger to ping for a damage for each attacking sliver.
He then has plenty of triggers that triggered at the same time. He can then choose targets one at a time. Afterwards you then get a chance to respond with your shieldmate.

Basically trying to resolve damage before he declared all of it. I
  tried to tell him that all of his creatures attack at the same time,
  thus he would have to declare the damage at the same time BEFORE he
  can pass me priority.

Mana abilities are the only abilities that don't use the stack. All these types of triggered abilities use the stack. Also an object on the stack cannot resolve unless the two players has passed priority consecutively.
You will always get a chance to respond to these types of triggered abilities and as you rightly allude all attackers are declared at the same time. He would have to choose targets for them all before he can pass priority.


text:
How to calculate the probability to get all cards of Exodia, the Forbidden One by drawing them from my Deck during the Draw phase?
In Yu-Gi-Oh!, there are some cards that allow to the duelist to win a duel automatically.
In this case, I'm focusing my question on Exodia, The Forbidden One. To win a duel using Exodia, you must have the five cards (parts of Exodia) in your hand.
These cards are (in no particular order):

Right Leg of the Forbidden One
Left Leg of the Forbidden One
Right Arm of the Forbidden One
Left Arm of the Forbidden One
Exodia The Forbidden One

I'm wondering:
How to calculate the probability to get all cards of Exodia The Forbidden One based on:

Parts of Exodia taken from the Deck during each Draw Phase with no additional card effects.

A Yu-Gi-Oh! deck has:

40 cards in total (35 monster, spell, trap cards and 5 Exodia cards).
There are only five Exodia cards (no copies).
Draw one card per turn.

I posted a question on meta about this subject.
The accepted answer should have a format similar to any of the linked answers.
I'm looking for a detailed answer that explains how to make those calculations and the obtained results as shown in this answer.

The above picture reflects the probability of drawing the full set of Exodia, dependent on the number of cards drawn overall. For example, there is a 0.000152% chance the player will draw Exodia in their opening hand, and a 87.5% chance they will draw it after seeing 39 cards out of their 40 card deck. If all 40 cards are drawn, there is a 100% chance the 5 Exodia cards will be drawn.
The Statistical Theory presented in the Question is best reflected as a Hypergeometric Distribution. Applied to this problem, the variables in questions are:
Variables
N = number of items in the population = number of cards in the deck = 40
k: The number of items in the population that are classified as successes. = number of Exodia Cards in the deck = 5
n: The number of items in the  sample = Variable through experimentation
x: The number of items in the sample that are classified as successes. = Number of Exodia Cards that must be drawn = 5
Narrative
There are 5 Exodia cards (k) in a deck of 40 cards (N). If the player draws all 5 Cards (x), the player wins the game. The interest of the Question is the probability of drawing all 5 cards via only the Draw Phase. The player will see five cards in the initial hand, and an additional card per turn from the draw phase, negating any external effects. From that, over the course of the game, the player will see 5 + number of turns cards in the game (x).
Equation
h(x; N, n, k) = [ kCx ] [ N-kCn-x ] / [ NCn ]
where [aCb] = a(a - 1)(a - 2) ... (a - b + 1)/b! = a! / b!(a - b)!
By applying the Known Variables above, the player can learn the probability they will draw the complete Exodia Set, dependent on how many cards they draw overall. In this, n ranges from 5 to 40.
Since doing a tedious calculation 36 times is tiresome, computational power is a treat. The Combination formula, [aCb], is available in Microsoft Excel. Setting up a worksheet, using the equations as in this chart:

Will support the evaluation of each step in the card drawing process, providing the resultant probability:


text:
What are the probabilities of getting any or all five cards of Exodia using a specified monster card effect
In Yu-Gi-Oh!, there exists a monster effect card called Morphing Jar, which has the following effect:

FLIP: Both players discard their entire hands, then draw 5 cards.

There are more (magic/trap/monster effect) cards that allow the duelist/player to draw a defined number of cards.
As an extension of my previous question, I'm looking for the probabilities of getting any or all five cards of Exodia using the quoted effect above.

the probability is 0 as morphing jar is banned

This questions is substantially different from the first version. Given the mechanics of Exodia, each of the five parts must be collected in hand. To support that, 0 Exodia cards can be drawn prior to the use of Morphing Jar. In this, the situation is similar to the linked question with the emphasized difference.
Variables
N = number of items in the population = number of cards in the deck = 40
k: The number of items in the population that are classified as successes. = number of Exodia Cards in the deck = 5
n: The number of items in the sample = Variable through experimentation
x: The number of items in the sample that are classified as successes. = Number of Exodia Cards that must be drawn = 0
Narrative
There are 5 Exodia cards (k) in a deck of 40 cards (N). If the player draws all 5 Cards (x), the player wins the game. The interest of the Question is the probability of drawing all 5 cards After using Morphing Jar and with subsequent draw Phases. The player will see five cards in the initial hand, and an additional card per turn from the draw phase, negating any external effects. From that, over the course of the game, the player will see 5 + number of turns cards in the game (x). 0 Exodia cards can be present in those x cards, because Morphing Jar forces the hand to be discarded.

Per the image, the chances of drawing zero Exodia cards decays the longer the games go on. When the player uses Morphing Jar, assuming he or she has drawn zero Exodia cards, he or she has a chance to draw zero to five Exodia cards with the effect. While the math is similar to the linked question, each is a distinct case.
Equation and Additional Variables
d = the number of cards drawn so far = range (6, 35)
x = the number of Exodia cards drawn with Morphing Jar = range (0, 5)
n = the number of cards drawn by Morphing Jar = 5
h(x; N, n, k) = [ kCx ] [ (N-d)-kCn-x ] / [ (N-d)Cn ]
where [aCb] = a(a - 1)(a - 2) ... (a - b + 1)/b! = a! / b!(a - b)!
Again, these individual cases can be evaluated with Excel, to minimize the tedious nature of each combinatoric equation.

These images portray the probability the player will draw, zero through five, Exodia cards upon playing Morphing Jar, dependent on how many cards he or she has seen previously. The first graphs the data, the second is the raw data. The sum of the probabilities for each case, for any number of cards previously seen, is 100%.
The Rest of the Set
After playing Morphing Jar, the process for determining the probability for drawing the Exodia cards not seen is the same as described in the linked question.
d = number of cards drawn so far = range (6, 40)
e = number of Exodia cards in hand = range (0, 5)
N = number of items in the population = number of  cards remaining in the deck = 40  - d
k: The number of items in the population that are classified as successes. = number of Exodia Cards in the deck = 5  - e
n: The number of items in the sample = Variable through experimentation = range (1, N)
x: The number of items in the sample that are classified as successes. = Number of Exodia Cards that must be drawn = 5 - e
h(x; N, n, k) = [ kCx ] [ (N-d)-kCn-x ] / [ (N-d)Cn ]
where [aCb] = a(a - 1)(a - 2) ... (a - b + 1)/b! = a! / b!(a - b)!


text:
Why do cards from Alpha have to be in opaque sleeves?
In this answer the tournament rules are quoted:

3.3 Authorized Cards
[...]
Players may use cards from the Alpha printing only if the deck is in opaque sleeves.

Why is this? As far as I remember there was an idea of having different card backs for each edition/expansion, but it was decided later to have the only one card back, which makes all cards compatible.
What makes cards from Alpha different so that they could be recognized without an opaque sleeve?

Related: http://boardgames.stackexchange.com/questions/5120/how-can-i-tell-the-difference-between-early-magic-the-gathering-card-editions (talks about differences between all early sets without set symbols; the answer specifically for alpha is buried in there)

Since the corners of alpha cards are distinctly different from the other editions of magic cards, it would be equivalent to playing with a marked deck, since presumably all your cards won't be alpha.


text:
How important is game theory in Dominion?
A lot of the strategic advice I've read for Dominion seems to be based around honing your deck based on fixed criteria - which cards are good, which work well together, when to start buying Provinces, etc.
But Dominion is a multi-player game, and clearly you are affected by the decisions that your opponent(s) make. Are they going for lots of attack cards, a "big money"-type strategy, or focusing on one particular action card? Are they ahead of you on points at a given moment?
My question is: how much is it important to consider the actions of your opponent(s)? Are "good strategies" always fairly good, and just need tweaking on the basis of what your opponent(s) do? Or is there a lot of game theory involved, such that your decisions depend almost entirely on what others are doing?
Advice in the question What are good standard tactics for Dominion? has only one answer of a few lines that addresses what your opponent(s) are doing. Surely there is more to it than that?

A lot of the strategic advice I've read focuses on 1 vs 1 games.

One of the clearest examples of game theory in Dominion shows up quite frequently in 2 player endgames, and it's called the Penultimate Province Rule (PPR). Basically, you should avoid buying the second to last Province if buying the remaining Province would allow your opponent to win.
Imagine a game where my opponent and I each have 3 Provinces, with 2 left in the supply. My opponent also has 4 Estates, while I only have 3. If I buy the penultimate Province, my opponent will probably buy the last one on his turn and win by a point (27-28). Instead of doing that, it's better for me to buy a Duchy (even with $8 or more). Now my opponent is in the same situation I was just in - if he buys a Province, I can get the last one on my turn and win (30-28). So his best option is to get a Duchy as well. We'll both continue to avoid the second-to-last Province, doing a "Duchy dance" until somebody's deck falls apart from the extra green cards or the Duchies run out.
In this example, knowing what your opponent is likely to do, and is capable of doing, is extremely important. Sometimes it's necessary to break PPR and hope that your opponent isn't able to snag the last Province, and it's good if you can time it so that this is more likely - perhaps you were able to attack, or maybe the opponent just had to shuffle at an inopportune time, or maybe he just missed putting his Alchemists on top. If you have to break PPR, it's best to keep an eye on what your opponent is doing so you can find the best time to strike.

Some cards are very dependent on the actions your opponents, and some are not.
e.g. buy Tribute if you see your opponent to the left buy lots of different cards, don't buy it if they are not.
However, in most cases, if  your strategy can be influenced by opponents actions, then it is best to proactively consider those potential influences even before they are made. You cannot quickly change strategies in dominion; once you commit to one, your course is mostly set.
Embargo is an example: when your opponent starts to pursue a strategy that requires many cards of a particular type, e.g, Conspirators or Cultists, then you can buy embargo to stop them from acquiring those cards.
Conversely, if your opponent would be able to disrupt your strategy with an embargo, it is probably a bad idea to pursue that strategy in the first place.
Or take Young Witch: if your opponent buys lots of bane cards, you probably do not want to buy young witches, and if your opponent buys lots of young witches, you want to buy bane cards.
But if the bane is a card that your opponent can easily buy without disrupting their flow, then buying young witches is a bad idea even before your opponent starts reacting to it.
Or take Possession: If your opponent buys possession, you definitely do not want to buy any Masquerades or Ambassadors, and need to get rid of your existing ones as soon as possible, because if they possess you while you hold one of these in your hand, they can steal your provinces.
But if you see that Possession is on the board, you may want to hold of on buying those Masquerades and Ambassadors in the first place. (Thought  Ambassador and Masquerade are both very strong opening cards, so you may still want some anyway).
The point is, an optimal strategy has to consider all the potential actions of your opponent, so it will most likely only need minor tweaking based on what your opponent actually does.
There are lots of specific counters that work well against a particular card: Jack of all Trades vs Ghost Ship, Minion vs Alchemist, Monument vs Possession. But in most cases, if a card can easily be countered, you should not buy it in the first place. So if everyone plays at a high level and avoids mistakes, there is little need to react to your opponents actions after they make them.

Some general guidelines:
If you see your opponents going for a strategy that will get them a lot of points, but will take a lot of time, you are best served in pursuing a strategy that nets less points over time, but can end the game sooner.
I.e. if they ramp up their engine to buy all the provinces in a single turn with a mass bridge combo, buy some provinces and try to end the game on three empty piles.
If you see your opponents in a 4+ player game buying lots of attack cards, focus on buying cards that help you instead of hindering others, since your opponents will take care of attacking each other for you. When three other players distribute curses, you will only get slightly more curses than the other players if you refrain from distributing curses yourself.


text:
In Agricola, why are Minor Improvements not separated by number of players whereas Occupations are?
In Agricola, Occupations cards are each marked with 1+, 3+ or 4+, indicating the number of players for which they are valid. For example, you cannot be dealt a 3+ or 4+ card in a two-player game. With a few exceptions (such as those that refer to the "Travelling players" space) the 3+/4+ cards would be playable, and potentially useful, in any game, but presumably they are restricted for purposes of balance.
Why do the Minor Improvements not follow the same system? There are a number of cards where their behaviour changes directly in response to number of players, especially in the I deck (e.g. Slaughter-house, Milking shed, Punner). Others don't directly refer to other players but still change in their utility, for example because of different availability of certain actions (e.g. Bake bread; see also here).
Intuitively, in designing the game I feel it would have made sense to have the same system for both Minor Improvements and Occupations: either decide that both should be available in all games, and accept that some will be more useful than others for a given number of players, or categorise them both in order to fine-tune the balance.
Is there any reason that they follow two different systems?

Yikes, that is a good question. I've been looking at the cards for a while and trying to think about them abstractly, but not coming up with anything at the moment. My first thought was that most of the Minor Improvements deal with directly gaining resources while the Occupations kind of change play style, but that doesn't seem to hold true in all cases.

The purpose of the marking is to help the players to remove the cards from the deck before playing which do not fit the player count.
Specifically, many of the occupations refer to spaces on the board that are not present in lower player counts, such as "Travelling Players", which is only present with 4 or more players, and thus all of its associated occupations are only relevant with 4 or more players.  The Occupation cards are marked based on number of players so that you can remove the ones that are not valid for your player count.
However, Minor Improvements are valid at all player counts, so you do not need to go through and remove any of them.
Uwe Rosenberg could have designed the Minor Improvements such that you removed some of them at lower player counts (in which case those would be marked), but he did not choose to do so.

This seems kind of circular. They're not marked, so they have to be valid in terms of rules (or the game would be broken), and from that you conclude they don't need to marked. And sure, they're valid, they make sense within the rules. But they don't seem to be balanced exactly the same for all numbers of players, so it'd be sane to limit them. Conversely, many of the occupations restricted to higher numbers of players would work as written, so they're clearly restricted for balance/gameplay reasons.

Or if you meant to be saying that the minor improvements make perfect sense for gameplay at all numbers of players, while the occupations don't... well, the question is why.

I tried to clarify my answer.  The main reason why some occupations do not make sense for all player counts is that they activate based on spaces on the board that do not exist in those player counts.  This does not happen with Minor Improvements.

Hm, that's true of some occupations, but there are a ton of more-players-only ones that do not depend on spaces on the board. You can read through a list here - just from a quick glance, the first three all are marked for player number, and don't use anything that isn't always there. As the OP pointed out, it seems to be more about things that work better or differently with more players, and that is true of many minor improvements as well. Maybe it's more common in occupations, though?

Its true for more occupations.  But maybe the answer is just "Because thats the was Uwe Rosenberg designed it"


text:
Can I use Lucky Cigarette Case to avoid activating Dark Pact?
Can I use Lucky Cigarette Case to increase a fail roll 1 on 2 and thus avoid activating dark pact condition?

(2) Lucky Cigarette Case
Trinket
Once per round, you may add 1 to the result of 1 die when resolving a test.

No.
Its effect only applies to tests (where you test one of your Investigator's five skills).
It does not apply to checks like the Dark Pact condition has (or any other check where you roll a dice without reference to a specific skill).


text:
Delayed effects after player's loss
I would like to know what happens to delayed abilities, or abilities like "until your next turn" when the controller of that spell/ability loses and leaves the game.
For instance, suppose you cast Cruel Entertainment, and then the first controlled player kills you, the second player still will get controled by the first one?
Also the first ability from Liliana, the last hope, which says "+1: Up to one target creature gets -2/-1 until your next turn", will the affected creature restore its power/thoughtness immediatelly after the Liliana controller dies?
Also note this excerpt from this answer:

A delayed triggered ability (DTA) follows the same rules. A DTA is a
  triggered ability that creates instances of itself on the stack that
  are also called "triggered abilities".

Is the effect from Cruel Entertainment a delayed ability, or is it just a effect whose effect spans more than the current turn?

Cruel Entertainmet's effect will still work in full as long as the two targeted players are in the game, whether or not the player who cast the spell is still in the game. And Liliana's ability will last until her controller's next turn would have started.
The following rules about Multiplayer games are relevant:

800.4a When a player leaves the game, all objects (see rule 109) owned by that player leave the game and any effects which give that player control of any objects or players end. Then, if that player controlled any objects on the stack not represented by cards, those objects cease to exist. Then, if there are any objects still controlled by that player, those objects are exiled. This is not a state-based action. It happens as soon as the player leaves the game. If the player who left the game had priority at the time he or she left, priority passes to the next player in turn order who’s still in the game.

800.4b If an object would change to the control of a player who has left the game, it doesn’t. If a token would be created under the control of a player who has left the game, no token is created. If an object would be put onto the battlefield or onto the stack under the control of a player who has left the game, that object remains in its current zone. If a player would be controlled by a player who has left the game, he or she isn’t.

800.4j When a player leaves the game, any continuous effects with durations that last until that player’s next turn or until a specific point in that turn will last until that turn would have begun. They neither expire immediately nor last indefinitely.

"Objects" in 800.4a refers specifically to the things defined in rule 109.1:

An object is an ability on the stack, a card, a copy of a card, a token, a spell, a permanent, or an emblem.

Importantly, this does not include effects that were created by spells or abilities, and rule 800.4j explicitly points out that effects created by a player stick around after that player leaves the game. So if a player casts Cruel Entertainment and then leaves the game, the effect will still exist in the game.

Therefore even if the player who cast the spell dies, the two other players still get to control each other?

Yes, that is how it works. I've clarified the answer to state that more explicitly.

Nothing changes for the other players, since the abilities have resolved and no control effects are for the player who left.
The relevant rule is:

800.4a When a player leaves the game, all objects (see rule 109) owned by that player leave the game and any effects which give that player control of any objects or players end. Then, if that player controlled any objects on the stack not represented by cards, those objects cease to exist. Then, if there are any objects still controlled by that player, those objects are exiled. This is not a state-based action. It happens as soon as the player leaves the game. If the player who left the game had priority at the time he or she left, priority passes to the next player in turn order who’s still in the game.

As for "until your next turn", there's another subclause about that:

800.4j When a player leaves the game, any continuous effects with durations that last until that player’s next turn or until a specific point in that turn will last until that turn would have begun. They neither expire immediately nor last indefinitely.

You seem to have found a pretty old version of that rule. The current equivalent of that rule is 800.4a, which notably doesn't mention "combat damage on the stack". 800.4b and 800.4j are also relevant to the question.

If one of the players chosen in Cruel Entertainment leaves the game before they can control another player's turn, they are no longer a player and therefore cannot control anyone's turn.
If an ability specifies "until your next turn," but you have left the game, the ability will last until when your next turn would have begun according to what the turn order was while you were still in the game.


text:
Love letter handmaiden card play
Playing with my 10 year old niece.  She ropes me into it without much info.  I read about 2 player game and 3 cards up and she insists the old love letter game was different and wanted to throw away the rule book in rage. I think she simply never learned all the rules. Most rage-inducing was the hand maiden card. I interpreted the rules as saying that she must target herself in a 2 player game when I had handmaiden out. Reading the above just confuses me more. Do I need to read the rulebook? How does handmaiden work if she must play princess or guard?
In Love Letter, can you discard a card instead of playing it?

Sometimes kids have their own interpretation of the rules. You can either correct them or play along. The later version is often the most adult reaction.

Possible duplicate of In Love Letter, can you discard a card instead of playing it?

@JoeW This question was asked after reading that other question and being unclear about it.

This definitely isn't a duplicate at all. This is about how the Hand Maiden works, specifically what you do when all opponents have a Hand Maiden out. The other question is about if you are allowed to discard a card without performing the text.

@Gendolkari and my answer in that question also answers this question which is why I raised the duplicate flag.

@JoeW So it does... but the other question could have been answered without mentioning the Hand Maiden at all; you just chose to give a lot more detail in the answer. So this might be a case of 2 different questions where a comprehensive answer could answer both. He also said that "reading the above" confused him, presumably meaning reading your answer. But he wasn't clear about what he was confused by. I think we might need more clarification on his question here...

@Gendolkari Do you mean give an answer that says you have to use the cards abilities except in certain cases and not explain them? That sounds like a partial answer to me. To fully answer the question it was necessary to also explain what happens when you can't use a cards ability.

You are correct: where appropriate you must target yourself if all other players in the game are affected by a Handmaid card, although the effect of this is not as intrusive as you would think.
The rulebook (pages 19-20) expands upon the Handmaid card, specifically stating:

If all players other than the player whose turn it is are protected by Susannah, the player must choose him- or herself if possible.

However the rulebook also expands upon each other card in the deck (pages 15-23), and states that the only card that will (must) affect yourself in this case is the Prince:

If all other players are protected by the Handmaid, you must choose yourself.

The rest of the cards either do not target other players, or are specifically expanded upon to say they have no effect.


text:
Can a noncreature artifact be destroyed by reducing toughness?
I was reading through the answers of this question when I suddenly wondered about Vehicles in their artifact state.
They have a listed Power and Toughness. If I were to reduce that toughness to 0 and the Vehicle is not crewed (i.e. does not have the Creature type, only Artifact), is it destroyed?
Are there other examples of this, like enchantments that have a power and toughness even though they are (at the moment) not creatures? Can those permanents be destroyed by reducing toughness?

The Gods from Theros aren't creatures sometimes.

208.3. A noncreature permanent has no power or toughness, even if it’s a card with a power and toughness printed on it (such as a Vehicle).
208.3a If an effect would be created that affects the power and/or toughness of a noncreature permanent, that effect is created even though it doesn’t do anything unless that permanent becomes a creature.

Thus, they have no power and toughness that can be reduced to below 0.

@diego Edited. I used magiccards.info for the rules (I couldn't access wizards official page), and it seems they were outdated.

Good example of, though it'd be nice if you directly answered the question about noncreature artifacts too.

The rule directly below the quoted rule seems to answer the question much more directly, so I just edited it in.

No, it will not be destroyed. The most direct way to reach this conclusion is to look at the rule that specifies that creatures with zero or negative toughness will die:

704.5f If a creature has toughness 0 or less, it’s put into its owner’s graveyard. Regeneration can’t replace this event.

This rule applies only to creatures, not to noncreature artifacts (like unanimated vehicles). There is no corresponding rule for vehicles, artifacts in general, or any type of noncreature permanent. (It wouldn't make sense because noncreature permanents don't have toughness.)
Another argument is a little more technical. Even when a creature does have zero or negative toughness, it's not destroyed. "Destroy" has a specific meaning in Magic; it's one particular way that a permanent might be caused to die, but but not the only way. Reducing a creature's toughness to zero or less is a completely different way. One of the differences is that regeneration can save a creature which would be destroyed, but it does not save a creature with zero or negative toughness.
Other answers have identified other justifications for the same conclusion, which I will not repeat here.

This misses a reason, fyi: a noncreature can't have toughness at all, so a noncreature has no toughness to reduce to 0 or below.

@doppelgreener I intentionally omitted that because rule 704.5f makes it irrelevant, and it would be a distraction from my point. I believe this answer is a sufficient explanation without that fact. (Though an answer that does mention that could be perfectly valid.) I'll clarify this answer to point out that there are other explanations.

No, and you can't even target the vehicle with effects that target creatures, such as Tragic Slip, unless that vehicle has been turned into a creature. Until a vehicle is crewed (or granted creatureship through some other means like Start Your Engines), it has no power or toughness.
From the Gatherer rulings for an arbitrary vehicle:

Each Vehicle is printed with a power and toughness, but it’s not a creature. If it becomes a creature (most likely through its crew ability, but the Kaladesh set includes other such effects), it will have that power and toughness.

Correct answer but inaccurate statement: targeting has nothing to do with the vehicle having toughness, and everything to do with it being a creature.

@monoRed I agree. Unless it is a creature, you can't target it with effects that target creatures, such as reducing toughness. Toughness is a characteristic only attributable creatures, so anything that reduces toughness could never target a permanent that isn't a creature.

There are effects that can target non-creature permanents that affect P/T, such as Aether Meltdown, and it is possible to have +1/+1 or -1/-1 counters on non-creature permanents. They're not common, but they exist.

@monoRed Aether Meltdown enchants a vehicle, but that vehicle's power can't be reduced until it becomes a creature. While it's possible to have +1/+1 counters on a non-creature permanent, those counters have no effect unless the permanent becomes a creature since the permanent has no power or toughness.

Right, you can't affect power and toughness because they're not there, but that doesn't stop them from targeting the vehicle. If I have a spell that says "target permanent gets -2/-2 until end of turn", I can target a land or a planeswalker or a vehicle and it won't do anything (unless they turn into a creature later that turn), but it's a legal target.

@monoRed As of now there are no cards that give a permanent -X/-X. I'll change the wording in my first sentence to clarify about creature effects.

There is at least one card that gives a noncreature permanent +1/+1. See Veteran Motorist. It stands to reason that if a card exists that can give a noncreature permanent +1/+1, then a card could be printed in the future that gives -X/-X.

For an existing 'real-world' example: The vehicle could pick up a -1/-1 counter as a creature, return to being a vehicle at EOT when the crew ability wears off, and then have that -1/-1 counter replicated (many times over) with Clockspinning.


text:
In magic the gathering can I tap a creature at the attacking/blocking phase?
I was looking at this link
and was kind of confused. In Magic, when can I tap my opponent's creatures to prevent them from attacking?
So if a instant says tap target creature and they attack I have basically have to either do 2 things. Asks if they are on combat phase or if they rush to attacking phase say something like before you attack.
I was wondering because if you wait for them to declare attackers then you tap target creature they have to reconsider if they want to attack.
On another note there is a card that taps target attacking or blocking creature if I'm correct (might be exile) if so what are the rules on that?

If I can give you one point of advice try to get on MTGO. The visual representation of the phases in a turn will be of great help to you.

You can always ask your opponent to "rewind" phases if they attempt to skip through them.  According to the rules, each player gets a chance to act within all phases, however, many players choose to skip through the phases in interests of saving time. A player is never allowed to "rush" you through a phase. They will need to reset their creatures to how they existed before attackers were declared.
In this particular case, if they move to attack step before you get a chance to respond, I would politely inform them that I wish to cast a spell during the "begin combat" phase.
For your side note: there are many cards such as Celestial Flare that effect attackers or blockers (scroll down to the bottom for example rulings that I believe you will find helpful)

Good answer, but it might be worth pointing out that even though your opponent can't rush you through a phase, it doesn't mean you can just wait for your opponent to declare attackers and then back up and try to tap something. Rushing you through a phase only means that they didn't even give you a chance to play something in that phase if you wanted to.

@DavidZ You can wait for your opponent to declare attackers before informing him that he isn't in his declare attackers step yet. Free information for you. More details here, if you are interested. The gist of that post is that pausing does not communicate acceptance of a shortcut.

The untapped phase being the notable exception to when players get priority.

Players commonly say something like "combat?" or "attackers?" which is basically a short way of asking "I am ready to declare attackers, do you have any spells or abilities you want to use in the beginning of combat step?"  This is your last chance to tap anything.  If you say no then they can proceed with declaring attackers, which is a so called "turn based action" that you cannot interrupt.
If a player just starts turning things sideways and declaring attacks without giving you a chance to act, you can ask them to please rewind to the Beginning of Combat Step.  However, you are not allowed to "fish" for information about their intended attackers and then try to use abilities.
A creature becomes an 'Attacking Creature' as soon as it's declared an attacker, so you can target it with "target attacking creature" spells/abilities anytime from before declaring blockers up to End of Combat before the second main phase starts.
Likewise a declared blocker is a valid target for 'Blocking Creature' spells/abilities before or after combat damage, until the second main phase starts.
This sometimes catches new players off guard with a card like Celestial Flare since if you attack with say, two weak creatures and a strong one, I could kill your two weak creatures with blockers then cast Celestial Flare during the End of Combat Step and force you to sacrifice your strong creature

The obvious time to tap thing like this is to do it in the beginning of combat step. That is to say after the first main phase but before attackers are declared.
If you tap things in your opponents main phase he can still use the permanents tap abilities in response and play things at sorcery speed. Which is bad.
The beginning of combat step is after the main phase though so no sorcery speed things can be played then but it is still before attackers are declared so tapping creatures here will keep them from attacking (Unless your opponent has a way to untap them before attackers are declared.)
Lastly you should know this but your opponent cannot steamroll you into not doing things in certain parts of the turn. He cannot go from the main phase to the declare attackers phase without giving you a chance to do things in the beginning of combat step.
Phases are only ended when priority is skipped by both players on an empty stack. Don't get intimidated like this.


text:
Why is Sunken Hollow a rare?
Yesterday I was opening some boosters from the new Oath of the Gatewatch expansion, and got Sunken Hollow as a rare.

(Tap: Add Blue or Black to your mana pool.) Sunken Hollow enters the
battlefield tapped unless you control two or more basic lands.

To be honest I was kind of dissappointed to get a land for a rare (then again, I also got Nissa, Voice of Zendikar, so I can't complain), but it also made me wonder why it is a rare? What are the exact advantages of this card? The gatherer website has some rulings on this card, but I can't really make much of them, or see how this would affect a game.

I don't have time to research and provide a full answer, but keep in mind that some of the most sought after cards for tournament play are rare lands, like shocks and fetches. Many modern decks have a very expensive landbase because the cards that help fix your colors tend to be rares.

Because its an incredibly good card?

Given the relative low price of the cards in this set, I'd be very happy with a $4 card..

Most people would be thrilled to get one I guess. It's actually the second most expensive rare of Battle for Zendikar according to magiccardmarket which is the most popular website in Europe for buying and selling cards

By the way, you say you were opening Oath of the Gatewatch boosters but this is a Battle for Zendikar card. Are you sure it was an Oath of the Gatewatch booster? In that case it must have been an expedition land which is around €30 at the moment

@IvoBeckers It couldn't have been that either - Oath's Expeditions are an entirely different set from the BFZ expeditions, and Sunken Hollow was already an Expedition in BFZ.

Sorry, yeah I opened Battle for Zendikar  packs too. Mixed it up :(

@StevenStadnicki aah ok. I didn't know that.

Take a look at some common modern decks and their pricing. You'll notice that the mana base (the lands) make up a significant portion of the cost in each deck. As a new or casual player this is less important, and the lands seem less exciting. However, part of the reason that they're valuable is that they're so versatile; almost any deck in those colours can use several of them.

Man, I got a horrible card.  It is just a 0 cost artifact that produces 1 colored mana.  I mean, lands already cost 0 mana, and there are more ways to destroy artifacts than lands!  Sucks to be me.

@Yakk I'll trade you this awesome giant firebreathing dragon for it!  (Although to be fair I think there were more ways to destroy land at the time!)

The land is a rare for a couple reasons:

It is a land that can provide two colors and it has the chance to enter untapped. Entering untapped is important for maintaining tempo.
It is a dual land*, in the classic sense of having two basic land types(Island Swamp). Lands with two basic types are very important, especially when fetch lands are currently in standard. A Plain-Island fetchland could get a Sunken Hollow, allowing the player access to black mana.

*I call it a dual land, but there are many lands that can be considered dual. Any land that produces two (or more) types of mana may be considered dual, even if they aren't a basic land type (e.g. Llanowar Wastes produces green and black, but isn't a forest nor a swamp, and costs life to make colored mana). Many dual lands enter tapped, which trades mana fixing for speed. Some do give you a slight benefit (1 life, scry 1, relevant land type).
And of the dual lands with two land types, each of them is slightly different. The original dual lands always entered untapped. Shock lands enter tapped unless you pay 2 life but it can be untapped the first or second turn. The dual land you have won't normally enter untapped until the 3rd turn or later.

To be clear, "dual land" is not a technical term, but is jargon that the land has multiple basic land subtypes.

@HaoYe "dual land" means it produces two colors, not that it necessarily has multiple basic land subtypes, right? (e.g. Llanowar Wastes is also a dual land, though it has no subtypes) Though this answer indeed uses it to mean the subtypes.

The MTGSalvation Wiki's page on the subject agrees with Jefromi's definition.

@Jefromi - True - I should have specified, "in the context of this answer".

@HaoYe Or maybe it'd improve the answer if it avoided using the term in an unusual way? (JonTheMon - I'd be happy to edit but not sure if you agree.)

The popular term for the cycle of lands that includes Sunken Hollow is battle lands.

@Jefromi Calling the Tango Lands 'dual lands' is a very common use of the term. In fact, "dual lands" by common mtg slang means a land that has two land types. While it may not be the wiki definition, it is the most common use of the term.

@Waterseas Yes, I completely agree that the tango lands are dual lands.  The disagreement here is only about the two types vs two colors thing (i.e. whether it's good to say "they're dual lands: they have two types). I'm not sure I agree with your assessment of common usage of the term. I totally believe that you've heard it in the "two types" sense, I'm really not sure that's common. If you don't believe that wiki, Wizards also routinely uses the "two colors" sense: http://magic.wizards.com/en/articles/archive/making-mana-2014-06-27

You might expand a bit on what the original duals are and what fetch lands and shock lands are by providing example cards. Maybe also talk about the monetary value of those cards to give a picture of how good and sought after they are by experienced players

If I hear "dual land" I only think of the ABUR originals, everything else is some other type of land. That said I don't think the current text in this answer is confusing.

It's not confusing, because the answer explains what it means. I guess I just don't get the point of saying "a dual land, in the classic sense of having two basic land types" when you could just say "it has two basic land types." The term isn't the important thing, the characteristic of the card is, so using the term just creates a momentary distraction for people who don't understand the term the same way - and propagates a meaning of the term that's different from what Wizards uses.

Thanks for the answer, it's very clear. I didn't actually realise it had multiple types as well, so that's interesting. The comments were also very helpful in seeing how it can be combined with other cards. To make your answer even better you might consider putting some of those examples in :)

The short answer is that it's because of the New World Order, the massive redesign of how complexity was handled in MTG releases from late 2011.
The things that now cause a card to be put at a higher rarity are:

Strength of the card overall. More powerful cards are rarer so it's harder for someone to just load their deck up with them and crush people unlucky enough to not have those cards.
How complex the card is to understand, in terms of its actual behaviour. So a card that requires a lot of text, or careful understanding of priority, is more likely to be rare.
How complex the card is to understand strategically. So a card that has simple mechanics but looks "useless" might be rarer to make you think about what's so special about it (because at a common you might just think it was a rubbish card used to bulk up the set).
How complex the card is, in terms of interactions with other cards. If there's a three-card combo that results in a crazy chain reaction where you have to carefully pay attention to the order of execution to understand what's going on, at least one of those cards is probably going to be put at rare.

So rare cards are ones that either feel special to get in a booster (because they're that good), or that you have to think about how to best use (and so you don't get cognitive overload with lots of complicated cards at common). In the case of a dual land, it's usually a bit of both. The ability to choose which colour of mana you're producing is incredibly powerful, because it makes it easier to mix two colours in your deck without worrying about mana screw, or to splash a colour you wouldn't otherwise include. Imagine if your opponent was playing an apparently straight black creature deck and suddenly dropped a couple of these. Why would he need blue mana? Is he going to summon a massive creature, or maybe he's got some spell counters available?
As pointed out in other answers, the fact that it can be played untapped means that you don't sacrifice tempo to get the dual land out, either. With many dual lands, the bonus of having that flexibility is countered by needing to wait an extra turn to make use of it (barring some ability to untap a land). So as long as you've already got a couple of lands out, this is a penalty-free dual land, meaning that it's at full power by turn 3 in many cases (and potentially earlier if you can get around the one-land-per-turn rule somehow).

Haven't dual lands (the "good" ones anyway) pretty much always been rare, even before New World Order? They certainly still make sense as rare with New World Order, of course, not disagreeing with that.

@Jefromi the original article states "something R&D has been up to for over three years (and the work leading up to it for three more), a little something we call New World Order.". New World Order wasn't made up in an instant, it was built over Magic history to balance flaws in the original design. It did not take much time to notice the power and complexity of the original dual lands, I guess.

True. Also, I think NWO made more of a difference based on complexity than based on power in general.

That's true. Power was probably always a factor in rarity, but moving complexity to the rarer cards was a deliberate choice in NWO.

I guess giving it a higher rarity worked, because it did make me think about why it actually was a rare. Thanks for the clear explanation :)

Nothing about Dual lands is to do with NWO. NWO is about complexity at common only, so you'd still have to explain why they aren't at uncommon. Also, the Duals aren't that complex, as they already put Gates and Tarkir Lifegain Duals at common within the last 3 sets. Heck, Unknown Shores and Holdout Settlement are both at common in Oath of the Gatewatch and are significantly more complex.

As you learn more about magic, you're going to learn that land choice is one of the most important things.
It's rare because it is a land that offers you more than one color and CAN come in untapped.  It's all about the speed.
In standard play this is important, but not game-breaking by itself.  If you shift to more open formats you learn very quickly the difference it makes to have a land come in untapped and offer two or more colors.


text:
Are there any cards that permanently take control of opponents creature
I know that the cards I'm familiar with such as Act of Treason and Act of Aggression all specify gaining control until end of turn. I'm wondering if something such as Illusory Gains, Beguiler of Wills, or Blatant Thievery would take control of a creature permanently. I know that the answers on this question Does Illusory Gains make someone else's Commander my own forever? indicate that is not the case but I'm wondering if there is a rule that indicates that effect doesn't last when it's not specified and furthermore are there any cards that do specify the effect lasting permanently?

Could this not have been answered with a simple gatherer search?

@NeilMeyer The OP didn't understand how to tell whether a card caused a permanent or temporary change of control, so... no. I think you're focusing too much on the title, which isn't actually the entire question.

Control-changing effects aren't really special cases. What you're seeing here is just that some effects are permanent and some aren't. If you put Goblin War Paint on a creature, it gives that creature +2/+2 and haste - but if the aura goes away, so does that effect. It doesn't give +2/+2 and haste forever, just as long as it's around.
Specifically, continuous effects generated by an object last only as long as that object generating them is around:

611.3b The effect applies at all times that the permanent generating it is on the battlefield or the object generating it is in the appropriate zone.

and continuous effects generated by spells or abilities last as long as they say they're going to last, and if no duration is specified they last until the end of the game:

611.2a A continuous effect generated by the resolution of a spell or ability lasts as long as stated by the spell or ability creating it (such as “until end of turn”). If no duration is stated, it lasts until the end of the game.

Also perhaps relevant is:

611.3a A continuous effect generated by a static ability isn’t “locked in”; it applies at any given moment to whatever its text indicates.

So an Aura that has an effect on the creature it's enchanting always applies just to that creature, even if it gets moved around.
Illusory Gains is an example of an effect generated by an object that's not around forever in the realm of gaining control, but a more obvious one is the classic Control Magic. Its effect lasts only as long as the aura is on the battlefield enchanting a creature. If you Control Magic an opponent's creature, and they destroy the Control Magic, they get their creature back. If you move it to a second with an Aura Finesse, you'll lose control of the first creature and gain control of the second creature.
Illusory Gains is the same idea. It gets moved around, and it only says you control the creature it's enchanting, not any other ones, so when it moves away from a creature, there's no longer an effect giving you control of that creature.
Another way a continuous effect might not last forever is if it's created by a spell or ability which specifies a duration explicitly (like "until end of turn"). This is what's going on with Act of Treason. That case is pretty obvious from the text on the card.
The last case is if the spell or ability which creates it doesn't specify a duration. In that case, it lasts until the end of the game. So Beguiler of Wills and Blatant Thievery give you control of things indefinitely: they just say gain control, and don't say "...until end of turn" or anything like it to specify a duration.Since the rules work this way, there aren't cards that explicitly say "gain control forever"; they don't need to.

I get it now... I just wasn't paying enough attention to the fact that it was an enchantment vs. a sorcery... makes complete sense now... thanks

Just do a search for "gain control" excluding turn or "end of turn".  Many of those cards have conditional control, but they last past the end of the turn.
Search example: http://magiccards.info/query?q=o%3A%22gain+control%22+-o%3Aturn&v=card&s=cname

That search request won't work with cards like https://scryfall.com/card/pthb/124p/the-akroan-war that have both group of words, but on different sentences, so you need to use a regular expression. Here's another try