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If I have Sakashima of a Thousand Faces out, a Krark's Thumb and a Copy Artifact that copies Krark's Thumb what happens when I have to flip a coin? Does it go infinite and result in a draw? Do I flip two coins? Do I flip four coins?

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Krak's ability is a replacement effect. The relevant rule is

614.5. A replacement effect doesn’t invoke itself repeatedly; it gets only one opportunity to affect an event or any modified events that may replace that event. Example: A player controls two permanents, each with an ability that reads “If a creature you control would deal damage to a permanent or player, it deals double that damage to that permanent or player instead.” A creature that normally deals 2 damage will deal 8 damage—not just 4, and not an infinite amount.

Like the example, two Krark's Thumbs would cause you to flip four coins.

These flips technically aren't at the same time, but you can generally get away with flipping four coins at the same time and taking whichever you prefer. However, if they want, your opponent can insist on you flipping them two at a time. You can probably also declare before you flip any of them which result you prefer, then flip all of them at the same time; this would probably fall under the general concept of "shortcut". It's generally obvious which result you prefer, but if you don't want to reveal it, and your opponent is a stickler for the rules, you'll have to flip two at a time. Obviously, if the coins come up with different results, then which one you pick will reveal which you prefer, but if you flip two at a time, and they all come up the same, you can keep which you would have preferred secret. This is more of an issue if you had two Krark's Other Thumbs and you would roll a die: if you want to roll all four dice at the same time and it's not obvious what your preference ordering is, you have to declare it ahead of time, and it'll probably be faster to just roll the dice two at a time.

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  • With the die rolls, it also shouldn't matter that you only see two of the dice at first. As long as you can order the results from better to worse, you can always pick the better one of any two rolls. It would matter if the combination of two dice was what mattered, though. E.g. if you're looking for a pair from two rolls, seeing all four dice at the same is much better than a one-of-two pick twice. – ilkkachu May 23 at 14:16
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There is a Gatherer ruling on this that appears to apply here. The first copy of it would work as normal and the second copy would replace the flip of those two coins with two coins each.

You would flip 4 coins and chose which one you want.

  • 1 coin flip becomes 2 coin flips from the first copy
  • 2 coin flips from the first copy each get replaced with 2 coin flips from the second copy
  • 4 coins get flipped in the end.

The ruling says:

If an effect tells you to flip more than one coin at once, this replace each individual coin flip. For example, if an effect tells you to flip two coins, you don’t flip four coins and ignore any two; you flip two coins, flip two coins, and then ignore one flip from each pair of flips. You will know the results of all simultaneous flips before choosing which to ignore.

It should be noted that a replacement event can only happen to an event once so this can't go infinite.

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Your specific case, you have two Krark's Thumb in play. Krark's ability is a replacement effect. Replacement effects can't apply to the same event more than once. (Rule 614.5 in the article I linked to.)

As the controller of both thumbs, you get to decide what order the replacement effects apply. The order doesn't matter in this case.

So, you flip a coin...

  • First Krark's thumb fires, and instead of flipping one coin, you flip two coins, and get to pick the result.
  • Second, you apply the second Krark's thumb, so for each of those two coins, you flip two coins (a total of four flips).

If you are looking for a heads (for example) the probability you will get a head in this scenario is 1 - probability(no heads) = 1 - 1/2^4 = 15/16. You are very likely to get the heads compared to usual.

If you have N total thumbs in play, the probability you will get a head now becomes:

  • 1 - 1/2^N.
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