I have heard that the distribution in a 6 max game is similar to that of a 9 or 10 handed game where the extra players have folded. I am wondering how true that is.

Seems like there may be a higher probability of high cards in the remaining players hands and in the deck in the latter case since some players have folded. My assumption here is that if they (the players that folded) had a higher than normal amount of high cards, then it would be more likely that someone had opened.

  • Possible duplicate of Are mucked and burnt cards significant in odds calculation?
    – paparazzo
    Apr 19, 2017 at 19:32
  • The distribution does not change. A hole card is a down card. Folded cards are not exactly random and that is commonly referred to as card removal effect. In a larger game you have to opportunity for more folds. The link covers your question.
    – paparazzo
    Apr 19, 2017 at 19:35
  • Just imagine a game with 26 Players, so all Cards are dealt out. Now assume that 20 players folded. Now you have your 6 players left. Do you think these hands are stronger than the first 6 hands dealt(which would be your 6 player game)? Apr 20, 2017 at 15:16
  • i think there may be a higher probability of high cards in in the case where 20 players folded. but i don't know how to estimate that.
    – Ray Tayek
    Apr 20, 2017 at 17:36
  • 1
    @RayofCommand i ran some old simulation code that indicates that if 13 of the players folded (17%) then the average rank (2-14) of the remaining cards is 8.29 vs 7.94 when anyone opens with a pair of sevens or better.
    – Ray Tayek
    Dec 6, 2021 at 0:18

1 Answer 1


Probability is a measure of information. It's not about where the cards are--it's about what you know about them.

Let's say you have a flush draw on the turn--9 outs. What odds should you use for betting? You should assume a 9/46 chance you'll hit that spade. Now take 10 cards off the bottom of the deck stub and throw them out the window. What are your odds now? 9/46. The fact that cards moved doesn't change what you know about the next card to come--it's just as likely to be a spade as it was before. Now go to the window and peek at the cards on the ground. Two of them are spades. What are your odds now? 7/46. Cards didn't move, but now you have more information.

As far as probability goes, all unknown cards are just unknown cards, whether they're in the muck, the stub, an opponent's hand, or the floor.

  • But you do have information about played versus mucked cards. Some cards (e.g. Ace) are played more often than others. 2-7 are mucked more often than others.
    – paparazzo
    Apr 19, 2017 at 20:37
  • 1
    That's true, but probably not terribly useful. A player could easily muck A6o, but call with 67s, so you can't really assume that mucked cards are much more likely to be 7's than A's. But you might, say, assume that the stub is generally rich in high cards after many players have folded and adjust one's odds a bit. Apr 19, 2017 at 20:44

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