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I know of hands where the pot gets split among 2 or 3 players, but could it ever occur that the same happens for 4, 5, 6 players and so on up to 9, at least from a theoretical point of view? If so, with which probability respectively? Of what order of magnitude are we talking about? Thanks!

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    Sure it can and does happen, if the board is the nuts, typically with a straight flush or quads. I've been in one hand with 4 or 5 players, where the board was quads with an Ace kicker. I couldn't tell you the odds, though. – Herb Apr 1 at 21:39
  • Thank you. I didn't think of that, it sure is true! As a side question, do you think that when we read Tie as % in Equity Calculators the programmer referred to 1-1 ties only, or actually the probability of all the possible ties that can arise, summed together, as I'm referring to in my question? Thanks again. – PedulliF Apr 2 at 2:31
  • It should be all possibilities of a tie, depending on the way the programmer found the equity of the hand. If the programmer used a large number of simulated hands this possibility should be included although it would be an extremely small portion of possibly outcomes. – Clarko Apr 3 at 7:54
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Sure. If the flop comes AKQJT with no flush possibility, then everyone involved will tie

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Definitely possible, but exceptionally unlikely that all players would remain in a hand long enough to realize this possibility.

The stronger and more correlated the board gets, the less likely it is that players' hole cards will play in the winning 5-card hand. Boards that contain an entire straight, flush, or full house are rare and will often result in a chop for this reason.

From a theoretical standpoint, as many as 22 players could be dealt into a hand and split a pot. There are 52 cards in the deck and we need 5 for the board and 3 total burn cards. That leaves 44 cards for each player's 2-card hand (44/2=22). If the board runs out AKQJT-suited (royal flush) and all players remain in the hand, then all 22 players would split the pot since no other cards can better the winning hand.

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It's probably more interesting to think about this question for games like Omaha where players can't "play the board" (i.e. exactly 2 hole cards and 3 board cards are used to make the player's hand).

In that case:

Flushes and quads can never chop.

Full House can only ever chop 2 ways.

Trips, pairs, and high card winning hands could chop a maximum of 4 ways if the players play the exact same kicker cards (For example: Board shows A, A, A, x, x, and four players all have K, Q, kickers with no pocket pairs and no flush).

Straights can theoretically chop up to 7 ways in Omaha, if all 5 straight cards are on the board. For example: board shows a straight (A, K, Q, J, 10) with no possibility of a flush. Any player with any two of those cards in the hole would make the same straight. Besides the board, there are 15 such cards left in the deck for a maximum of 7 different identically ranked straights to happen simultaneously.

With fewer straight cards on the board, that drops to a maximum of a 4-way chop, for similar reasons to the examples with trips and pairs.

Don't know the exact odds of each scenario, but you should be ably to plug them into any online odds calculator. Adding high-low rules would add another layer of complexity, and give some rare opportunities for an even split up to 8-ways.

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