All-in and side pots

An all-in player can win from each opponent only as much as he put in himself. Everything the players matched up to his stack goes into the main pot, which all of them can win. Whatever the bigger stacks bet beyond that goes into a side pot that only they can win. Several all-ins make several side pots.

At the showdown the pots are settled one by one, each among the players who paid into all of it. A bet that nobody could match is not a pot at all: it goes back to the player who made it.

Our engine builds the pots the way a dealer stacks chips: in layers. It takes how much each player put in over the whole hand and sorts the amounts. The smallest all-in sets the first layer: everyone who put in at least that much adds the same amount, and that is the main pot. The next amount sets the next layer, and so on.

1. Sort the players by how much they put in during the hand.
2. The first layer is the smallest amount. Everyone contributes up to that level; this is the main pot.
3. The next layer is the next amount minus the previous one, paid by everyone who put in at least that much. This is side pot 1.
4. Repeat up to the biggest stack. If only one player paid for the top layer, nobody matched it, and those chips go back to him.

Two details matter. The chips of a player who folded stay in the pots he paid into, but he cannot win any of them. And two neighbouring layers with the same contenders are merged: if nobody went all-in between them, they are one pot.

Scribes’ Table, blinds 50 and 100. Ramses is on the button with 12,000, Ahmose in the small blind with 2,000 and Nefertari in the big blind with 5,000. Ramses goes all-in; Ahmose calls with everything he has, and so does Nefertari.

Nobody can match the last 7,000 of Ramses’ bet, so it goes straight back to him. All three contest the 6,000 main pot; only Nefertari and Ramses contest the 6,000 side pot. The cards: Ahmose holds A♣ A♦, Nefertari K♣ K♦, Ramses Q♣ Q♦, and the board 2♠ 7♥ 9♠ J♦ 4♣ helps nobody.

• Main pot, 6,000: Ahmose’s aces. He turned 2,000 into 6,000.
• Side pot, 6,000: Ahmose has no claim on it. Of the other two, Nefertari’s kings beat the queens. She finishes with 6,000, a gain of 1,000.
• Ramses loses 5,000 and keeps 7,000.

Notice that the best hand at the table could win no more than three times its own stack — 2,000 from each player, its owner included. The rest of the chips were decided between the other two.

Same table, four players. Ramses acts first with 10,000 and raises to 300. Tiye on the button goes all-in for 1,500, Ahmose in the small blind all-in for 4,000, Nefertari in the big blind calls 4,000 out of her 9,000, and Ramses folds.

Ramses’ 300 stays in the main pot even though he folded. The first layer, 300 from everyone, and the second, 1,200 from each of the three still in, have the same contenders — Tiye, Ahmose and Nefertari — so they merge into one main pot of 4,800. The side pot is 2,500 from each of the two bigger stacks.

Tiye has 9♣ 9♦, and the board 9♠ 5♥ 2♦ K♣ 7♠ gives her three nines. Ahmose holds A♠ Q♣ and Nefertari A♦ Q♥ — exactly the same hand.

• Main pot, 4,800: Tiye. Her 1,500 more than triples.
• Side pot, 5,000: Ahmose and Nefertari tie and split it, 2,500 each.
• Result: Tiye 4,800 (+3,300), Ahmose 2,500 (−1,500), Nefertari 7,500 (−1,500), Ramses 9,700 (−300).

We played both examples through our poker engine with these cards and bets; the pots and stacks are exactly what it produced.

Enter how much each player put into the pot during the hand, tick who folded and rank the hands: 1 for the best, equal numbers for a tie. The calculator uses the same code as our tables to build the pots, return unmatched chips and split ties.

When a pot is split, it is divided equally and rounded down. Any chips left over go out one at a time to the winners, starting with the first winner to the left of the button and going clockwise. Every pot is split separately by the same rule.

For example, three players split a pot of 3,350. Each gets 1,116, and two chips are left. Nefertari in the big blind is the first winner to the left of the button and gets one, Ramses next to her gets the other, and Tiye on the button gets 1,116. At our blinds the leftovers are usually a chip or two, but the rule is applied every time, so the totals always add up.

An all-in does not always reopen the betting. On the flop Ramses bets 1,000. Nefertari has 1,400 left and goes all-in, a raise of 400 — less than the 1,000 a full raise needs. Tiye, who has not acted yet, may call 1,400, fold or raise to at least 2,400. But when the action gets back to Ramses, he can only call the extra 400 or fold: he has already acted, and a short all-in does not give him another chance to raise.

Several short all-ins can add up to a full raise. If the bet has grown by at least the size of the last full raise since a player last acted, that player may raise again. Our engine tracks this exactly.

• A short blind. A player with 70 chips in the big blind posts 70 and is all-in. Everyone else still has to call the full 100 to play.
• Calling for less. If you face a 1,000 bet with 600 left, you call all-in for 600. The bettor’s extra 400 goes into a side pot if someone else calls it, or back to him if nobody does.
• Everyone else all-in. When all your opponents are all-in, you cannot raise — there is nobody left to call. You can only call or fold.

Once fewer than two players can still bet, the betting stops. The remaining board cards are dealt street by street with no pauses for action, and then the hands are shown. At our tables every hand that reaches the showdown is turned face up, so nobody can hide a losing all-in. The table announces the winner of each pot, and the Last hand button replays the whole hand with every pot, down to “wins side pot #1”.

If you lose an all-in and have no chips left, you keep your seat. You can top up between hands with at least the table’s minimum buy-in; if you do not, you leave the table after ten minutes and the seat goes to someone else.