Reading three boards at once

At a Patch-Patch table you are playing three poker hands at once, and each one is decided against a different board. Reading them one by one is slow and misses what makes the game different: the cards on one board, and the cards in your hand, tell you things about the other two. This article is a method for reading all three boards together, with the numbers behind it.

Step 1: what is the best hand on each board?

For each board, find the nuts, the best hand anyone could hold there. The board's shape tells you most of it:

Remember the Omaha rule: every hand is exactly two cards from a hand and three from the board. A flush needs two of the suit in the hand; four of a kind on a paired board needs the other two cards of that rank.

Step 2: use the cards you can see

You see far more cards than in any other poker game: your twelve and all fifteen board cards by the river. Every one of them is a card nobody else can hold. Before deciding that a hand beats you, check whether its cards are even available.

Here is a hand on the river, heads-up. Your three hands are shown with what they make.

Board 1: a lock. The board has three hearts and no pair, so the best possible hand is the highest flush. A flush with the ace and queen on the board and the king in a hand is the top one, and you hold the king of hearts. Nobody can beat you here: the card in your hand is what makes it certain.

Board 2: strong, but beaten by four of a kind. The board is double-paired, 7-7-3-3. Your aces full of 7s beats every other full house possible here (the other two aces are on boards 1 and 2), but four 7s or four 3s beat it. The 7 of clubs, the 7 of hearts, the 3 of spades and the 3 of diamonds are all unseen.

Board 3: the low end of the straights. 10-8 with queen-jack-9 makes a queen-high straight, but king-10 makes the king-high one. All three remaining kings and three of the four 10s are unseen.

Step 3: count what twelve cards hold

This is where Patch-Patch differs most from Hold'em and Omaha. An opponent holds twelve cards, so he holds the cards that beat you far more often than intuition suggests.

On the river heads-up, you have seen 27 cards: your 12 and the 15 on the boards. The other 25 are unseen, and your opponent holds 12 of them. So:

Applied to the example:

• Board 2. Four of a kind needs both remaining 7s or both remaining 3s. Each pair is in his hand 22% of the time, and one of the two pairs about 40% of the time. A full house on a double-paired board is far from safe against twelve cards.
• Board 3. King-10 needs one of the three unseen kings and one of the three unseen 10s: he holds at least one of each about 76% of the time. The low straight is more often beaten than not.

These are the odds before anything he did in the hand. They are a baseline: his bets and checks move them, but against twelve cards the baseline is much higher than in a two-card or four-card game.

Step 4: remember he had to split his cards too

Holding the cards is not the same as having played them on that board. Your opponent split his twelve cards on the flop, just as you did, and every two cards he put on board 3 are two cards he couldn't use on boards 1 and 2. So read his boards together:

• If he bet strongly from the flop, which board was it for? Look back at what each flop showed: a hand that was already made on the flop is the likeliest reason.
• When one of his boards is clearly strong, the cards that make it are not available for the others.
• When all three boards look strong for him, ask whether twelve cards can really cover all three. Sometimes they can; often one of them is a bluff or a draw that missed.

Step 5: turn three readings into one decision

Every decision in Patch-Patch covers all three boards at once: there is no folding one board and playing another. So add your three readings up as boards you expect to win:

• Board 1 is certain: one board.
• Board 2 holds about 60% of the time: six tenths of a board.
• Board 3 holds about a quarter of the time: a quarter of a board.

That is close to two boards, before any read on how he played. Heads-up, more than one and a half boards is a profitable hand overall, and more than one board is enough to call a pot-sized bet, as Scoop or split explains. Here a call is clear; whether to bet the river yourself depends on what he calls with.

Three-handed, the counting gets starker

With three players, the two opponents hold 24 of the 25 cards you haven't seen. Any unseen card is in one of their hands 96% of the time on the river. On the example's board 2, four of a kind would be out there far more often, and on board 3 a king and a 10 would almost certainly be held by someone. Three-handed, the second-best hand on a board is often just second. Heads-up vs three-handed Patch-Patch goes into the differences.

A routine for every street

1. For each board: what is the nuts?
2. For each: what do I hold, and what beats it?
3. Which of those cards can I see? Which are unseen?
4. How often do twelve cards hold them? (Heads-up on the river: one card about half the time, a specific pair about one time in five.)
5. Add it up in boards, and decide once for the whole hand.

The hand rankings page has the "exactly two plus three" rule with its traps, which is the first thing to check on any board.