How Double-Board Bomb Pot Equity Works

In a double-board bomb pot, every equity question is a joint question: both runouts come from one shared deck, so the boards are correlated and can’t be scored one at a time. This page explains what single-board tools get wrong about PLO bomb pot equity — and what the numbers a joint calculation produces actually mean.

One deck, two boards — why the boards are correlated

After the two flops, the turns and rivers of both boards are dealt from the same remaining deck. That has two consequences:

A card can only land once. The 2♥ can complete your flush on Board 1 or on Board 2 — never both. Any outcome that needs the same physical card on both boards has probability zero.

Outs are shared. If seven hearts remain and Board 1’s runout consumes two of them, only five are left for Board 2. Hitting one board makes hitting the other less likely. The boards are negatively correlated exactly where it matters — your chance to win both.

The double-counting mistake single-board tools make

A single-board calculator can only see one board at a time, and that fails in two ways.

It counts dead cards as live outs. Run Board 1 through a single-board tool and it has no idea Board 2’s flop exists — those three cards stay in its deck. In the example below, that alone turns a 33.9% flush arrival into an imaginary 39.5%.

Combining two answers assumes independence. Multiplying two single-board win rates to estimate a scoop treats the boards as independent decks. They aren’t — the same outs serve both — so independence overstates how often one hand wins both. And scoop, chop, walk away with nothing are joint outcomes that two separate single-board answers simply don’t contain.

A worked example, with exact numbers

PLO4 double-board bomb pot, two players at the flops:

Hero holds the nut flush draw on both boards; Villain has flopped top set on both. Seven hearts remain in the deck — and both boards are drawing from the same seven.

First error — the invisible flop. Ask a single-board tool about Board 1 and it doesn’t know J♥ and 6♥ are already gone to Board 2. It sees nine unseen hearts instead of seven and gives Hero’s flush a 39.5% chance of arriving; with both flops actually on the table it’s 33.9%. (Pure combinatorics — count for yourself: at least one of 9 hearts in 2 cards from 41, versus one of 7 in 2 from 38.)

Second error — independence. Even after fixing the dead cards, multiplying Hero’s two per-board win rates overstates the full scoop, because a heart spent on Board 1 can’t arrive on Board 2. Exhaustive joint enumeration of all 442,890 runouts gives the true numbers:

Scoop, chop, per-board — what the numbers mean

A joint double-board calculation reports, for every player:

Equity — your average share of the total pot, which decomposes as half of Board 1 equity plus half of Board 2 equity. It’s the right number for long-run value, but it’s an average over very different outcomes.

Scoop — the probability you are the sole winner of both boards at once. This is the number independence gets wrong, and the one that decides whether a big bet or raise is printing or lighting money on fire.

Pot-share distribution — how often you take nothing, a quarter, a half, or the whole pot. Two hands with identical equity can have wildly different distributions, and the distribution is what your stack experiences.

Exact enumeration vs Monte Carlo

Small spots are enumerated exhaustively — the worked example is all 442,890 runouts — and marked EXACT. Larger spots (early streets, ranges, more players) switch to Monte Carlo, marked SIMULATED with a 95%-confidence margin of error next to every number. Either way, both boards are dealt together from one deck in every runout — the correlation is never approximated away.

Seats don’t have to be exact hands: describe a player with a range or leave them fully random — bomb-pot-realistic, since nobody folds preflop. New to the format? Start with what a bomb pot is.