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Omaha Odds, Explained

After reading this you can read Omaha win, tie and equity percentages correctly, understand why four hole cards do not mean four times the flushes, and check the engine's numbers against the counting math yourself.

What the calculator does

Omaha deals each player four hole cards instead of two. At showdown you must use exactly two of those four cards, combined with exactly three of the five board cards. That single rule drives everything about the game. The calculator takes two to nine four-card hands and an optional board, then reports each hand's chance to win, to tie, and its total equity (win share plus a fair split of ties).

Here is a hook. Give a player As Ah Ks Kh and put three hearts on the board. It looks like a flush every time. It is not. You hold only two hearts, and two hole cards plus three board hearts do make the flush, so that specific hand works. But swap to As Ah Ks Kd with three board hearts and you have no flush at all, because only one heart is in your hand and you cannot borrow a third heart from anywhere. The counting is different from hold'em, and small mistakes here cost real money.

When to use it, and when not

Use it to settle "who was ahead" after a hand, to study how equities run close in Omaha, and to see how much a specific board texture helps or hurts a holding. It answers the equity question: if this exact spot were replayed to the river many times, what fraction does each hand win?

Do not read equity as a call-or-fold answer by itself. Equity ignores position, stack sizes, betting rounds still to come, and the fact that you rarely get to the river for free. To turn equity into a decision, combine it with the price you are being offered. The Poker Pot Odds and Outs page does that step. For split-pot Omaha, where a low hand can scoop half, use the Omaha Hi/Lo Odds Calculator instead, because this page scores high hands only.

The two-and-three rule and why it changes the counting

In hold'em you can use zero, one or two hole cards. In Omaha the count is fixed at two hole and three board. This constrains how many made hands your four cards can form.

A four-card hand contains \binom{4}{2} = 6 distinct two-card combinations. Each of those six pairs is a separate candidate to combine with the board.

\binom{4}{2} = \frac{4!}{2!\,2!} = 6

Here \binom{4}{2} is the number of ways to choose 2 cards from 4. So your hand really plays as six two-card hold'em hands at once, and the best of them wins. That is why Omaha equities cluster: with six two-card combos each, two random hands are far closer than two random hold'em hands.

The most expensive beginner error is counting a four-flush in hand as a flush. Four hearts in your hand plus two on the board is not a flush, because you can only use two of your hearts and there are just two on the board, for four hearts total. You need three hearts on the board to make a flush at all, and then the extra hearts in your hand are dead cards.

How the engine computes the numbers

When you set a flop (3 cards) or a turn (4 cards), the number of possible runouts is small enough to count exactly. With a flop down and enough cards removed, the remaining runout is enumerated card by card, so the result is an exact fraction, not an estimate. With four board cards set, only the single river card varies.

Preflop is different. With nine unknown board cards and two to nine hands, enumerating every runout is far too large, so the engine runs a seeded Monte Carlo simulation: it deals many random complete boards, scores each, and averages. The Simulation boards presets trade speed for precision.

The sampling error of a percentage from n simulated boards behaves like a proportion. The standard error is roughly:

SE = \sqrt{\frac{p(1-p)}{n}}

Here p is the true equity and n is the number of boards. For p = 0.5 and n = 150{,}000, SE \approx \sqrt{0.25 / 150000} \approx 0.00129, about 0.13 percentage points. At n = 1{,}000{,}000 it falls to about 0.05 points. Quadrupling the boards halves the error, so precision improves slowly.

Standard error in percentage points falls as boards rise. The curve flattens: going from 500,000 to 1,000,000 boards only cuts error from about 0.07 to 0.05 points.

A worked example: aces versus a suited rundown

As Ad Ks Kd against Th 9h 8d 7d, preflop

This is the demo. One hand is two premium pairs with two suits. The other is a double-suited connected rundown that makes straights and flushes easily. Load it and press Calculate.

  1. The aces hand plays six two-card combos: AA, KK, AK (four ways). Its power is high pairs and top two pair.
  2. The rundown plays combos like Th9h, 8d7d, T8, 97. It draws to straights on many boards and to two flush suits.
  3. Over a large simulation the aces hold a clear but far from crushing edge. Expect roughly 62% for the aces and 38% for the rundown, with ties near 0.1%.

Compare this to hold'em, where a pair of aces crushes a lower pair about 82 to 18. Here the premium double pair keeps only about 62 percent against a coordinated rundown, because each side has six combos and many ways to improve. That compression is the defining feature of the game.

The double pair leads about 62 to 38: a real edge, yet far smaller than the same confrontation would produce in hold'em.

A four-card Omaha hand contains six two-card combinations. As you add more coordinated cards (suited and connected), the number of combos that can make a straight or flush rises, which is why rundown hands run close to big pairs.

Reading and interpreting the results

Three numbers appear per hand. Keep them distinct.

Win %
The share of runouts this hand wins outright. Whole pots only.
Tie %
The share of runouts where this hand ties at least one other. The pot is split.
Equity %
Win % plus each tie's fair fractional share. This is the number to use for expected value: your long-run share of the pot.

Equity across all hands sums to 100 percent, since every runout awards exactly one pot's worth of value. If two hands each show 40 percent equity and a third shows 20 percent, those add to 100. Ties matter more in Omaha than you might expect, especially on paired boards and boards that play a straight for everyone.

To convert equity into a call, weigh it against the pot odds you are getting. If you have 45 percent equity and only need 33 percent to break even on the call, calling is correct on that street. The pot odds page handles that arithmetic.

Common mistakes

Beyond the four-flush trap, watch these.

  • Counting a set with only one board card. To make a full house you still use exactly two hole cards. A single pair in hand plus one matching board card is trips using two hole cards and one board card, which is fine, but a lone hole card cannot pair the board.
  • Treating equity as fold equity. Equity is showdown value only. It ignores the times an opponent folds, which is a separate part of a hand's real profit.
  • Over-trusting tight preflop reads. A hand that is a favorite preflop can be a large underdog on the flop. Re-run the numbers when the board arrives, because a flop set is enumerated exactly and often more informative.
  • Ignoring the dead cards in your own hand. Extra suited or connected cards you cannot use still remove outs from opponents, which slightly changes their draws. The engine accounts for this; hand-counting often does not.

Related calculators

For the two-hole-card game, the Texas Hold'em Odds Calculator gives exact equities without simulation in most spots. For stud variants, see the Seven-Card Stud Odds Calculator, the Razz Odds Calculator, and the Stud Hi/Lo Odds Calculator. Outside poker, the Lottery Odds page covers k-of-N draws.

Frequently asked questions

Why is pocket aces so much weaker in Omaha than hold'em?

In hold'em pocket aces beat a random hand about 85 percent of the time. In Omaha, both players hold six two-card combos, so both improve on far more boards. Strong Omaha hands run close, often within a few percentage points of even.

Can I really not use three of my four hole cards?

No. You use exactly two hole cards and exactly three board cards, every time. Four of a suit in hand is not a flush, and three of a kind in hand is not a set on its own.

Why do preflop and flop results feel different in accuracy?

Flop and turn spots are enumerated exactly, so the numbers are precise fractions. Preflop uses Monte Carlo simulation, so those numbers carry a small sampling error, around 0.13 percentage points at 150,000 boards.

How many boards should I simulate?

The 150,000 default is accurate to about a tenth of a percentage point, which is enough for study. Use 500,000 or 1,000,000 when you want to compare two spots that differ by only a fraction of a percent.

Do ties really matter?

Yes. On boards where a straight plays for everyone, or on paired boards, ties can be several percent of outcomes and split the pot. Equity already folds each tie into a fair fractional share.

Try it yourself in the tool

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