Texas Hold'em Odds, Explained

After reading this you will know exactly what a win, tie and equity percentage means in hold'em, how the calculator produces them, and how to read a matchup without fooling yourself.

The Texas Hold'em Odds Calculator takes two to nine starting hands and an optional board, then reports how often each hand wins, ties and its overall equity. Give it As Ah against Ks Kh preflop and it will tell you that pocket aces win about 82.4% of the time, kings win about 17.1%, and the two split the rest. Those numbers are the foundation of almost every correct decision at the table.

What the calculator answers

Three numbers describe every player in a showdown from the current street forward.

Win %: The fraction of possible runouts where this hand alone holds the best five-card hand at the river.
Tie %: The fraction of runouts where this hand shares the best hand with one or more opponents.
Equity %: Win probability plus an even share of every tie. If a hand wins 40% outright and ties another 4% two ways, its equity is 40 + 4/2 = 42%. Equity is the fraction of the pot the hand collects on average.

The three win percentages plus the tie mass always sum to 100%, because every runout produces exactly one outcome. Equity across all hands also sums to 100%, since one full pot is shared out on each board.

When to use it, and when not

Use this calculator to study spots away from the table: preflop all-in confrontations, semi-bluff draws on the flop, or how much a specific hand needs to call. It answers "if the money goes in now and we run it out, how often do I win?" It does not model betting, position, or your opponent's tendency to fold. A hand with 35% equity is not automatically a call. You still need the pot odds.

For that second step, once you know your equity, use Poker Pot Odds & Outs to compare it against the price of a call. For other games, see the Omaha Odds Calculator, the Seven-Card Stud Odds Calculator, and the low and split variants below.

Equity is not a call. Equity tells you how often you win the pot. Whether you should put money in depends on how much is already there and how much you must add. A 25% equity draw is a fine call getting 4-to-1 and a clear fold getting 2-to-1.

The math behind the numbers

A hold'em showdown is a counting problem. Fix everyone's hole cards and the board cards you already know, then look at every way the remaining board can be completed. For each completed board, rank the seven-card hands and award the point to the best.

The number of runouts to enumerate is a combination. With u unknown cards left in the deck and r board cards still to come, the count is:

N = \binom{u}{r}

Here u is 52 minus every card already fixed (hole cards plus known board), and r is the number of board cards still missing (2 after the flop, 1 after the turn). Each of those N boards is equally likely, so a hand's win probability is simply its winning boards divided by N:

\text{equity} = \frac{\text{wins} + \sum \frac{1}{t}\,\text{ties}_t}{N}

The tie term splits each shared board by the number of players t sharing it. Two hands splitting a board each get 1/2; three-way, 1/3.

When the board is set to a flop or turn, N is small enough to enumerate exactly. A turn with two known hands leaves 44 unknown cards and r = 1, so N = 44 boards. A flop leaves 45 unknowns with r = 2, giving \binom{45}{2} = 990 boards. Both are instant and exact.

Why preflop uses simulation

Preflop the counting explodes. With two known hands, 48 cards remain and the full board is five cards: \binom{48}{5} = 1{,}712{,}304 boards. That is still enumerable, but add more players and it grows fast. Rather than enumerate, the calculator deals a large seeded sample of random boards and counts outcomes, which is Monte Carlo simulation.

The standard preset deals 150,000 boards. The sampling error on a percentage from n independent boards is roughly:

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

where p is the true probability. For a 50% matchup at n = 150{,}000, that is \sqrt{0.25/150000} \approx 0.00129, about 0.13 percentage points. So a reported 50.0% is almost certainly within 0.2 to 0.3 points of the truth. Push to 1,000,000 boards and the error falls to about 0.05 points. The seed keeps runs repeatable: the same input gives the same output every time.

The error shrinks with the square root of the sample. Quadrupling the boards roughly halves the error.

Aces against kings, run it out

Load the demo: As Ah on the first line, Ks Kh on the second, no board. Press Calculate.

Four known cards leave 48 unknown, so the exact board space is \binom{48}{5} = 1{,}712{,}304 runouts.
The simulation deals 150,000 of them at random. Aces win on the great majority: no pair beats them unless the board brings a king, a straight, or a flush that favours kings.
Kings win mainly when a third king lands, roughly a 1-in-4 chance to hit one across five cards, tempered by boards where aces still make a straight or flush.
The reported figures land near 82.4% for aces and 17.1% for kings, with about 0.5% ties (shared straights or a board that plays itself).

Because ties are small and split evenly, equity is close to the win figures: about 82.7% for aces and 17.3% for kings.

Pocket aces hold about 82% equity against a single lower pair. The classic "80/20" shorthand rounds this off.

See how the board reshapes equity

The most instructive thing a static page cannot show is how one card swings a race. The widget below lets you deal the flop and watch equity jump.

Reading the results without fooling yourself

A few habits keep the numbers honest.

First, equity is forward-looking from the current street. It does not credit money already in the pot, and it assumes the hand reaches showdown. Second, ties matter more than they look in some spots. Two players holding Ah Kh and Ad Kd tie almost every board that does not make a flush, so each has near 50% equity built almost entirely from ties. Read the tie column, not just the win column. Third, small equity gaps are inside the simulation noise. At 150,000 boards a reported 50.1% versus 49.9% is a coin flip; do not treat 0.2 points as a real edge.

Common mistakes

Enter cards as rank then suit with no space inside a card and a space between the two cards: As Kd, not AsKd or A♠ K♦. Use T for ten. Suits are s h d c.

The most frequent errors are structural, not mathematical. Reusing a card is impossible: if a hand holds As, no other hand and no board can hold As too. Confusing equity with the correct action leads people to call every draw; run your equity through pot odds first. And treating a preflop simulation figure as exact to the tenth of a point overstates precision. If you need a razor-thin number for a study, switch to the 1,000,000-board preset and read the result to one decimal.

Related calculators

For four-card games and split pots, use the Omaha Odds Calculator and the Omaha Hi/Lo Odds Calculator. For stud, see the Razz Odds Calculator and the Stud Hi/Lo Odds Calculator. When you want a lottery example of the same combination math, the Lottery Odds calculator counts \binom{N}{k} outcomes the same way this page counts runouts.

Frequently asked questions

Why do aces beat kings about 82% and not 80%?

The "80/20" figure is a rounded shorthand. The exact heads-up equity for a pair of aces over a pair of kings is close to 82% including the small tie share. When both aces block the kings' suits, as with As Ah against Ks Kh, the blocked flush outs push it up to about 82.7%. The calculator reports the real number for the exact cards you enter.

Is the preflop result exact or approximate?

Preflop it is a seeded Monte Carlo estimate. With 150,000 boards a 50% figure carries about 0.13 points of standard error. With a flop or turn on the board, every runout is enumerated and the answer is exact.

Why does the same input always give the same percentages?

The simulation uses a fixed seed, so it deals the same sequence of boards each time. That makes results reproducible. Changing the board count preset changes the sample and can shift the last decimal.

How many hands can I compare at once?

Two to nine, matching a full hold'em table. Every added hand removes two cards from the deck and changes the runout space, so the equities always add to 100% across the hands you enter.

What does a high tie percentage mean?

It means the hands often make identical five-card hands, usually because they share ranks or the board plays large. Two hands with the same two ranks in different suits tie on most boards, so their equity comes mostly from split pots rather than outright wins.

Try it yourself in the tool