Poker Hand Odds
Poker is all about probabilities. Players who know how often certain hands occur make better decisions at the table.
On this page, you will find the frequency and probability of every five-card poker hand. You will also learn how poker players convert probabilities into poker strategy.
Finally, you will see a clear warning about a common mistake with two-card odds.
Whether you are new to poker probabilities or want to sharpen your understanding, this page gives you both the numbers and the context.
Poker probabilities
The probability of a poker hand depends on the total number of possible five-card combinations from a standard 52-card deck.
There are 2,598,960 total combinations.
For each hand, the probability is calculated by dividing that hand frequency by the total number of combinations.
The odds are defined as (1 / w) - 1 : 1, where w is the probability.
The frequencies in the table below are exact. The probabilities and odds are approximate.
Frequency of five-card poker hands
The table below lists all poker hands from rare to common.
The royal flush is included in the straight flush category. A royal flush can be made in four ways, one for each suit.
The odds against a royal flush are 649,739 : 1.
When ace-low straights and straight flushes are not counted, straights occur slightly less often. In that case, they occur 9/10 as often as usual.
| Hand | Frequency | Probability | Odds against |
|---|---|---|---|
| Straight flush | 40 | 0.00154% | 64,973 : 1 |
| Four of a kind | 624 | 0.0240% | 4,164 : 1 |
| Full house | 3,744 | 0.144% | 693 : 1 |
| Flush | 5,108 | 0.197% | 508 : 1 |
| Straight | 10,200 | 0.392% | 254 : 1 |
| Three of a kind | 54,912 | 2.11% | 46.3 : 1 |
| Two pair | 123,552 | 4.75% | 20.0 : 1 |
| One pair | 1,098,240 | 42.3% | 1.37 : 1 |
| No pair | 1,302,540 | 50.1% | 0.995 : 1 |
| Total | 2,598,960 | 100% | 0 : 1 |
Calculating odds in poker
Poker players use odds to calculate the profitable value of a hand over the long term.
Odds are expressed as a win-over-loss ratio.
The conversion to a probability percentage works like this:
- win / (win + loss) = probability
A chance of 1 in 4 converts to:
1 / (1 + 4) = 20% probability
In this article, odds are always expressed as odds for, meaning win over loss.
The correct strategy for an action like check, fold, call, or raise depends on the pot odds your opponents offer.
The lower the pot odds for calling a bet or raise, the more logical a fold becomes.
The higher the pot odds, the more logical a call becomes.
If you must call $1 to win a $1,000 pot, there is almost no hand you should fold. You only need to win once in a thousand times for that call to become profitable.
Your chance to win is the chance that your hand is strongest at showdown, or that every other player folds.
Both factors matter when choosing the right action.
Read more about this in our article about calculating outs.
Texas Hold’em calculation example
In Texas Hold’em, you calculate the chance of hitting an out on the next card with this formula:
number of outs x 2 + 1
If you have a flush draw with nine outs, you have roughly 19% chance to make the flush on the next card.
That comes from:
9 x 2 + 1 = 19%
With two cards still to come, meaning the turn and river together, use:
number of outs x 4 - 1
This gives an approximate total percentage.
To make a decision based on odds, your card odds must be at least equal to the pot odds.
If you have a 19% chance to make a flush, you need at least 5 : 1 pot odds.
That means you may call a maximum of 20% of the total pot for the action to be profitable long term.
The percentage method and ratio method help you calculate this quickly at the table.
Two-card odds
Many poker strategy sites advise calculating hand odds on the flop across both the turn and river.
They do this by multiplying the number of outs by four instead of two.
This gives a useful picture of your total success chance at any moment after the flop.
However, using these two-card odds to compare with pot odds is a common mistake.
It can lead to expensive miscalculations.
Why two-card odds are misleading
A hand with five outs has a winning chance of 4 : 1 across two cards.
However, it has only 8 : 1 odds if you count only the next card.
If you use the two-card odds of 4 : 1 to make a pot odds decision, you may call a $10 bet in a $40 pot.
That gives 5 : 1 pot odds on a total pot of $50.
If you miss on the turn and your opponent bets another $10, the pot becomes $70.
Now you look at 7 : 1 pot odds against 8 : 1 hand odds.
That ratio justifies a fold, even though you already invested $10 based on an overly optimistic estimate.
Therefore, always base hand odds for pot odds comparisons on the next card.
This applies whether that next card is the turn or the river.
Use two-card odds only as an informative estimate of your total success chance.
Do not use them as the foundation for a call-or-fold decision.
Pre-flop hand matchups
Besides the chance of making a certain five-card hand, it also helps to know how strong your two starting cards are before the flop.
The table below shows common pre-flop confrontations with their approximate equity.
Exact percentages may vary slightly depending on suits.
| Situation | Example | Hand 1 | Hand 2 |
|---|---|---|---|
| Overpair vs. two undercards | AA vs KQ | ~83% | ~17% |
| High pair vs. low pair | KK vs 22 | ~82% | ~18% |
| Two overcards vs. low pair | AK vs 22 | ~49% | ~51% |
| Dominated hand | AK vs AQ | ~74% | ~26% |
| Two high cards vs. two low cards | AK vs 72 | ~65% | ~35% |
| Suited connectors vs. overpair | 98s vs AA | ~22% | ~78% |
The so-called coin flip stands out.
This means two high cards against a low pair.
The pair is a small favorite because it is already a made hand.
However, once one of the high cards hits the board, the equity changes sharply.
This situation often occurs in tournaments during pre-flop all-in confrontations.
Frequently asked questions about poker hand odds
odds for = win / lossA probability of 20% means you win 1 out of 5 times. That gives odds of 1 : 4.
The other way around:
1 : 4 = 1 / (1 + 4) = 20% probabilityFinal thoughts
Insight into hand odds and probabilities forms a foundation of good poker strategy.
The frequency table shows how rare strong hands really are.
Meanwhile, pot odds logic determines when a call or fold is the most profitable choice.
The warning about two-card odds is crucial.
Players who use the next card as their benchmark avoid profitable-looking calls that still lose money.
Combine this with the percentage method or ratio method for quick calculations at the table.