Poker math
Poker probabilities cheat sheet: the odds every player should know
MyClubGG Editorial Team 4 min readUpdated हिन्दी में पढ़ें
Quick answer
The poker odds worth memorising are few: you are dealt a pocket pair 5.9% of the time, a pair flops a set about 11.8% of the time, and a flush draw hits by the river 35% of the time from the flop. Combine these with pot odds (a half-pot bet needs 25% equity) and you can make most calls correctly.
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In this article
How to use this cheat sheet
You don’t need to be a maths whizz to play good poker. You need a handful of numbers you know by heart and the habit of comparing them to the price you are paying. This page collects the ones that come up most. For the method behind them, see our poker math lessons.
Starting-hand odds
There are 1,326 possible two-card starting hands, which group into 169 distinct hands. Each pair has 6 combos, each suited hand 4 and each offsuit hand 12.
|
You are dealt… |
Probability |
Roughly 1 in… |
|---|---|---|
|
Any pocket pair |
5.9% |
17 |
|
A specific pair (e.g. A♠ A♥ or any AA) |
0.45% |
221 |
|
A-K (suited or offsuit) |
1.2% |
83 |
|
Two suited cards |
23.5% |
4 |
So if you are waiting for aces, expect to wait around 221 hands on average. Browse every hand in our starting hands guide.
Flop odds
|
Situation |
Chance on the flop |
|---|---|
|
Pocket pair flops a set or better |
≈11.8% (1 in 8.5) |
|
Unpaired hand pairs one of its hole cards |
≈32.4% |
|
Two suited cards flop a flush |
0.84% |
|
Two suited cards flop a flush draw |
≈10.9% |
Two lessons hide in this table. First, set mining works only when stacks are deep enough to win a big pot the 1 in 8.5 times you hit. Second, unpaired hands miss the flop about two-thirds of the time, which is why continuation bets work so often.
Outs: from count to percentage
|
Typical draw |
Flop → river (two cards) |
Turn → river (one card) |
|
|---|---|---|---|
|
4 |
Gutshot |
16.5% |
8.7% |
|
6 |
Two overcards |
24.1% |
13.0% |
|
8 |
Open-ended straight draw |
31.5% |
17.4% |
|
9 |
Flush draw |
35.0% |
19.6% |
|
15 |
Flush draw + open-ender |
54.1% |
32.6% |
The rule of 2 and 4 gets you close: multiply outs by 4 with two cards to come, or by 2 with one. Nine outs × 4 = 36%, against the exact 35.0%. Clean outs are the ones that give you the best hand without helping your opponent.
Preflop equity and famous match-ups
Against a random hand
If all the chips went in before the flop, here is how often each hand wins against one random hand:
|
Hand |
Equity vs 1 random hand |
|---|---|
|
AA |
85.3% |
|
KK |
82.5% |
|
AKs |
67.0% |
|
AKo |
65.4% |
|
22 |
50.4% |
|
72o |
34.5% |
|
32o |
32.3% |
Against five random hands, AA drops to 49.6% and 72o to 8.5%, the lowest of all 169 hands. More opponents means less equity for everyone, even aces.
Famous match-ups
|
Match-up |
Result (all boards) |
|---|---|
|
AA vs KK |
AA wins 81.1%, ties 0.4% |
|
QQ vs AKo |
QQ wins 57.0% |
|
22 vs AKo |
22 wins 52.7% |
|
AKs vs QQ |
AKs wins 46.0% |
|
AQo vs AKo |
AQo wins 23.7%, ties 4.6% |
|
KQo vs AJo |
KQo wins 40.1% |
The classic “coin flip” (pair vs two overcards) is close to 50/50 but slightly favours the pair. A dominated hand like AQ against AK is in serious trouble. Test your own match-ups with the poker odds calculator.
Final-hand odds in Hold’em
How often your best five cards out of seven (two hole cards plus five on the board) make each hand:
|
Hand |
Probability |
|---|---|
|
Royal flush |
1 in 30,940 |
|
Straight flush |
1 in 3,590 |
|
Four of a kind |
1 in 595 |
|
Full house |
2.6% |
|
Flush |
3.0% |
|
Straight |
4.6% |
|
Three of a kind |
4.8% |
|
Two pair |
23.5% |
|
One pair |
43.8% |
|
High card |
17.4% |
Two pair or better turns up a lot more than beginners expect, which is why one pair is rarely strong at showdown in a big pot. See every hand explained in our poker hand rankings.
Pot odds and bluff odds
To call a bet of X when the pot (including that bet) is P, you need equity of X ÷ (P + X). A bluff of size B into a pot P needs to work B ÷ (P + B) of the time.
|
Bet size |
Equity needed to call |
How often a bluff must work |
|---|---|---|
|
⅓ pot |
20% |
25% |
|
½ pot |
25% |
33% |
|
⅔ pot |
28.6% |
40% |
|
Pot |
33% |
50% |
|
2× pot |
40% |
67% |
Worked example: on the turn the pot is 60bb and your opponent bets 30bb (half pot). You have a flush draw: 9 outs, 19.6% with one card to come. You need 25%, so a pure call loses chips unless you expect to win extra on the river. Check spots like this with the pot odds calculator.
Common mistakes with odds
- Using the two-card number with one card to come. If your opponent will bet again on the turn, you only get one card for this call.
- Counting dirty outs. A card that completes your straight but also makes someone else’s flush is not a clean out.
- Ignoring how many opponents are in. Equity against one player and against four are very different.
- Remembering results, not decisions. A 19.6% draw will hit about one time in five. That is maths, not bad luck.
Frequently asked questions
What are the odds of being dealt pocket aces?
About 0.45%, or 1 in 221 hands. Any pocket pair at all comes about 1 in 17 hands.
How often does a flush draw hit?
From the flop to the river it hits 35.0% of the time; with one card to come it is 19.6%.
What is the probability of flopping a set?
With a pocket pair you flop a set or better about 11.8% of the time, roughly 1 in 8.5 flops.
What equity do I need to call a pot-sized bet?
About 33%. You are calling one pot to win a final pot of three, so you need to win one time in three.