acalculator

What are my poker odds of hitting?

Enter your outs and how many cards are to come to see the exact chance to hit, and the pot and call to see the break-even chance. The results are mathematics, not advice.

Your numbers

Cards to come
Pot odds
Chance to hit by the river
34.97%

Outs: 9. The chance to hit by the river is 34.97% (1.86 to 1 against).

Chance to hit on the next card
19.15%
Odds of hitting by the river
1.86 to 1 against
Rule of 4 and 2
36%
Break-even chance for the call
16.67%
Pot odds
5 to 1

Chance to hit by the river: 34.97%. Outs: 9. The chance to hit by the river is 34.97% (1.86 to 1 against).

Chance to hit by the river by outs

The results are maths only. They are not betting advice or a promise of a return. Bet only what you can afford to lose. For help with gambling, call 1-800-GAMBLER. Terms of use

How to calculate

Computes the exact chance of hitting one of your outs in Texas hold’em by the river or on the next card, compares it with the rule of 4 and 2, and gives the break-even chance from the pot odds.

Example with the default inputs (Outs 9, Cards to come On the flop (2 to come), Pot before the call $100.00, Amount to call $20.00): Outs: 9. The chance to hit by the river is 34.97% (1.86 to 1 against).

Method: Flop: P(hit by river) = 1 − C(47 − outs, 2) ÷ C(47, 2) = 1 − (47 − outs)(46 − outs) ÷ 2162; turn: outs ÷ 46. Break-even chance = call ÷ (pot + call).

  • Only your two cards and the board are known: every unseen card is equally likely to come, including cards other players hold or folded.
  • Every out gives you the hand you want and no out also helps an opponent more.
  • The flop chance counts both the turn and the river, as when all the money goes in on the flop.
  • Results are mathematics, not advice.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Outs 9, Cards to come On the flop (2 to come), Pot before the call $100.00, Amount to call $20.00 gives Chance to hit by the river 34.967623%, Chance to hit on the next card 19.148936%, Odds of hitting by the river 1.86 to 1 against, Rule of 4 and 2 36%, Break-even chance for the call 16.666667%, Pot odds 5 to 1.Source: hand calculation in content.mdx: 1 − (38 × 37) ÷ (47 × 46) = 756/2162 = 34.97% (flush draw)
  2. Outs 8, Cards to come On the turn (1 to come) gives Chance to hit by the river 17.391304%, Chance to hit on the next card 17.391304%, Rule of 4 and 2 16%, Odds of hitting by the river 4.75 to 1 against.Source: hand calculation in content.mdx: 8 ÷ 46 = 17.39% (open-ended straight draw on the turn)
  3. Outs 15, Cards to come On the flop (2 to come), Pot before the call $50.00, Amount to call $50.00 gives Chance to hit by the river 54.116559%, Rule of 4 and 2 60%, Break-even chance for the call 50%, Pot odds 1 to 1, Odds of hitting by the river 1.18 to 1 in favour.Source: hand calculation in content.mdx: 1 − (32 × 31) ÷ 2162 = 1170/2162 = 54.12%

How it works

On the flop you can see 5 cards (your 2 and the 3 on the board), so 47 are unseen. On the turn, 46 are unseen. Every unseen card is equally likely to come.

On the flop (two cards to come). You miss only when both the turn and the river are non-outs. The number of ways to choose 2 of the 47 unseen cards is C(47, 2) = 47 × 46 ÷ 2 = 1,081, and the ways to choose 2 non-outs is C(47 − outs, 2). So:

P(hit by the river) = 1 − C(47 − outs, 2) ÷ C(47, 2) = 1 − (47 − outs)(46 − outs) ÷ (47 × 46)

The next card (the turn) hits with chance outs ÷ 47.

On the turn (one card to come). P(hit) = outs ÷ 46, which is also the next-card chance.

Other outputs:

  • Odds of hitting, from the exact numbers of misses and hits (turn and river pairs on the flop, cards on the turn): when misses are at least as many as hits, misses ÷ hits written “x to 1 against”; otherwise hits ÷ misses written “x to 1 in favour” (15 outs on the flop: 1170 ÷ 992 = “1.18 to 1 in favour”).
  • Rule of 4 and 2 = outs × 4 on the flop, outs × 2 on the turn, in percent.
  • Pot odds = pot ÷ call, written “x to 1”; the pot includes the bet you face. The division is exact on the decimal numbers as typed (1.005 ÷ 1 is exactly 1.005).
  • Both “x to 1” numbers are rounded to 2 decimals with halves rounded away from 0 (1.005 gives 1.01, 1.004 gives 1), and trailing zeros are dropped (5 to 1, 1.5 to 1).
  • Break-even chance = call ÷ (pot + call), in percent. It is shown only when both the pot and the call are entered. The pot must be above 0.

Outs may be from 1 to 20.

Assumptions

  • Cards other players hold or folded are unseen and count as possible.
  • Every out completes your hand, and none of them gives an opponent a better hand.

Worked examples by hand

9 outs on the flop (a flush draw), pot 100, call 20. P = 1 − (38 × 37) ÷ (47 × 46) = 1 − 1406/2162 = 756/2162 = 34.97%. Next card: 9 ÷ 47 = 19.15%. Odds: 1406/756 = 1.86 to 1 against. Rule of 4: 9 × 4 = 36%. Pot odds 100 ÷ 20 = 5 to 1, break-even 20 ÷ 120 = 16.67%.

8 outs on the turn (an open-ended straight draw). P = 8 ÷ 46 = 17.39%; odds 38 ÷ 8 = 4.75 to 1 against; rule of 2: 16%.

15 outs on the flop (a flush and straight draw), pot 50, call 50. P = 1 − (32 × 31) ÷ 2162 = 1170/2162 = 54.12%; rule of 4: 60%; odds 1170 ÷ 992 = 1.18 to 1 in favour. Pot odds 1 to 1, break-even 50%.

A note on gambling

These results are mathematics, not advice. Every hand can lose. If gambling is causing problems for you or someone you know, the US National Problem Gambling Helpline is 1-800-MY-RESET (call or text).

Other questions people ask

What are outs in poker?

Outs are the unseen cards that would give you the hand you are drawing to. A flush draw has 9 outs (13 cards of the suit minus the 4 you can see), and an open-ended straight draw has 8.

What are the odds of hitting a flush draw?

On the flop, with two cards to come, 9 outs hit 34.97% of the time: 1 − (38 × 37) ÷ (47 × 46). On the turn, with one card to come, 9 ÷ 46 = 19.57%.

What is the rule of 4 and 2?

A quick estimate: multiply your outs by 4 on the flop (two cards to come) or by 2 on the turn (one card). With 9 outs it gives 36% and 18%, against the exact 34.97% and 19.57%. It overestimates more as the outs grow: 15 outs give 60% against the exact 54.12%.

How do pot odds work?

Compare the call with the pot you can win. Calling 20 into a pot of 100 risks 20 to win 100, pot odds of 5 to 1. The call breaks even on this bet when you win 20 ÷ (100 + 20) = 16.67% of the time.

Why does the flop chance count both cards?

It is the chance to hit by the river if you see both the turn and the river, as when all the money goes in on the flop. If you face another bet on the turn, use the one-card chance for each street.