# What are my poker odds of hitting?

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.

- Page: https://www.acalculator.org/game/poker-odds-calculator
- JSON spec: https://www.acalculator.org/game/poker-odds-calculator.json
- Version: 9424c08ac63c

## Default answer

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).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| outs | Outs | The number of unseen cards that would give you the hand you want (9 for a flush draw). |
| street | Cards to come | On the flop, two cards are still to come (turn and river); on the turn, one card (the river). |
| pot | Pot before the call | The money in the pot, including the bet you face, before you call. |
| call | Amount to call | The amount you must put in to call. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| chance | Chance to hit by the river | The exact chance that at least one of the cards to come is one of your outs. |
| next | Chance to hit on the next card | Outs ÷ unseen cards: 47 on the flop, 46 on the turn. |
| oddsAgainst | Odds of hitting by the river | Misses to hits as “x to 1 against” when a miss is at least as likely, else hits to misses as “x to 1 in favour”; 2 decimals. |
| rule | Rule of 4 and 2 | The quick estimate: outs × 4 on the flop, outs × 2 on the turn, in percent. |
| breakEven | Break-even chance for the call | The chance a call needs to break even on this bet alone: call ÷ (pot + call). |
| potOdds | Pot odds | The pot to the call, as “x to 1”, rounded to 2 decimals. |

## 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).

## Assumptions

- 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.

## Worked examples

1. outs = 9, street = flop, pot = $100.00, call = $20.00 gives chance = 34.967623%, next = 19.148936%, oddsAgainst = 1.86 to 1 against, rule = 36%, breakEven = 16.666667%, potOdds = 5 to 1. Source: hand calculation in content.mdx: 1 − (38 × 37) ÷ (47 × 46) = 756/2162 = 34.97% (flush draw).
2. outs = 8, street = turn gives chance = 17.391304%, next = 17.391304%, rule = 16%, oddsAgainst = 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, street = flop, pot = $50.00, call = $50.00 gives chance = 54.116559%, rule = 60%, breakEven = 50%, potOdds = 1 to 1, oddsAgainst = 1.18 to 1 in favour. Source: hand calculation in content.mdx: 1 − (32 × 31) ÷ 2162 = 1170/2162 = 54.12%.

## FAQ

### 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.

## Sources

- Grinstead and Snell, Introduction to Probability, 2nd ed., American Mathematical Society, section 3.2, combinations: https://math.dartmouth.edu/~prob/prob/prob.pdf
- Wikipedia, Poker probability (Texas hold ’em, outs): https://en.wikipedia.org/wiki/Poker_probability
- Wikipedia, Pot odds: https://en.wikipedia.org/wiki/Pot_odds
- National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/