# Poker Outs Calculator

> Computes the exact probability of hitting one of your outs by the next card or by the river in Texas hold'em from the number of outs and unseen cards, expressed as a percentage and as odds against, and compares it with the rule of 2 and 4 estimate.

- Calculator id: `poker-outs` · Category: Games & Betting Math (`gaming`) · Tool name: `calculate_poker_outs`
- Canonical page: https://tttkmbb.com/gaming/poker-outs · This document: https://tttkmbb.com/gaming/poker-outs.md · JSON definition: https://tttkmbb.com/gaming/poker-outs.json

## Purpose

Computes the exact probability of hitting one of your outs by the next card or by the river in Texas hold'em from the number of outs and unseen cards, expressed as a percentage and as odds against, and compares it with the rule of 2 and 4 estimate.

**Use when:** You know how many cards complete your hand and want the exact probability of hitting by the turn or the river, or the odds against to compare with pot odds.

**Do not use when:** You need the probability of specific starting hands or made hands (use combinations-permutations or hypergeometric-distribution), or games with a different deck. Mathematics only; not gambling advice.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `outs` | integer |  | required | Number of unseen cards that complete your hand (flush draw 9, open-ended straight draw 8, gutshot 4). (min 1, max 20) |
| `street` | enum: flop_to_river \| turn_to_river \| flop_to_turn |  | optional, default "flop_to_river" | Which cards are still to be dealt; sets the number of cards to come and the default count of unseen cards (52 minus your 2 hole cards and the board). |
| `unseen_cards` | integer |  | optional | Optional: cards not visible to you, if it differs from the default (e.g. 45 with one known folded card). Must be larger than outs. (min 2, max 50) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `probability_percent` | number | % | One card: outs/unseen; two cards: 1 − C(unseen − outs, 2)/C(unseen, 2). |
| `odds_against` | string |  | (1 − p)/p expressed as "x : 1", for comparison with pot odds. |
| `odds_against_ratio` | number |  | (1 − p)/p as a number. |
| `rule_of_2_and_4_percent` | number | % | outs × 2 with one card to come, outs × 4 with two cards to come. |
| `exact_vs_rule_difference` | number | percentage points | rule_of_2_and_4_percent − probability_percent; positive means the rule overestimates. |
| `cards_to_come` | integer |  | 1 or 2 according to the street. |
| `unseen_cards_used` | integer |  | Number of unseen cards the probability was computed with. |

## Formula

`one card: p = outs / unseen; two cards: p = 1 − C(unseen − outs, 2) / C(unseen, 2); odds_against = (1 − p) / p; rule_of_2_and_4 = outs × 2 (one card) or outs × 4 (two cards)`

Hypergeometric drawing probabilities that treat every card you cannot see (including other players' folded cards) as equally likely to be next. Probability mathematics only; not gambling advice.

## Data Sources

- Poker probability – Texas hold 'em outs and drawing odds (Wikipedia) — https://en.wikipedia.org/wiki/Poker_probability (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/poker-outs?outs=…`
- `POST https://tttkmbb.com/api/v1/calculate/poker-outs` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/poker-outs · OpenAPI operationId `calculate_poker_outs` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "poker-outs", "inputs": {…}}`

## Example

- Flush draw (9 outs) on the flop, two cards to come: inputs `{"outs":9,"street":"flop_to_river"}` → `{"probability_percent":34.97,"odds_against":"1.86 : 1","odds_against_ratio":1.86,"rule_of_2_and_4_percent":36,"exact_vs_rule_difference":1.03,"cards_to_come":2,"unseen_cards_used":47}`
- Flush draw (9 outs) on the turn, one card to come: inputs `{"outs":9,"street":"turn_to_river"}` → `{"probability_percent":19.57,"odds_against":"4.11 : 1","rule_of_2_and_4_percent":18,"exact_vs_rule_difference":-1.57,"cards_to_come":1,"unseen_cards_used":46}`

```
GET https://tttkmbb.com/api/v1/calculate/poker-outs?outs=9&street=flop_to_river
```

## Limitations

You need the probability of specific starting hands or made hands (use combinations-permutations or hypergeometric-distribution), or games with a different deck. Mathematics only; not gambling advice. Hypergeometric drawing probabilities that treat every card you cannot see (including other players' folded cards) as equally likely to be next. Probability mathematics only; not gambling advice. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why 47 unseen cards on the flop and 46 on the turn?**

52 cards minus your 2 hole cards and the 3 flop cards leaves 47; after the turn card 46. Cards in other players' hands or the muck are unseen and therefore still counted.

**How do I compare the result with pot odds?**

Odds against of 1.86 : 1 means you need the pot to offer at least 1.86 units for every unit you call to break even on this street alone (ignoring implied odds).

**Should I count outs that give an opponent a better hand?**

No; discount tainted outs (e.g. a flush card that also pairs the board for a possible full house) before entering the number.

## Related

- [Hypergeometric Distribution Calculator](https://tttkmbb.com/statistics/hypergeometric-distribution.md) — Probability of k successes when drawing without replacement, the general form of this calculation.
- [Combinations and Permutations Calculator](https://tttkmbb.com/math/combinations-permutations.md) — The C(n, 2) counts used for two cards to come.
- [Probability of Two Events Calculator](https://tttkmbb.com/statistics/probability-of-events.md) — Combine the drawing probability with other events.