Hong Life CalculatorsUnderstanding the poker pot odds and equity calculator — concept and principle
When an opponent bets and you hold a drawing hand in Texas Hold'em, the decision to call comes down to two numbers: the share of the final pot you must pay (pot odds) and the chance your hand improves to a winner (equity). This calculator gives both, using the exact draw probability and the quick "rule of 2 and 4".
How it is calculated
- Pot odds (equity needed): call ÷ (pot + call) × 100. "Pot before call" should already include your opponent's bet.
- Exact equity, two cards to come (flop to river): 1 − [(47 − outs) ÷ 47] × [(46 − outs) ÷ 46]. After the flop you know 5 cards (your 2 and the 3 on the board), so 47 are unseen.
- Exact equity, one card to come: outs ÷ 46 (on the turn, 46 cards are unseen).
- Rule of 2 and 4: outs × 4 with two cards to come, outs × 2 with one.
- +EV? "yes" when your equity is greater than the equity needed.
The principle
Calling is profitable in the long run when the money you expect to win exceeds the money you put in. If you call C into a pot of P and win with probability E, your expected profit is E × (P + C) − C. Setting this to zero gives E = C ÷ (P + C), the pot-odds threshold. The exact draw formula counts the opposite event: the chance that you miss on the turn and miss again on the river, then subtracts it from one.
Worked example
- Inputs: pot 100, call 25, 9 outs (a typical flush draw), two cards to come.
- Pot odds: 25 ÷ (100 + 25) = 25 ÷ 125 = 20%.
- Miss on the turn: 38 ÷ 47; miss again on the river: 37 ÷ 46. Product = 0.6503.
- Exact equity: 1 − 0.6503 = 34.97%.
- Rule of 4: 9 × 4 = 36%, a close shortcut.
- 34.97% is greater than 20%, so the call is +EV: yes.
| Pot before call | Pot odds (equity needed) |
|---|---|
| 25 | 50% |
| 50 | 33.33% |
| 75 | 25% |
| 100 | 20% |
| 125 | 16.67% |
| 150 | 14.29% |
| 200 | 11.11% |
How to read the result
The gap between your equity and the equity needed is your edge. Here you need 20% and have about 35%, a comfortable call. Typical outs: an open-ended straight draw has 8 (about 31.5% by the river), a flush draw 9 (35%), and a flush plus open-ended straight draw 15 (about 54%). With one card to come, the same flush draw is only 9 ÷ 46 = 19.6%.
Common mistakes
- Leaving the opponent's bet out of the pot, which makes your pot odds look worse than they are.
- Counting "dirty" outs that complete your hand but also give the opponent a better one.
- The rule of 4 overstates equity with many outs: 15 outs gives 60% by the rule but 54.1% exactly.
Frequently asked questions
What is the difference between pot odds and implied odds?
Pot odds use only the money in the pot now. Implied odds add the chips you expect to win on later streets if you hit.
How do I turn pot odds into a ratio like 4 to 1?
Divide pot by call: 100 : 25 is 4 : 1, which matches needing 1 ÷ (4 + 1) = 20% equity.
Why 47 unseen cards when other players hold cards too?
You cannot see their cards, so from your point of view they are random among the 47. On average this gives the same probability.
Sources: David Sklansky, The Theory of Poker, Two Plus Two Publishing (pot odds and implied odds)