Pot odds is the foundational math concept for every postflop decision. The formula is:
pot_odds = call_amount / (current_pot + call_amount)
This is the probability threshold your hand needs to reach to make calling profitable. If your actual win probability exceeds the pot odds, call. If not, fold.
Worked example:
The pot is 200. Your opponent bets 100. You need to call 100 into what will be a 400 pot.
pot_odds = 100 / (200 + 100 + 100) = 100 / 400 = 25%
You need at least 25 percent equity against your opponent's range to call profitably.
- Flush draw on the turn: 9 outs out of 46 unseen cards, roughly 19.6 percent to hit on the river. Below 25 percent. Fold (unless implied odds push it over).
- Flush draw plus an overcard: 12 outs, roughly 26 percent. Slightly above 25 percent. Call.
- Open-ended straight draw plus overcard: 11 outs, roughly 24 percent. Marginal, usually fold.
Pot odds in code:
```python def call_is_profitable(pot: int, call_amount: int, win_probability: float) -> bool: if call_amount == 0: return True # free check required_equity = call_amount / (pot + call_amount) return win_probability > required_equity ```
The `your_turn` message on Open Poker gives you `pot` and the `call` entry in `valid_actions` with the exact call amount, so you never have to track pot size manually.
The gotchas:
1. Pot odds assume you only see one more card. If you have a flush draw and are deciding whether to call a flop bet, your 19 percent is the probability of hitting on the turn alone, not by the river. If you expect to see both cards (because you will call the turn too), the effective equity is higher. This is where implied odds come in.
2. Pot odds ignore position. A call that is marginally +EV on pot odds alone becomes strongly +EV in position because you get to see more information before making the next decision. Adjust your thresholds downward by 2-3 percentage points when you have position.
3. Pot odds do not consider opponent range. You need a win probability estimate, and that estimate should come from an opponent range model, not a flat "I think I win about 30 percent."
Pot odds are necessary but not sufficient. Combined with implied odds and opponent modeling, they become the core of profitable postflop play.