Pot odds and equity
An opponent bets. You have a draw. You hesitate between call and fold. Most players decide on feel: "I'm drawing to a flush, I'll call." Feel is expensive. Here, the decision comes down to comparing two numbers, and you're going to learn to get them in ten seconds.
Pot odds: what you pay versus what you can win
Pot odds answer one question: what share of the final pot do you have to put in to continue?
pot odds = bet to call / final pot
The final pot is what's in the middle after your call: the pot before the bet, plus the opponent's bet, plus your call.
Example: the pot is 10 bb, the opponent bets 5 bb. If you call, the final pot is 10 bb + 5 bb + 5 bb, so 20 bb. You pay 5 bb for a final pot of 20 bb: your pot odds are 25.0%.
Remember the quick formula, the one the home page spot uses: pot odds = bet / (pot + 2 × bet), where the pot is the one before the bet.
Equity: your share of the pot
Equity is the share of the time you win the pot if all the remaining cards were dealt out. It doesn't depend on the bet: it depends on your hand, the board and what your opponent holds.
For a draw, you count it with outs: the cards that turn your hand into a winning hand.
The rule of outs, one card to come
If only one card is left to come:
equity = outs / unknown cards
The unknown cards are the ones you can't see: 52 minus your 2 cards, minus the community cards showing. On the flop (3 community cards), 47 are left. On the turn (4 community cards), 46.
A flush draw has 9 outs. On the turn, your equity is 9 / 46, so 19.6%. On the flop, if you only look at the next card, it's 9 / 47, so 19.1%.
Why "×2 / ×4" is only an approximation
You've surely heard it: "outs × 2 for one card, outs × 4 for two cards." That's a table shortcut, not a truth.
- One card, 9 outs: the shortcut gives 18.0%, the exact calculation 19.6%.
- Two cards, 9 outs: the shortcut gives 36.0%, the exact calculation 35.0%.
- Two cards, 15 outs: the shortcut gives 60.0%, the exact calculation 54.1%.
The more outs you have, the more "×4" overestimates. With a big draw, that's exactly where you make the wrong decision. Use the shortcut to get oriented, and the exact calculation for close spots.
The call / fold threshold
The rule fits on one line:
equity ≥ pot odds → call. equity < pot odds → fold.
You call if your share of the pot is at least what you put in to win it. Under the assumptions "only one card to come, all outs are clean, no implied odds," the calculation is exact, and that's what the home page spot has you practice.
Example 1: flush draw on the turn
Pot of 10 bb, opponent's bet of 5 bb. You have a flush draw: 9 outs.
- Final pot: 10 bb + 5 bb + 5 bb = 20 bb.
- Pot odds: 5 bb / 20 bb = 25.0%.
- Equity: 9 / 46 = 19.6%.
- Comparison: 19.6% is below 25.0%.
Fold, unless you have a real reason to expect extra winnings later (see the pitfalls).
Example 2: open-ended straight draw on the turn
Pot of 20 bb, opponent's bet of 5 bb. You have 8 outs.
- Final pot: 20 bb + 5 bb + 5 bb = 30 bb.
- Pot odds: 5 bb / 30 bb = 16.7%.
- Equity: 8 / 46 = 17.4%.
- Comparison: 17.4% is above 16.7%.
Call, but only just: the margin is 0.7 point. When the margin is that thin, a single dirty out is enough to flip the decision. Same bet, smaller pot, and this call became a fold.
Those 8 outs are clean because I set them up clean: that's the starting assumption. Now put cards on it. You hold 9♠8♠, the board reads T♥7♥2♥ 3♦. He bets with made flushes, sets and pairs of tens: A♥K♥, A♥Q♥, A♥J♥, A♥5♥, A♥4♥, K♥Q♥, K♥J♥, Q♥J♥, J♥9♥, 6♥5♥, TT, 77, 33, AT, KT, QTs, JTs, that's 49 combos. Against his flushes, your straight is worth nothing. Against his pairs of tens holding a heart, the 6♥ and the J♥ give him the flush. Net result: 6.0 outs on average instead of 8, and an exact equity of 13.6% against that range. Below the 16.7% price: the same call becomes a fold.
A two-card case from the lab's exercise series: flush draw on the flop against an all-in, pot of 10 bb, bet of 7.5 bb. Final pot 25 bb, pot odds 30.0%. The exact equity of the hand against the assumed opposing hand is 38.4%: call. After an all-in, no bet follows: the rule holds over two cards too, as long as you take the equity over both.
The pitfalls
- Dirty outs. An out that completes your draw but leaves you behind a stronger hand isn't an out. If your flush completes at the same time as the board pairs, or if the opponent already has a higher flush, you're counting too many outs. Remove the doubtful cards before you calculate.
- Made-up implied odds. "If I hit, he'll pay me off": possible, not certain. An opponent who folds on the river, or slows down when your draw arrives, pays you nothing extra. Implied odds get counted, they don't get assumed: without a specific reason, leave them out of the calculation.
- Forgetting the bet that follows. A call on the turn can cost you a second bet on the river. Your one-card equity only pays for the turn.
- Mixing up the pot and the final pot. If you forget to add your own call, your pot odds are wrong.
Key points
- Pot odds are what you pay divided by the final pot. Equity is your share of the pot. Equity at least equal to the pot odds: call.
- With one card to come, equity = outs / unknown cards. "×2 / ×4" is a shortcut that overestimates once you have many outs.
- Count only clean outs, and never assume implied odds without a reason.
Practice
- Play the home page spot: the call or fold spot gives you a draw and a bet, and shows you the calculation after your answer.
- Check your math with the calculator tool.