Pot odds and the rule of 2 and 4
Pot odds tell you what a call costs against what you can win. The rule of 2 and 4 turns your outs into a quick estimate of your chance to hit. Put them side by side and you know whether a call is worth it.
- pot odds: The price of a call: your call ÷ everything in the middle once you call. Win more often than that and calling pays.
- outs: The unseen cards that would turn your hand into the likely winner.
- rule of 2 and 4: A quick equity guess: outs × 4 when you will see both the turn and the river (someone is all in), otherwise outs × 2 per card to come.
- equity: Your share of the pot if every card were dealt out: how often your hand wins from here.
Counting outs
Cards that help
An out is an unseen card that completes your draw and should win the pot. On the flop you see 5 cards, so 47 are left. Hold four of one suit, a flush draw: 13 hearts − the 4 you can see = 9 make the flush.
A flush draw: 9 outs A♥5♥K♥9♥2♦
Open-ended straight draws
Four ranks in a row with room at both ends is an open-ended straight draw. A card at either end makes the straight, so 9-8-7-6 fills with any 10 or any 5. Each rank has four cards: 4 Tens + 4 Fives = 8 make the straight.
Open-ended: any 10 or any 5, 8 outs 9♣8♦7♠6♥2♣
Gutshots
One rank missing from the middle is a gutshot: only that rank fills it, so 4 outs, half an open-ender. J-Q-K-A and A-2-3-4 can only be filled at one end: 4 outs too. Two gutshots at once, a double gutshot, has 8, like an open-ender.
Gutshot: only any 10, 4 outs 9♣8♦J♠7♥2♣
Never count a card twice
A flush draw and a straight draw at once: 8 cards make the straight and 9 make the flush. But 2 of them make both, so they are on both lists. Count each card once: 8 + 9 − 2 = 15 outs.
15 outs, not 17 J♥10♥Q♥9♣2♥
Rule of 2 and 4
Times 4, times 2
The rule of 2 and 4: each card to come gives each out about a 2% chance. With the turn and river to come, outs × 4; with one card, outs × 2. 9 outs, both to come: 9 × 4 = 36%; counting every card gives 35.0%.
9 outs × 4 = about 36% A♥5♥K♥9♥2♦
A flop call buys one card
Times 4 assumes you will see both cards. If nobody is all in, a friend can bet again on the turn, so a call on the flop buys only the turn: use times 2 for that call. Times 4 is for when someone is all in.
Where the rule drifts
The rule runs high with lots of outs: with 15 outs and both cards to come it says 60%, and the exact chance is 54.1%. For big draws, take away the outs over 8: 60 − 7 = 53%.
15 outs: about 60% by the rule, 54.1% exactly J♥10♥Q♥9♣2♥
The price of a call
Before you call, work out the price: your call ÷ everything in the middle after your call. A 30 bb pot, a bet of 10, your call of 10: 10 ÷ (30 + 10 + 10) = 10 ÷ 50 = 20%. Win more often than that.
A caller before you
If another friend called the bet before you, their chips go in the middle too, and your price drops. Same 30 pot and 10 bet, a call of 10, then yours: 10 ÷ 60 = 16.7%. Count any calls before yours.
The same price as odds
Players also say the price as odds: what is in the middle against your call. 40 in the middle against your 10 to call is 4 to 1. It is the same thing as 10 ÷ 50 = 20%.
Outs to chances
The rule's estimate against the exact figure for the draws above, with every runout counted. The rule runs a little high for big draws.
| Draw | Outs | Two cards to come | One card to come |
|---|---|---|---|
| Gutshot straight draw | 4 | rule 16%, exact 16.5% | rule 8%, exact 8.7% |
| Open-ended straight draw | 8 | rule 32%, exact 31.5% | rule 16%, exact 17.4% |
| Flush draw | 9 | rule 36%, exact 35.0% | rule 18%, exact 19.6% |
| Flush draw with a gutshot | 12 | rule 48%, exact 45.0% | rule 24%, exact 26.1% |
| Flush draw with an open-ended straight draw | 15 | rule 60%, exact 54.1% | rule 30%, exact 32.6% |
Questions
What are pot odds in poker?
The price of a call: your call ÷ everything in the middle once you call. Win more often than that and calling pays. The pot is 20 and a friend bets 10. Call 10 and 40 is in the middle: 10 ÷ 40 = 25%, so you need to win at least 1 time in 4. Said as odds: 30 to 10, or 3 to 1.
What are outs in poker?
The unseen cards that would turn your hand into the likely winner. You hold four hearts after the flop, so the 9 hearts left are your outs.
What is the rule of 2 and 4 in poker?
A quick equity guess: outs × 4 when you will see both the turn and the river (someone is all in), otherwise outs × 2 per card to come. 9 outs on the flop with someone all in: about 36% by the river. With one card to come: about 18%.
Practise it in 5 minutes The pot math lessons, free.
Quads is for adults, 18 and over. It teaches with play chips only: there is no real money, ever.