The rule of 2 and 4
Estimating your chances without a calculator: outs times 4 on the flop, times 2 on the turn.
The rule of 2 and 4 is the handiest piece of mental arithmetic in poker: multiply your outs by 4 when two cards are still to come, and by 2 when one is left, and you have your chance of winning as a percentage. A flush draw on the flop with nine outs becomes roughly 36 percent, and about 18 on the turn. No tables, no software, just a multiplication you do while the action comes towards you.
First the outs, then the rule
The rule is step two of a sum that starts with counting outs: the number of cards that make your hand the best one. The standard numbers are quickly learned: four for a gutshot straight draw, eight for an open-ended straight draw, nine for a flush draw. If your out count is wrong, the prettiest multiplication still takes you the wrong way. Honest counting first, multiplying second. Do not forget the combined draws either: a flush draw plus an open-ended straight draw counts fifteen outs, and with monster draws like that the quick sum is the difference between hesitating and playing on with confidence.
Why times 2 and times 4 work
After the flop you know five cards: your own two and the three on the table. That leaves 47 unknown cards, so each out has a chance of 1 in 47 per card to come, rounded to 2 percent. With one card left, your chance is therefore roughly outs times 2. With two cards left you get almost twice that chance, hence times 4. The rule is not magic, it is a tidy rounding of a fraction you never want to work out exactly at the table. On the turn the fraction is even slightly kinder: 46 unknown cards instead of 47, which makes times 2 err on the cautious side and puts your true chance a fraction above the estimate.
How precise is the estimate?
Surprisingly precise, as long as your draw is of normal size. Nine outs on the flop: the rule says 36 percent, exactly it is 35. Eight outs: rule 32, exactly almost 32. Four outs on the turn: rule 8, exactly 8.7. In this range the deviation stays within about one or two percentage points, and no decision at the table hangs on that difference. What you then do with the percentage, at what price you may call, is the domain of equity and pot odds. A useful rule of thumb for rounding: with few outs the rule estimates a touch low, with many outs a touch high, so round in that direction and you are almost always on the right side.
The correction above eight outs
With big draws the times-4 version runs wide: fifteen outs times 4 would be 60 percent, while the true chance is 54. Happily the repair is just as simple: take outs times 4 and subtract the number of outs above eight. Fifteen outs: 60 minus 7 is 53, near enough. Twelve outs: 48 minus 4 is 44, against 45 truly. The times-2 version on the turn needs no correction; it stays close well beyond ten outs.
One warning about times 4
Times 4 assumes you actually get to see both cards to come. If your opponent bets the flop and you expect another bet on the turn that you cannot pay, then in reality you are buying only one card, and times 2 belongs there. So use times 4 mainly when you are all in or you see both cards for free. If you want to train this estimate until it runs automatically, try the free equity trainer: it lets you guess and then shows the true percentages.
frequently asked questions
Rule questions.
When do I use times 4 and when times 2? +
Times 4 on the flop, when two cards are still to come and you intend to see both. Times 2 on the turn, when one card is left. If you expect on the flop that you will have to fold to a bet on the turn, use times 2 there as well.
How far off is the rule of 2 and 4 from the true chance? +
Up to around eight outs the estimate sits within one or two percentage points of the exact figure. Nine outs, for instance, gives 36 percent by the rule and 35 percent exactly. Comfortably close enough for any decision at the table.
Does the rule still hold with a lot of outs? +
Above eight outs the times-4 version overstates more and more. The correction: take outs times 4 and subtract the number of outs above eight. Fifteen outs becomes 60 minus 7 is 53 percent, close to the true 54. The times-2 version needs no correction.
Why does this trick work at all? +
After the flop there are 47 unknown cards, so each out is about 1 in 47 per card, roughly 2 percent. One card to come means outs times 2, two cards to come means almost double that, hence times 4. The rule is simply that fraction, rounded for mental arithmetic.
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