Counting Outs and the Rule of 2 and 4

What an out is

An out is any unseen card that gives you the best hand. With four cards to a flush, nine cards of your suit are left, so you have nine outs. An open-ended straight draw has eight, and a gutshot has four.

Only count outs that actually win. A flush card that also pairs the board can give your opponent a full house, so experienced players discount outs like that.

The rule of 2 and 4

Multiply your outs by 2 to estimate the chance of hitting on the next card. On the flop, if you will see both the turn and the river, multiply by 4.

With nine outs that gives 18% for one card and 36% for two. The exact figures are 19.1% (9 of 47 unseen cards) and 35.0%.

Exact odds for common draws

From the flop to the turn, with 47 unseen cards: a gutshot (4 outs) hits 8.5%, an open-ended straight draw (8 outs) 17.0%, a flush draw (9 outs) 19.1%, and a flush plus straight draw (15 outs) 31.9%.

From the flop to the river, seeing both cards: a gutshot hits 16.5%, an open-ended straight draw 31.5%, a flush draw 35.0%, and a flush plus straight draw 54.1%.

Where the rule breaks

Times 4 overestimates big draws because it counts hitting twice. With 15 outs it says 60% when the truth is 54.1%. A common fix above eight outs is to subtract one point for every out over eight: 15 outs gives 60 − 7 = 53%.

The rule also assumes you get to see both cards. If your opponent can bet again on the turn, use the one-card figure and compare it with your pot odds for this street only.

Questions

How many outs does a flush draw have?

Nine. There are 13 cards of each suit; you hold four between your hand and the board, which leaves nine.

Is the rule of 2 and 4 accurate?

Within a couple of points for draws up to about eight outs. For bigger draws, times 4 overestimates, so subtract one point for each out above eight.