Counting Outs in Texas Holdem

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An "out" in poker is simply a card that can improve the value of your hand. For example, you hold JT in the pocket, the flop comes 389. At this point you have four consecutive cards (89TJ), which would form a completed straight with the addition of one of two specific cards (7 or Q). This kind of draw is called an open-ended straight draw. Since there are four 7s and four Qs in the deck, you have eight outs to complete your hand. An open-ended straight draw is a very common situation in Hold'em.

Another very common situation is a flush draw. Assume you have A(d)Q(d) in the pocket (a semi-strong starting hand). The board comes 4(s)T(d)J(d). With the two diamonds on the board you now have four diamonds, giving you a one card draw to a flush. Any diamond on the turn or the river will give you a five diamonds, a flush. Note also that you have the best possible flush because you hold the A(d) (unless a 7(d), 8(d), and/or 9(d) comes making a potential straight flush.) The best possible hand in poker, given the cards on the board, is called the nuts. With the above flop, you have nine outs to the nut flush, a very strong draw. (And, of course, you also have an inside straight draw with any K and a royal flush draw with the K(d). This is a very big drawing hand.)

In order to estimate the value of outs, we will approximate the percent of time that you will get the card you need by the 4&2 rule. If you have outs on the flop (with two cards to come), the 4&2 rule states that you will complete your hand by the river about four times the number of outs expressed as a percent. So using the first example in which there are eight outs drawing to an open-ended straight, you will get a Q or 7 to complete your straight about 32 (4 times 8) percent of the time. If you are counting outs on the turn (with one card to come), then you will have about two times the number of outs expressed as a percent. On the turn, an open-ended straight draw with eight outs will complete a straight about 16 percent of the time. Using the same procedure, a flush draw on the flop has a 36 (4 times 9 outs) percent chance to complete by the river. On the turn, a flush draw has an 18 (2 times 9 outs) percent chance.

Look back at the second example above, given the flop (the board is 4(s)T(d)J(d), a suited [two diamonds], ranked [JT], combo [JT] flop), how many outs do you actually have to win the hand if you are holding A(d)Q(d)? We already know that the flush draw gives nine outs. Notice also there is an inside straight draw if a K falls. In this case, any K will make a straight. Since you have already counted the K(d) as part of your flush draw outs, there are three additional K's in the deck that will make a straight.

In addition to the straight draws, you might win the hand if your A or Q pairs, because the A and Q are overcards to the board, giving you an additional three A's and three Qs as possible outs. The total number of potential outs for this hand is 9 (flush draw) + 3 (inside straight draw) + 3 (pair Aces draw) + 3 (pair Queens draw) = 18 outs total. Suited, ranked, combo flops like this one can produce situations with a high number of outs. Your opponents will frequently have a large number of apparent outs with a highly coordinated board, so expect vigorous betting.

Should you use 18 outs to estimate your chances of winning the hand? Let's assume you have only one opponent and that he made a standard raise pre-flop (about three times the big blind) from a late middle position (say position 5), which you just called with your A(d)Q(d) in the button position (position 7). When your opponent acts after the flop, he leads out with a bet of about one-half the pot. What does he hold and how does his holding affect your computation of outs?

There are two ranked cards on the board. If your opponent is a reasonable bettor, from late middle position he could easily have raised with AK, AQ, AJ, or even AT, KQ, KJ, KT, and perhaps QJ, AA, KK, or QQ. If he were holding a lower pair (JJ, TT, 99, 88, etc), he should have been tempted to raise more than a standard raise to make the call very expensive and thereby discourage a potential caller. He has also made a bet, more or less, in the possible range of standard continuation bets after the flop. He is probably not afraid of a call or raise here.

The best hand he might hold right now is three Js or three Ts. More likely, he holds a high pair (AA, KK, QQ), or a pair of Js or Ts with a strong kicker. Under any of these cases, the hand he now holds probably beats your current hand. If he holds an AJ, AT, QQ, or QJ, he already has a pair. The A or Q in your hand is counterfeited because, when another A or Q falls on the board, your opponent would make two pair or three of a kind, beating your made pair of A's or Q's.

Under these circumstances, the outs associated with the A and Q in your hand should be discounted. Rather than 18 outs, you probably have 12 to 15 solid outs (nine flush draw cards and three Ks), for a minimum 48 (4 times 12) percent chance of completing the hand by the river. Notice that if a K comes on the board, and if your opponent is holding AK, KK, KQ, KJ, or KT, he will be beaten because you would complete at least a straight. Clearly, however, with the holdings and flop discussed, you need to hit one of your outs to have any real confidence you can take the pot, so bet accordingly.