A "backdoor draw" is when you need both the turn and river cards to make your hand. This is also known as "runner-runner." An example would be when you hold two hearts and only one heart flops. You have a backdoor heart-flush draw since both the turn and river cards must be hearts for you to make a flush. Backdoor draws are normally viewed with disdain by otherwise decent players. Some players believe that they should be ignored and play no role in deciding whether or not to continue with a hand. The reason is, they are very unlikely to occur; therefore, they do not add greatly to your winning chances, according to some. In our example, what is the likelihood of catching a heart on both the turn and the river? On the turn, there are 10 hearts among 47 unseen cards. So, the likelihood of a heart showing up on the turn is 10/47. When this occurs, another heart has to show up at the river. At that point, there are nine hearts among 46 unseen cards, so the likelihood of a heart showing up at the river is 9/46. The probability of hearts showing up on both the turn and the river is (10/47) x (9/46), which is about 4.2 percent, or almost 23-to-1 against. Yet, despite the difficulty in making a backdoor draw, there are situations in hold'em in which having the backdoor draw turns a fold into a call. This is especially true when there are other ways of improving to the winning hand in addition to your backdoor draw. These situations tend to occur when the pot is large or when your pot odds are very favorable, as is often the case when you are in one of the blinds, usually the big blind.
On the other hand, some players use a backdoor draw as an excuse to continue with a hand that should be folded. When they catch a tenuous draw, like a gutshot-straight draw or just overcards, they think that any shortfall between their pot odds and their drawing odds are made up for when they have a backdoor draw. But in these cases, there are often other factors to consider. How many opponents are involved? How likely are you to win if you hit your primary draw? Often, when these other factors are taken into account, the backdoor draw does not add enough value to hang around.
Perhaps the following hands will illustrate some of these situations. Because the hands were taken from live play, not all of the decisions leading up to the problem in question are fully correct, but most of them are reasonable.
Hand No. 1 ($15-$30 game): You have the A
7 in the big blind. A solid player opens with a raise from under the gun. You know this player would raise from this position with only a pocket pair of tens or better, or A-K or A-Q, and nothing else. A middle-position player cold-calls, as does the cutoff. The other players fold, and you call. There is $130 in the pot and four players. The flop arrives with the 9 8
2
, giving you an ace overcard with a backdoor nut-flush draw as well as a runner-runner straight draw. You check, the preflop raiser bets, and the other two players fold. What should you do?
Answer: Call. There is $145 in the pot and it costs you $15 to call, so your current pot odds are almost 10-to-1. About 13 percent of the time you will catch an ace by the river. Given there's an ace in your hand, when one appears on the board, there is only one way for your opponent to have A-A, eight ways for him to have A-K, and eight ways for him to have A-Q, for a total of 17 hands. But there are 24 hands in which he has K-K, Q-Q, J-J, or 10-10. So, when an ace appears, you become a favorite to have the best hand. About 4 percent of the time you will make a flush. Another 4 percent of the time you will make a straight. When you hit either of these backdoor draws, you are an overwhelming favorite to have the best hand. Your overall winning chances are better than 20 percent by the river, which makes you a 4-to-1 dog. Also keep in mind that if you catch a 7, giving you a pair, you are only a slight underdog to have the best hand, since there are 24 hands in which your opponent has A-K or A-Q (given that you have an ace), and 27 hands in which he has pocket tens or better. Of course, there are many scenarios in which you will lose additional money on the turn when you call to see the river and don't catch anything. Occasionally, you will improve on the turn, only to have your opponent catch something at the river that gives him the best hand. You also could improve and lose, anyway. When these things happen, you lose additional money. But when your current pot odds are 10-to-1 and your drawing odds are 4-to-1, you have a large overlay. I believe your overlay, especially in a heads-up situation, merits calling here.
Hand No. 2 ($30-$60 game): You are in the big blind with the 9 8. An early-position player opens with a raise, the cutoff and button both call, and the small blind folds. You have observed that the early-position player limps in with tens, but raises with jacks or better, as well as A-K and A-Q. You call. There is $260 in the pot and four players. The flop arrives with the 10 5 2, leaving you with a runner-runner flush draw and a runner-runner straight draw. You check, the preflop raiser bets, and the other two players fold. What should you do?
Answer: Call. Let us examine this problem using a reasonable set of assumptions. There are 24 hands in which he has an overpair and 32 hands in which he has just overcards. So, more than half the time, an 8 or a 9 will be an out that gives us the best hand. We also will make a pessimistic assumption that our opponent will always bet the turn. When he doesn't, that helps our hand, giving us a free card to the river. It should be noted that many players will not follow through with a bet on the turn with just overcards after they have been called on the flop. Many of them will check it back on the expensive street, not realizing that they are frequently giving a free card instead of taking one. As an aside, when the turn does not get bet, we can catch an 8 or a 9 at the river and overtake his hand. If the turn is a queen or a 6, giving us a gutshot-straight draw, a free card allows us the possibility of making our gutshot straight at the river. Next, we will assume we will call his turn bet whenever a club appears (10 cards), a jack that is not a club (three cards), a 7 that is not a club (three cards), a 9 (three cards), and an 8 (three cards). This totals 22 cards among 47 unseen cards. When we make a hand that is better than one pair, we will bet the river; otherwise, we will check and call with only a pair. We will assume that he will call our river bet about half the time, either because he has an overpair, has caught top pair, or is worried about being bluffed out. We will make a pessimistic assumption that we lose all the time whenever we check, he bets the river, and we call, because we will assume that he would not bet the river with a good ace to show down. When we call and any one of the 25 blanks arrives on the turn, we have lost our $30 flop bet. So, mathematically, this is a loss of (25/47) x ($30), or about $16. Now, let us examine the other times when we catch a helping card. The likelihood of catching a flush card and missing at the river without even catching a pair is (10/47) x (31/46), which is about 14 percent. The likelihood of catching a nonclub jack or a nonclub 7 on the turn but missing our straight at the river without even catching a pair is (6/47) x (32/46), or about 9 percent. So, 23 percent of the time we will catch a flush draw or a straight draw on the turn and totally bust out at the river. When this happens, we will lose a $30 flop bet and a $60 turn bet, for a total of $90. So, our expected loss is ($90) x (23%), or about $20.
The chance of making a flush, a straight, two pair, or trips is about 8 percent. When this happens, we win the $290 that is already in the pot, plus another $60 on the turn, plus another $60 at the river about half the time (which adds about $30). So, our win figures to be $380. Our expected gain is ($380) x (8%), or about $30. Finally, we will make a lone pair about 22 percent of the time. His chances of having an overpair are about 43 percent. His chances of having overcards are 57 percent. Almost all of the scenarios in which he pairs one of his overcards on the turn or the river are already accounted for in the other cases. The only scenario unaccounted for would be the one in which we pair on the turn and he pairs one of his overcards at the river. The likelihood of this happening is on the order of 1 percent, and would have a negligible influence on the bottom line calculation, so we will ignore it. Therefore, we will assume that if we make a lone pair, we will win 57 percent of the time and lose 43 percent of the time. When we win, we will win the $290 already in the pot, plus $60 on the turn, but nothing at the river, so our win will be $350. Our expected win is (22%)x(57%)x($350), which is about $44. The other 43 percent of the time we will lose a $30 flop bet, a $60 turn bet, and a $60 river bet, for a total of $150. Our expected loss in this scenario is (22%)x(43%)x($150), which is $14. So, for the lone pair case, our expected win is $44-$14, or about $30.
Now, adding up all these cases results in a net profit of $24 (-$16-$20+$30+$30). This is slightly less than one small bet in our $30-$60 game. Note that without the backdoor draws, it would be wrong to continue beyond the flop.
Hand No. 3 ($30-$60 game): You are two off the button and open with a raise with the K 10. The cutoff three-bets and everyone folds to you. You call. There is $230 in the pot and two players. The flop is 7 6 5, leaving you with two overcards and a backdoor-flush draw. You check and your opponent bets. What should you do?
Answer: Fold. Your pot odds are almost 9-to-1 and you have six outs to top pair, which is a 7-to-1 shot. Does the backdoor-flush draw coupled with having a small overlay merit playing on? Not really. The problem is that even if you catch top pair, you have no way of knowing whether or not it is any good, since your opponent could have a bigger king or even a bigger 10 for his preflop three-bet, as well as any number of other holdings that beat you. So, when you improve, you cannot play aggressively. In fact, improvement may cost you additional money. The small benefit of having a backdoor draw does not compensate you enough for your weak holding and poor position.
Hand No. 4 ($10-$20 game): You are in early position and open with a raise with the A Q. Another early-position player, two middle-position players, and the big blind call. There is $105 in the pot and five players. The flop arrives with the K 8 3, giving you an overcard with a backdoor nut-flush draw. The big blind bets. What should you do?
Answer: Fold. A big blind who leads off into a crowd of four other players, including a preflop raiser, almost certainly has a top pair of kings, especially given a ragged, rainbow board like this one. You are dead to an ace (three outs) and a runner-runner flush. A three-outer is a 15-to-1 shot and your current pot odds are less than 12-to-1. Does the backdoor draw add enough value to take off a card here? No, because the majority of your winning chances stem from catching an ace, which may not win. But the real problem is that you are being bet into with three players behind you who cold-called your preflop raise. You could call now, only to be raised later. When this happens, it costs additional money to take off a card.
Hand No. 5 ($10-$20 game): You are in the big blind with the 10 6 and get a free play after an early-position player, a middle-position player, the button, and the small blind all limp in. There is $50 in the pot and five players. The flop comes 9 7
3, giving you a gutshot-straight draw with a backdoor-flush draw. You check, the early-position player bets, and the middle-position player and the button both call. The small blind folds. What should you do?
Answer: Fold. There is $80 in the pot and it costs you $10 to take off a card. Your current pot odds are 8-to-1. Your four-outer to a straight is an 11-to-1 shot. Unfortunately, your backdoor-flush draw does not turn this into a call. The reason is, your gutshot is not to the nuts and/or can be counterfeited at the river. One of your three opponents could have J-10, which is a common limping hand, giving him a bigger straight if an 8 arrives. The other problem is that an 8 may arrive on the turn but then get followed by a 10, 6, or jack at the river, making a larger straight or the same straight possible in one of your opponents' hands. These seem like remote possibilities, but in my opinion they negate the value of your backdoor-flush draw.
Editor's note: Jim Brier has co-authored a new book with Bob Ciaffone entitled Middle Limit Holdem Poker. It is available through Card Player.