Adjusting for Weak Draws in Limit Hold'em

It's tempting, when you hold a marginal hold'em hand, to look for reasons to continue. Among the reasons we often can spot if we're willing to look hard enough are inside-straight and backdoor-flush draws. All else being equal, inside straights come in about 16.5 percent of the time (5.1-1 odds against), and backdoor flushes come in only 3 percent of the time (a ridiculous 32.3-1 against). You can sometimes get odds to pursue an inside-straight draw on its own merits, although the conditions have to be just right. But what about the backdoor flush? Does any draw with such a small chance of coming in merit your attention? The backdoor-flush draw does have the advantage that by the turn, your odds will be either vastly improved or completely ruined. This makes it tempting to take off a card and see if something develops. And, of course, other good things can always happen: The turn may bring a scare card; you could pair up and/or get a free river card; or, your opponent may emit a tell, inviting you to steal the pot. But in terms of the value inherent in your cards, can the backdoor-flush draw ever factor into your decisions?



One time that the odds of making a backdoor flush might come into play is when your opponent has flopped a four-flush. In this case, if your backdoor draw is to a bigger flush, your opponent needs to hit exactly one of the suit instead of at least one. What's more, the extra suit in your hand is one less available to your opponent. With the flush ace in your hand, only one of your six overcard outs puts a scary three-flush on board. Without it, two of them will. How big a difference does all this make? We can check a few simple probabilities to get some idea.



Imagine that you have A-K with a board of the Q 6 2, and your opponent has a flush draw with, say, the J 9. You have the lead with your overcards. If your ace is a diamond, your opponent needs exactly one diamond, and you'll win 52.2 percent of the time. If your ace is in hearts, that not only throws another diamond back into the deck, but increases the chances that you'll pair up and still lose. Your winning rate drops all the way to 45.8 percent. The balance is delicate enough that you've gone from a slight favorite to a slight underdog. So, on the face of things, having the backdoor draw has made your hand more likely to be playable.



Suppose that the board is the Q 8 2, giving your opponent an inside-straight draw, as well. With the diamond, you'll win at showdown 44.8 percent of the time. Without it, you can expect to win only 38.8 percent of the time. From your opponent's point of view, having the inside-straight draw and those three extra outs means he has about an extra 7 percent chance of winning. But his adjustment for your backdoor flush is the same 6 percent (give or take), with or without the straight draw.



In themselves, these numbers aren't that meaningful. You'll rarely have such a good read on your opponent, especially in a limit game, that you can narrow his hand down to one of these possibilities. Your opponent could easily have complete garbage, or even the same hand that you have. Perhaps you don't have a good enough read to feel comfortable betting overcards no matter what the board looks like. But in that case, your best estimate showdown percentage is just a weighted average based on all of your opponent's possible holdings. Even if you can't do all of the calculations on the fly, knowing roughly the magnitude of the adjustment for something like a backdoor-flush draw is better than not knowing.



The adjustment is in the neighborhood of 6 percent in both of the above cases, and this holds roughly true for other similar situations, as well. For example, if you have top pair versus a flush draw, and no backdoor-flush draw, you'll win roughly 63.4 percent of the time. With the backdoor draw, you'll win 69.0 percent of the time. So, if you're dead certain that your opponent has a flush draw, and the percentages figure into your decision, it's about a 6 percent adjustment. If the flush draw is one of two equally probable cases, having the backdoor-flush card should be about a 3 percent adjustment. Any adjustment for the other case would be calculated separately.



Are these adjustments liable to make a difference in practice? Although one of the cases I picked at random did flip-flop the favorite and underdog, it should be fairly rare that the backdoor-flush draw will be a deciding factor, especially given the degree of uncertainty about your opponent's cards. On the other hand, even though most decisions will hinge on larger factors, an accumulation of smaller adjustments can tilt the balance on occasion. At the very least, it should be better to know how big the adjustment is than to have no idea.



Certainly there's much more to poker strategy than showdown equity, except in some fairly specific situations. And we can probably do even better just with these simple equity calculations. We could break these hands down into more detail, because when you miss your backdoor flush, it makes a difference if you hit a costly card on the turn or not.



That's an exercise for another day.



Of course, although I've set this up so that your opponent has the fat draw and you have the big cards, the numbers are applicable either way. It just happens that you're more likely to read your opponent for a regular flush draw than you would an overcard draw. If you know your opponent has a non-pair that missed the board (no four-flush), the probability that he has a backdoor-flush draw is seven-fifteenths, or 47 percent. In that case, you'd do fine just to split the difference and give your opponent credit for an extra 3 percent chance of winning.



To run off these situations, I've used the freely available pokersource package (in particular, the hcmpn example program), which is available from pokersource.sourceforge.net. It's mostly for programmers, but fortunately you can now run these simple simulations via many web sites, and through various downloadable tools. If you aren't already in the habit of doing so, I highly recommend running little comparisons like this whenever you have a question about how different factors affect your equity. Whether the answers surprise you or not, it's always helpful to know for certain.



Daniel Kimberg is the author of Serious Poker and he maintains a web site for serious poker players at www.seriouspoker.com.