Updated on 09/18/2011 2:06AM

Looking to draw to a flush? You'd better think twice

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Of all the potential hands that players seek to make while playing Texas hold 'em, none is prettier than a flush. Perhaps that aesthetic appeal is what makes otherwise rational poker players routinely abandon common sense and simple mathematics in pursuit of the lovely sight of five suited cards.

Flushes, however, are as treacherous as they are beguiling. Granted, they're fun and they do beat straights and trips, but they're harder to hit than many players think and they often lose to higher flushes and full houses in monster pots that can knock you down or out of a no-limit game or a tournament.

The first thing to realize about drawing for a flush is that just because you are dealt two cards of the same suit does not give you a "good chance" of making a flush, even with five community cards to come. In fact, you are a 15-1 underdog to turn those two suited hole cards into a flush by the river. Unless there are other compelling factors at work, simply picking up two suited cards is not in itself a reason to stay in a pot, but plenty of players do.

The exception is when the unsuited value of your cards still constitutes a hand worth playing and the flush possibility is just a nice bonus. A starting hand such as A-Q suited is an especially strong one because you probably would play an unsuited A-Q anyway and the flush draw is an unlikely but valuable little kicker.

In addition to staying in with a weak suited hand, the biggest miscalculation that players make about flushes is in assessing their chances to complete the draw if the flop leaves them with a four-flush. I have heard many players say casually that they think they have about a 50-50 chance to hit a flush if, say, they see the flop with two diamonds and two more hit the board. They figure there are two more cards to come, and four suits, so they have two cracks at hitting a 1 in 4 proposition.

This might sound right at first, because if you were to randomly select two cards from a fresh 52-card deck, you are indeed 50-50 that one of them will be a diamond or any other particular suit. (You're actually a hair better than 50-50, because if the first card isn't a diamond you now a have a 13 in 51 rather than 13 in 52 chance of getting one on the second card; but let's not split hairs.)

In the post-flop four-flush hold 'em situation, however, you are far less than 50-50 to find that diamond, because you're not getting the turn and river cards from a fresh 52-card deck. You're getting them from a deck in which you know the identity of five "missing" cards - the two in your hand and the three on the board from the flop - and four of those five cards are diamonds.

So you're not drawing two cards from a 52-card deck with 13 diamonds; you're drawing from among 47 unseen cards that now include only nine (13 minus 4) diamonds. So you've gone from a 13 of 52 chance of getting a diamond, a 25 percent possibility, to a 9 in 47 chance, which is only a 19.1 percent chance. If you miss that, your chances on the river card are now 9 in 46, or 19.5 percent. So your chances aren't 25 plus 25 percent, they're 19.1 plus 19.5 percent, means you are less than 39 percent rather than 50 percent to hit a flush.

And remember, that's just to complete a flush, not necessarily to win the hand. Full houses are far more common in hold' em than in other five-card games, not only because you are making the best five-card hand from seven cards but also because full houses become much likelier with five community cards that often include a pair. Many a flush-chasing player has been knocked out of a big game or tournament when the river card completes his flush but also pairs the board to give someone else a full house. Also, if your two suited hole cards don't include the ace, there's always the chance that someone else has completed a higher flush. In these cases, hitting your flush on the river can go from exhilarating to bankrupting very quickly.

Given that your chances of completing a four-flush draw after the flop are actually closer to 39 than 50 percent, it should be obvious that this is a hand you never want to play heads-up. That's like betting an even-money shot at the racetrack that you believe has far less than a 50 percent chance of winning. If you don't understand why that's a bad idea, you shouldn't be playing cards - or if you are, you should be playing with me. I will send a car.