Poker News

Richard Burke

LindaMae is twenty-something and blonde. Attired in shorts and a tight tank top in summer, she has all the attributes of girldom and then some. She plays low-limit Hold’Em at my local casino and does well at it, picking off bluffs thrown at her by men addled by her good looks. She’s not stupid, far from it, but she’s hopeless at math, so it’s understandable that she asked me why she never flopped a Flush, and so seldom a good Flush draw.

I explained that if she didn’t look at her hand then the Flop would be suited 60.2% of the time. By suited I mean that there would be two or three trumps on the Flop, given by 4*((C(13,2)*39+C(13,3))/C(52,3). LindaMae supposed so, but why couldn’t she look at her cards, she asked, how could looking at her hole cards change the Flop? I explained that of course looking at her hole cards wouldn’t change the Flop. Looking at her hole cards changes what we can predict about the Flop, because we then have more information. Without looking at her cards, we can predict that the Flop will come suited in diamonds, one fourth of 60.2%, about 15% of the time.

Suppose you looked and saw J_-T_ in your hand, I told her. We can then predict that the Flop will come suited 60.3% of the time, slightly more often than if you didn’t know you had two diamonds. Since you know you have those two diamonds in your hand, you know neither can be on the table, and the chance for a Flop suited in diamonds has to be less than 15%. LindaMae agreed that that stood to reason and nodded her head. (That’s when I noticed her blondeness had dark roots.) I told her that we can confidently predict the chance of having a suited Flop, given thather hole cards are suited, as 11.8%, (C(11,2)*39+C(11,3))/ C(50,3). We can predict the Flop will have precisely two diamonds 10.9% of the time. And the Flop will have three diamonds 0.8% of the time, about once in 119 Flops! That’s why you think you never flop a Flush, I told her, because it is pretty rare. Flopping a good Flush draw is more frequent, about once in nine Flops, I told her. Even in the event that you flop a good draw, the chance that you’ll make a Flush by the River is modest. The chance that you won’t make a Flush by the River is C(38,2)/C(47,2), so the chance that you will is one minus that, or 35%.

There is a small chance that, starting with suited hole cards, you’ll make a backdoor Flush, I said. The chance that there’ll be exactly one trump on the Flop is given by C(11,1)*C(39,2)/C(50,3), 41.6%. The chance that the next two cards will also be trumps is C(10,2)/C(47,2), about one time in 24. Unless the hand has other potential, backdoor Flush draws usually fail the risk-reward test and should be released. Having a suited starting hand is nice, I said, it’s certainly better than not having one, but players generally expect more of their suited starting hands than chance allows. If you’re hoping for a Flush, then prepare for disappointment because it hits less than 6.4% of the time, roughly once in sixteen times that you start with a suited hand. LindaMae nodded and swung back into battle.

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