by Richard G. Burke

Fred likes to fish, so he and his wife rented a Reno resort hotel room for a week. She enjoys  the pool while he—armed with flies, rods, reels, waders, and a sack lunch—fishes in the nearby mountains’ catch-and-release streams. After supper they head to the casino, she to play bingo or the slots and he to the nightly low-entry-fee, no-limit hold’em tournament in the poker room.

 You need to understand that Fred doesn’t wail about his poker results; win or lose, he has a ready smile and a cheery attitude. Just the same, he came as close to wailing as I ever heard when he called me that night.

 His tournament started at 7 p.m. with five full tables of ten, paying five places. Each player started with $1,500 in tournament chips. The blinds started at $25-50 and went up every 20 minutes. After two-and-a-half hours of solid play, catching a few hands, and stealing blinds upon occasion in the right spot, Fred moved to the final table.

 He made some hands and held on to his stack until he and five others remained. In middle position, he had only six times the big blind left when the dealer delivered him As-Qd, and he shoved. The button called with Ah-Qc. Everyone else folded. They tabled their hands and waited for all the cards to come out. Fred figured on a chop.

 When the dealer laid Qh-7h-2d on the flop, Fred knit his brows. When the dealer turned the 4, he crossed his fingers. When the dealer laid the Jh on the table, he relaxed his brows and fingers, wished everyone good luck, and left to find his wife and any place which served adult beverages.

 When he called he asked what the odds were against his opponent drawing out that way. He thought the odds against hitting a flush with only one in the hand more or less equaled the odds of being struck by lightning!

 “Not so,” we told him, “You’ve done it to opponents yourself. When you do it to others, it just seems ordinary. It’s about the same as hitting a one-outer on the river—which equals 43-to-1 against— which happens in every poker room every day. In fact, drawing out on someone with four or five trumps equals 45-to-1 against.” The computations go like this. Starting with an unsuited hand, you can make a flush with four or five trumps on the table in either of your suits. Twelve cards remain of both your suits, so the probability that you flush with either suit with four trumps on the table equals 2*C(12,4)*C(36,1)/C(48,5) and the probability that you flush with either suit with five trumps equals 2*C(12,5)/C(48,5).

 Being independent events we can add them to find the probability of either: 0.020814 plus 0.000925 equals 0.021739, or odds against of exactly 45-to-1.

 I reminded Fred that we published a similar result in the column, “Double-Suited,” which appeared in Poker Player Newspaper’s July 9, 2007, issue. (In brief, Linda Mae loved to talk up her “double-suited” hold’em hands so as to convince her opponents that she was a total air head, when to the contrary she usually cleaned their clocks. You can review that column and others by clicking the “Back Issues” link at www.pokerplayer. newspaper.com.)

 Fred vaguely remembered that column, but he said it didn’t hit home until that fourth trump flushed away his tournament chances. Did the certain knowledge that his opponent hit a 45-to-1 shot make Fred feel any better?

 It did not.
 

 Do Puts and Calls interest you? Check out these revolutionary new equations from poker and investment expert Richard Burke at http://www.postalnet.com/ OptionValueEquations.html. E-mail your Hold ’Em questions to burkecaltech@cox.net