Poker News

Richard Burke

He was still talking about it when I sat down at the $4-8 Hold’Em table on a Saturday afternoon in late winter. His name was Warren and his friend’s name was Rob. They had come to town for a convention and had decided to stay over and play a little low-limit poker. Both were twenty-something, good-looking, trim, and unmarried I surmised becausethey were freely able to stay an extra day or two. Warren told me I wouldn’t believe it, but a few hands ago he had flopped Quads and Rob had hit runner-runner Quads to beat him!

Normally, I just pretend to listen to bad-beat stories. I smile and nod and all that, but I’m imagining that I’m in Bali or Bangkok or Burma until the beatee finishes his tale of woe. It’s always the beatee who tells a bad-beat story. He’s the victim, like Joe Btfsplk, Al Capp’s comic strip little character who had a perpetual rain cloud over his head. This was different, Warren was the beatee and he wasn’t acting liking a victim, he was glad about it. His buddy had beaten his Quad Eights with runner-runner Quad Tens, and he was smiling!

My local card room didn’t have a bad-beat jackpot, so Warren hadn’t won thousands, he had lost money on the hand, but that didn’t matter to him. What was important to Warren was that something so rare had happened, and that it had happened to him and his very best friend in the whole world. He had started with 9h-8h and flopped 8c-8d- 8s, wasn’t that simply amazing? Rob had started with black Tens and had hit Th-Td on the Turn and River! Wasn’t that incredible! Could anything be more divine? Rob had won the pot and Warren was so happy for him!

As I waited to catch a winning hand, I wondered if Quads v. Quads was really all that rare. Later I ran the numbers and found it really was rare. The probability that all the cards of any two ranks would have been dealt out among the twenty-five cards for the ten players and five community cards is 13*12*C(44,17)/C(52,25), or .2242. The chance that three cards of one rank would flopped and then two cards of the other rank would be runner-runner is C(4,3)/C(25,3)*C(4,2)/C(22,2), or .00004517. The chance that the two other cards of the Quads would be would be in anyone’s hand is (17!!/19!!/3), or .01754. Multiplying obtains the probability .0000001777, one chance in 5.6 million that the event would happen on any one deal. The odds against Rob’s being the beater and Warren’s being the beatee were larger, by a factor of 90. If Rob and Warren had been at the table for 21⁄2 hours, then the chance of the event’s happening was still one in 6 million. Warren was quite right. That was a deal worth remembering for a long time.

Quads’ losing to any Quads is rare. Flopping Trips to make Quads and then losing to runner-runner Quads is fifty times more rare. If Rob and Warren were to play for a lifetime, then it’s one chance in a hundred they’d ever be a hand so rare again. Warren was excited about it because it signified that they were bound by cosmic forces, and that they would remember that hand and talk about it for the rest of their lives. Wasn’t that just fabulous?

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