Poker News

Richard Burke

In a ten-handed $4-8 Hold’Em game on a sultry afternoon in early summer, I was down about half a rack when Fred trudged into the poker room of my local casino. I hadn’t seen Fred lately and asked him why. He said that Internet poker had him in thrall for a week or so. He thought he could sharpen his final table play for regular tournamentsby playing lots of single-table tournaments on the ‘Net. Just getting to the final table is my problem, so I could neither agree nor disagree. Fred said that he had just finished second in a No-Limit Hold’Em single-table tournament. Headsup, he went all-in with pocket Sixes and lost to pocket Nines. “What were the odds of that?” he asked. And besides, it seemed to him that whenever he had a pocket pair that an opponent also had a pocket Pair, and sometimes two had pocket Pairs.

“Was it true that his having a pocket Pair increased the chances of someone else having one?”

A little, I conceded. Heads-up, if Fred didn’t have a pocket Pair, then the probability of his opponent’s having one is about 1 in 17.0, as given by (6*2+44*3)/(50*49). If Fred did, the probability that his opponent would have a pocket Pair is a shade more likely, (2*1+48*3)/(50*49), about 1 in 16.8.

It depended on how he looked at it, I told Fred. If, before the hand were dealt, he were to bet that he would be dealt a pair and that his heads-up opponent would also be dealt a pair, then fair odds would be 285 for 1. Given that he had a Pair, then fair odds would be 16.8 for 1.

Fred thought for a bit and asked, “Weren’t my chances about 50-50 after I went all-in?” I told Fred his chances would be about 50-50 if he had a pocket Pair vs. unpaired higher cards, because, barring Straights and Flushes, the two higher cards had about a 50-50 chance to pair up or better by the River. (That situation is frequently shown on televised poker tournaments.)

Heads-up Pairs are different, I told Fred. Because the chance that either will improve is fairly small, the higher Pair will usually prevail. Barring Straights and Flushes, the chance that Fred would make a Set and his opponent wouldn’t improve is given by C(2,1)*C(44,4)/C(48,5), or .198, about one in five. In other words, the higher Pair is an 80-20 favorite.

That’s why you have to be careful when you risk your stacks with a pocket Pair, I told Fred. On the Internet, where the only possible “tells” are the size and tempo of your opponent’s bet, if there’s rapid, substantial, pre-Flop betting, you should release your small Pair. But if you’re short-stacked and/or about to be “blinded off,” then you grit your teeth, take a chance and hope for a bluebird.

In a brick-and-mortar poker room, you have a better chance to “tell” whether your opponenthas a pocket Pair and if so, how high. Except for tournaments, Fred played only limit Hold’Em, he said. I told him the odds are the same, the difference is the downside: when you lose your entire stack in no-limit Hold’Em then you have to leave the table; in limit Hold’Em, you can lose a few hands and buy another rack if you want. Fred said he knew that play very well.

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