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How Bad are the Beats?
Steve Brecher
September 19, 2005

While playing online Poker, I have said that there are three topics I won't discuss in table chat; politics, religion, and whether online poker is rigged. That's because many people's opinions on those topics are hardened and not amenable to friendly or productive discussion.

Away from the table, I'll venture a couple of comments about improbable events in poker. While not direct instruction in the tactics and strategy of play, these comments may help you take "bad beats" in stride -- and that, in turn, is an essential part of poker maturity.

First, let's consider what most would view as a typical "bad beat" -- a lower pocket pair winning against a higher pocket pair in hold 'em, such as KK beating AA. When those hands share one suit, the chance of the worse hand winning is about 18%. The chance of the lower pair winning twice -- that is, the next two times that such hands happen to go against each other -- is about 3%. If in one session of play, a lower pocket pair beat a higher pocket pair twice, that might seem a little, well, weird to some players.

Consider another situation involving chance. When two dice are thrown, the chance of rolling "snake eyes" (1-1) is about 3% -- about the same as a lower pocket pair beating a higher pocket pair twice.

Suppose there were 600 craps tables using standard, unaltered dice with nine players around each table -- a total of 5,400 players -- and these tables operated for a three-hour "session." How many players would observe snake eyes being thrown at least once? The statistical expectation result is not important. The point is that it's easy to intuitively see that a large number of players would.

Further, do you think some players might see snake eyes thrown several times in an evening -- say, three or four times? (That is equivalent to six or eight poker "bad beats.") And if some of those players would be inclined to report their observation on forums and in chat, then it might seem to some as if the dice were "fixed."

Let's go back to poker. Recently, I played a hand of No-Limit Hold 'Em. An opponent four seats in front of the button open-raised pre-flop. It was folded around to me in the big blind, and I called. I semi-bluff check-raised the flop, continued with a semi-bluff bet on the turn, was raised all-in, and called the raise. I made my draw on the river. After the hand my opponent chatted:

opponent: ur horrible steve
opponent: why the [****] did u call that?
opponent: horrible that this site rewards that

(Confidential to opponent: I know these comments were made in the heat of the moment after a big loss and don't necessarily reflect your considered view.)

Let's take a look at my call on the turn. I held Ad Td; my opponent held Kd Kc. The board was Qd 9d 7h Jc.

With my opponent's actual holding, I had 16 outs to win the pot on the river, making me a 1.75 to 1 underdog. Of course, it could have been worse for me against other holdings, but even the worst case for me would have been to be up against K-T (a made straight), and then I would have been only a 3 to 1 underdog.

After my bet and the opponent's all in-raise, I was getting pot odds of 3.7 to 1 to call, so the call is clearly correct. But it seemed to my opponent -- and to at least one observer -- that I made a bad call, and that my winning with a 36% chance to do so when I called was a bad beat for my opponent.

The moral of this story: While "bad beats" (low-probability events) do occur, sometimes a closer examination of a poker hand can change first impressions and allow you to continue to play with a cooler, clearer head.

Steve Brecher

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