Lesson: 27
How Bad are the Beats?
Steve Brecher
September 19, 2005
While playing on Full Tilt 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 on Full Tilt Poker. 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.
What's Your Starting Hand Really Worth?
- By Steve Brecher
Pro Tip: 37
What's Your Starting Hand Really Worth?
Steve Brecher
November 28, 2005
Most players know that pre-flop position is important in hold 'em. The earlier your position, the more players there are behind you and, unless you hold pocket Aces, the bigger the chance that one of them will have a hand better than yours.
There is another aspect to position: It's better to act after your opponent(s) rather than before. But for this tip, I'm going to investigate the chances that a player behind you will have a better hand.
There is no universal definition of what "better" means when comparing hold 'em starting hands. For this article, I needed some reasonable, quantifiable criterion. So in the following, I'm assuming that one hand is "better" than another if its showdown equity is greater. A hand's showdown equity against another hand is the average portion of the pot it will win across all possible combinations of board cards. This is similar to the percentages that TV poker programs display next to player hands when the players are all-in. If you're interested in investigating this for yourself, there are several free computer programs and websites which calculate the showdown equities of user-specified competing hands.
For example, Ah 2d all-in pre-flop against Kc Qc will, over all possible boards, win an average of 53.9% of the pot. So the A-2 is the "better" hand against K-Q suited by our definition. Obviously, it is not better for all purposes; at a full table I'd usually open-raise in early position with K-Q suited, but toss A-2 offsuit.
Given some specific hand category – such as K-Q suited – we'll need to know the chance that a random hand dealt from the remaining 50 cards will be "better." This requires that we have a showdown equity calculation for each of the 1,225 possible opposing hands and tabulate against how many of them the K-Q suited has the worse (less than 50%) equity. It turns out that 238 of the 1,225 possible opponent hands are "better" in this sense. So we say that the chance of a random hand being better than K-Q suited is 238/1,225 or 19.4%; conversely, the chance that a random hand will not be better is 80.6%. This tabulation would be too tedious to do by hand. For the example results below, I developed some simple software to do the calculations.
Suppose that you are considering an opening bet pre-flop. There are players yet to act behind you. I'll denote the number of hands to play behind you as N. For example, if you're on the button, then there are two hands - the blinds - behind you, and N would be equal to 2. What is the probability that none of some number of random hands will be better than yours? It is the chance that one random hand will not be better than yours multiplied by itself N-1 times, which is the same as saying it's that probability raised to the Nth power. For example, if there's a 40% chance that a random hand won't be better (i.e., a 60% chance it will be better), then the chance that none of three random hands will be better is 40% x 40% x 40%, or 0.4 to the 3rd power, which equals 0.064. Hence, the chance that at least one of the three hands will be better is 1.0 - 0.064 or 0.936 or 94%.
I think the most interesting thing about these numbers is the difference between earlier and later positions. This is something to consider when you're thinking of open-raising in early position.
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