This guy I know says he played 4 tournaments at the WSOP last year and claims that every hand he was knocked out with, he was a 96% and above odds on favorite. Says he got a suckout every time. When I asked him to describe the hands at one of the poker games we play at, he got really defensive towards me and wouldn't answer the question. Is this a statistical anomaly? This is worse than having AA losing to AK 4 times.
If you consider the question "what is the chance of losing 4 times as a 96% favorite, if those are the only games you ever play", then the answer (via the binomial distribution) is .00025%
There are many many problems with this.
1. Consider the difference between "what is the chance that my next 2 flips are both heads" and "what is the chance that in all future flips, I will have at least 1 two in a row streak?". For the first, the answer is 1/4, for the 2nd it's basically 100%. If he's played dozens or hundreds of tournaments, the chance of such a streak is MUCH higher than if he only played the 4. See what I mean?
2. you can often partition the data available to you in a way that makes it seem less likely.
3. people lie to themselves. I have seen it every day. He probably doesn't remember the details of the hand and by the time he got around to writing it down or simulating it, had mentally modified it to be more favorable to himself. I have literally watched people do this. (If he even knew what outs his opponent really had, I have also seen people say "that was the only card in the deck you can win with", when actually I had many other outs that would have worked. Often they appear to really believe this and it tilts them. It's weird.
Buzz's #3 is the most likely answer. It's set over setting somebody four times in a row and having them beat you with quads all four times. Buzz's #1 and #2 are also very true but I'll tell you if this actually happened your mate should at least consider the possibility that he was cheated (though, especially given your description, I'd guess he's just lying/mis-remembering).
Its pretty standard i think for a good player to get eliminated by suckouts typically. Contrary to cash games that you can be happily bluffing often or semibluffing and lose your stack this way and meta game saves the day later anyway (or your main concern is plus EV not high risk bust out concerns) , in tournaments unless you play a ton of them at the same time you tend to be careful when you risk everything. Since the elimination takes place by someone larger than you and the typical term larger is not just a bit over but usually many times or at least 50% larger stack and rarely by very close stacks, the all in both are involved is typically not seen as risk sensitive for the "idiot" eliminating you so it may be a semibluff by them or a total bs bluff or a spite all in call preflop with garbage or a marginal push or call with a draw, you name it that happens to be bad EV (if you outplay them) or marginal minus etc . The guy that is loaded can afford to risk losing more than the guy that has the smaller stack so typically the elimination for a careful frequently cashing player will be a bad beat. That i think is nearly standard for players that are in the tight careful camp and outplay opponents by forcing all ins with excellent odds.
Now taking it to 95% or whatever is kind of bs because typical great edge all ins post flop are 90% or 70%,80%. So without human bs bias a reasonable claim is to lose back to back 4 times with say 80% edge maybe 75% as avg vs draws (set vs flush draw etc). But since by definition the last hand you lose is the one you are eliminated with and typically it will fit that profile unelss you are eliminated with a very small stack, i see nothing spectacular about a claim that in my last 4 tournaments i was eliminated with bs bad beats. Thats exactly the norm actually unless you go out with small stack (implying when you pushed you were called etc in what made sense ICMwise but still it was risky to be against better if called etc).
So basically try to derive true anomaly only by looking in the spectrum of how a particular player is eliminated typically because it is unique to their style of poker play. If there is a bias to be eliminated often with 70% edge or more when stack is over 20bb for example and you have a distribution that your avg elimination stack is 15bb plus or minus 7bb etc you realize that its no longer so unreal bad to be out by say 4 85% order events. Mostly because the 85% elimination will tend to happen more often that you think (ie more often 15% of the time) because the expected elimination all in probability is already up there in the 70% avg area anyway. See what i mean? Its like saying that there are 50% men and 50% women in this planet and why on earth am i eliminated past 10 times by men only??? Clearly you ignore that more men that women play tournaments etc in establishing your amazement at the result.
See it like that too; Most people tend to die when they are sick or suffering from something. Soldiers in a war tend to die in great health typically. So if you were given 3000 men and that they died in great avg health you would be shocked if you picked the names from a list that was given to you and their names spanned alphabet (last name say) and races somewhat randomly nicely reflecting general population name and race frequency properties, until you were told of course that those were Iraq war soldiers. Because a soldier will tend to die young and in good health or not die at all. The list is not a random population list, its a particular group list that fight and tend to be in great condition. Same with elimination events in tournaments. Maybe a good player before getting eliminated has already survived another 3 80% all in events before that point. So that last 80% elimination is no longer as spectacular. After 4 tries getting eliminated that way tends to happen about 59% of the time now if your all in style fits that great edge search routine!!!
Last edited by masque de Z; 05-29-2012 at 05:51 PM.
Thank you for the answers guys! Appreciate the detailed responses. I am not an expert in poker theory but the guy kept mentioning this on facebook and at the table that he was a 95% favorite in all 4 tournaments and I had to call him out on it. He is a real douche at the table and he claims that he didn't play well at our tournament( he was eliminated in 4th place of a 18 player tourney) because I "tilted" him with that question and I messed up his game lol.