Theory: Gigabet's "bands" and "The Finch Formula" Grand Unification

[justT]

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I really don't understand? Doubling up oin the first hand in a 100 person tournament should increase your chances of winning by 100%, and thus make them 2%. This will however not increase your EV by 100%, assuming the tournament isn't winner take all. No one else in the tournament should gain any chance of winning the event just because you busted another player. Yes they gain EV if it pays multiple spots, but they don't suddenly have a greater chance of winning first place, that would make no sense.

Just as if you busted everyone but one player on the first hand, your chances to win would be 99%, and your one opponent would have the same chance to win the event as when they first bought in, despite being up against one opponent. Thus your opponent would have gained absolutely from you eliminating all other 98 players, assuming this was a winner take all format. (I know its impossible but just giving random example)


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I was struggling with the same problem last night. I worked the probabilities for a double up in a field of 10, 100, and 1000. I lost the exact numbers but they were something like 1.99, 1.98, 1.95 respectively. The first question is why would it go down for larger fields? I think it makes sense that the more poker there is to be played, the less meaningful your double up is. I suspect it has to do with someone getting extremely lucky (like hitting 17 reds in a row at the roulette table) and/or with you getting extremely unlucky (betting red 17 times in a row only to have it come up black each time). The less poker there is to play, the less that these extreme cases come into play and the closer a double up in chips is to a double up in probability. It doesn't prove anything, but I think that's where it's hidden.

Okay, second question using your example. If I've eliminated 98 players, how can my chance of winning be less than 99%? Or a different way of putting it, how can my beating 98 players increase the one remaining players probability of winning. Okay, back to the string of really lucky events, cause that's what the one remaining player is going to need to beat you. If you had eliminated only 97 players, then there would be one other player who could get extremely lucky and beat both of you. By eliminating that player, you take away the chance of that happening and thus actually increase the probability, albeit VERY slightly, for your one remaining opponent to win. IOW, he ONLY needs to worry about hitting his 17 reds in a row, he doesn't have to worry about the case where he hits his 17 reds in a row but then other short stack then proceeds to hit his 17 reds in a row to beat him.

I gotta go kill a chicken or something.