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#41
10-15-2005, 11:19 PM
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Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
[ QUOTE ]
[ QUOTE ] 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%. [/ QUOTE ] Not quite. Your stack is not exactly 2Q, as Q has increased by the elimination of one player. The new Q is T/(N-1) where T is the total chips in play, and N is the starting number of players. Your stack after doubling is 2T/N, which is slightly smaller than 2Q after the elimination. [ QUOTE ] This will however not increase your EV by 100%, assuming the tournament isn't winner take all. [/ QUOTE ] As I've said repeatedly, I'm not calculating EV. Just estimating odds of winning. [/ QUOTE ] Im not talking about Q or anything, I'm talking about how you have exactly 2% of the chips in play when you double up, as opposed to 1%. This should double your chances of winning exactly, in a purely theoretical sense. I'm sorry but I am seeing or hearing absolutely no factual data to back up any of the math/formulas above. 
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#42
10-15-2005, 11:20 PM
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Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
In a winner take all format, the players should benefit ZERO from the elimination of another player. Would you rather play a satellite headsup with a 9-1 chip advantage or a 10 player satellite where everyone has equal chips? For events where all players are of the same skill, each scenario should be exactly the same.
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#43
10-15-2005, 11:22 PM
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Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
[ QUOTE ]
Every major poker book out there says the same thing. Your next X chips is not worth as much as your first X chips. But it is worth something. That pretty much describes logarithmic growth. [/ QUOTE ] Please tell me what poker book says this! In almost all cases they are talking about tournaments in which the prize doesn't all go to first place! Again, you are presenting formulas and theories as though they are fact and that because when you plug in certain numbers, that the "EV" seems to go down, actually means that it does. I disagree with this and have seen no proof whatsoever to follow this line of reasoning/theory.
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#44
10-15-2005, 11:23 PM
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Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
[ QUOTE ]
There is some mathematical basis to assume your chance of winning is exactly proportional to your stack and the total number of chips in the tournament (especially for a single table). [/ QUOTE ] I will say it again. This is not surprising, nor is it inconsistent with my theory, as over short distances, logarithmic growth is very close to linear growth. So for any chip gain less than a double, my formula and a strict cEV = $EV approach will return nearly identical results. It's once you go past a double that they start to diverge. Most models I've seen consider only single hands, usually against one other player, thus a double (or slightly more due to dead blinds) is as high a result as is tested. It's no surprise that this model works reasonable well in those scenarios. But my formula will give essentially the same results there, with the added benefit of handling multi-player scenarios better. Furthermore, ICM is an excellent tool for single-table analysis, and I don't suggest we replace it in those scenarios. It's not very effective for MTTs, however, because of the enormous range of stack sizes involved, among other issues. That is the problem I am trying to solve.
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#46
10-15-2005, 11:33 PM
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Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
[ QUOTE ]
I'm sorry but I am seeing or hearing absolutely no factual data to back up any of the math/formulas above. [/ QUOTE ] Factual data will require a great deal of stochastic analysis. I'll get around to that after a couple more runs of trying to optimize my formula. But even in a field of players with equal skill, your chances of winning simply cannot be completely determined by your stack size alone in a large field, because you cannot continue to grow your stack at the same rate once you're ahead of everyone else. Here's another way of looking at it: When you're behind everyone else, all of your chips are "working," meaning that if you get the nuts, you can invest every single chip you have for a gain. Once you have more than everyone else, though, whatever you have in excess cannot be invested at all. It's like forcing you to take that money out of your savings account and stuff it in your mattress at home. It's still worth something, but it's not as valuable as money in a savings account.
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#47
10-15-2005, 11:37 PM
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Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
I apologize, but using such analogies won't help to convince me. You also seem to fail to mention the fact that when you go allin and you don't have the nuts, you don't lose all of your chips as you would if you were shortstacked. I am really having trouble with your thought process on this one.
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#48
10-15-2005, 11:42 PM
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Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
[ QUOTE ]
Again, you are presenting formulas and theories as though they are fact and that because when you plug in certain numbers, that the "EV" seems to go down, actually means that it does. I disagree with this and have seen no proof whatsoever to follow this line of reasoning/theory. [/ QUOTE ] I'm not suggesting that my formula is factually correct. I am only defending the non-linearity of the relationship. My formula is just a first attempt at approximating it. As for proof, it's very difficult to present hard proof without statistical analysis of thousands of tourneys. I'll get around to that at some point. In the mean time, I'm just giving analogies to try and help you understand what I'm getting at. By the way, just as an aside, the curve I use is called a "logit" and is frequently used in various areas of statistical analysis. It's equivalent to an improper integral of a portion of the normal curve.
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#49
10-15-2005, 11:57 PM
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Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
[ QUOTE ]
I apologize, but using such analogies won't help to convince me. [/ QUOTE ] Do you want hard statistical data? I don't have it, yet, but I assure you that there is none supporting your position in a large tourney. [ QUOTE ] You also seem to fail to mention the fact that when you go allin and you don't have the nuts, you don't lose all of your chips as you would if you were shortstacked. [/ QUOTE ] Of course I understand that. The log curve handles this perfectly, as it is very steep at first. Consider a 2-person tourney. My curve is centered around the average stack. Thus when you firt pass your opponent, chips you gain are relatively high in value. But when you're WAY ahead of your opponent, those next few chips don't matter as much. [ QUOTE ] I am really having trouble with your thought process on this one. [/ QUOTE ] Perhaps I'm not doing a good job of getting myself across. In any event, I hardly expected to convince everyone right from the start. But tell me this: Let's say you're in a field of 1000 people, and you start with 25% of the chips. Do you really think you have a 25% chance of winning? I don't.
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#50
10-15-2005, 11:59 PM
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Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
[ QUOTE ]
Can you please try to explain exactly why the chips lose value when you gain more of them in a winner take all format? [/ QUOTE ] Let's say the buyin for a winner-take-all tourney is $100, and you start with 1k chips. Late in the tourney, you have 500k chips. At that point, I offer to sell you another 1k chips for another $100. Will you take me up on my offer?
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