The Wotmog theory
Mason, this is proven by the Wotmog theory which states:
<font color="red"> If your original stack is worth more than fair chip value (because it is in the hands of YOU), then the average value of the other starting stacks must be worth less than fair chip value because they are in the hands of the NON-YOU player. The value of any further accumulated stacks by YOU is a formula involving the NON-YOU stack value, your skill advantage, # of players remaining, and prize pool distribution. </font>
Let’s think of a $10 buy-in 10-player winner-take-all tournament for $100. You are an exceptional player and your expectation is a return of $20.
Everyone has a stack of chips. If you double through to 2 stacks, you might think your expectation becomes $40. Another double through to 4 stacks and it becomes $80. A third double through to 8 stacks and it becomes $160, and you still haven’t won the tournament. But that cannot be correct, since the total prize pool is only $100 (add to that the fact that for a MTT, the maximum prize is significantly less than the total prize pool)
If your original starting stack was worth $20, then the other 9 stacks on the table can be worth only $80, or $8.89 each stack. Wotmog states that when you win the tournament by accumulating all of the chips, you now own all stacks and their original values [(1x$20) + (9x$8.89)=$100] When you double through, you accumulate one of the $8.89 stacks. The value of that added stack to your original stack would be a complex formula involving the components outlined in Wotmog, but cannot be as high as $20 since continuing to add $20 together you will reach $200 at the end, which is twice the prize pool.
The value would be closer to $8.89 than to $20, which sounds like alot less than $20, but even if it were exactly $8.89, that nearly doubles your profit margin from $10 profit to $18.89 profit.
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