Conjecture and Question

[DonT77]

Well, I think you make a good case that doubling-up early in a 10-player, winner-take-all tournament won't double your $EV; but I don't think this line of thinking carries forward to say a 1000-player tournament with escalating, non-linear payouts.

In a 1000-player tournament, if a player repeatedly doubles-up until he has let's say half of the chips in play, then obviously his $EV won't double-up each time - but we (Mason's conjecture) are only concerned about what happens when the player doubles-up the first time.

Let's say there is an $EV multiplier associated with each double-up. Now, according to this:

"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)"

each time you double your chips the $EV multiplier should be less each time, However in larger MTTs sometimes (like once in the money where the money is flat but then escalates rapidly) doubling-up more than triples your $EV.

Clearly there is a complex, non-linear relationship between cEV and $EV throughout the course of a large MTT that can not be explained by simple examples given the complexity of the variables involved (including payout structure and the accumulating benefits of a big stack).