[TaintedRogue]

I do not believe you can use a math model to determine if your expectation is more/less than double.
If you are a good player, who, when the *correct* odds of you placing in the top 3 of an event are X, you MUST increase your stack size as the tournament progresses, in order to retain that X expectation, just like everyone else has to increase their stacks.
There will be aberrations in the growth of your stack and the extremities of those aberrations will cause a temporal adjustment of X.
There is an IMMEDIATE and DEFINITIVE increase in table command, when the best player at the table, doubles his chips on the 1st hand.
When that situation occurs, the last thing on the player's mind: How much did doubling up just now, increase my X?

I may be simple minded........however..........I do not believe that MATH can be used to determine the odds of one's ability to place in the money when there are so many variables involved in a tournament.