[locutus2002]

Hi,

Your conjecture that expectation does not double even though your chip count has is true and is probably understated. It’s more likely that twice the chips has the same EV for a player early on, than twice the EV.

Every players plot of EV to chips is going to have several characteristics that are identical.
1) EV(zero chips) = 0
2) EV (55M chips or 100%) = $7.5M or 100% of the chips
3) EV(chips) is a convex function: this is intuitively obvious since the payout structure is goes to the top 10% in increasing amounts, chips won at the end are much more valuable in $ than chips won in the beginning (percentage wise). The proof for this is like the proof for iso-utility lines in economics.

The implications are far reaching:

1) Players EV functions are ALWAYS convex, if they weren’t they would cross other players EV functions at some point and the better player would have lower EV for the same number of chips.

2) All players are below the WOTMOG line ~ 1 (for large field size). Definition of convex. This implies that even the greatest player in the world; lets say Greg Raymer, has an EV less than $1363 with a stack of T10,000 at the beginning of the tournament. (based on 55M chips and $7.5M 1st place.)

3) Somewhere around the bubble is where the slope of the convex function > 1 for most players when chips won are more valuable than chips lost EV(2XT) > 2 X EV(T)

Maybe someone talented with math can draw some graphs.