FWIW here are my calculations based off 20500 hands played, 1,450,000 won by Jungleman and a SD/100 of 150BBs.
First column is Jungleman's winrate, second column is his probability of winning the challenge. This doesn't factor in the winning player adjusting their strategy, so in reality Jungleman's win % is higher. Other than that the maths is very solid. Amount won/lost per hand is anything but normally distributed, but the amount won/lost per 29500 hands
is.
FWIW assuming Jungleman's pre-match winrate was normally distributed with expectation 0 and standard deviation 10, after 20500 hands his winrate is N~(8.4,7.2). There's an 87.81% chance that he's a winning player.
If Jungleman's winrate is 0 the fair buyout price for Durrrr is $1,340,584. Again this assumes no tactical adjustment so the actual fair buyout price is higher. If Jungleman's winrate is ~1.1bb/100 Durrrr should immediately concede the challenge.
In answer to your actual question, if you bet at evens, if you assume Jungleman's winrate is 0 and the winning player won't adjust strategy (the last two are dubious to say the least), the fair buyout price is $4.2k.
Last edited by PartyGirlUK; 07-25-2015 at 08:14 AM.