Another Simulation That Sheds Light on Chips Changing Value

[pzhon]

Ok, I can't stand to see incorrect answers posted, even though I maintain that this is a poor thought experiment since playing-UTG-against-cheating-idiots is so different from poker.

Let value(n) be your equity with a stack of size n. value(1)=1.

The probability of winning with which you should push is value(n-1)/(2n+8), so that you are indifferent to folding to get a stack of n-1 worth value(n-1) and pushing to get a share of the 2n+8 pot. You should push with at least (value(n-1)/(2n+8))^(1/9).

value(n) = value(n-1) ((value(n-1)/(2n+8))^(1/9)) + Integral (2n+8) x^9 dx from (value(n-1)/(2n+8))^(1/9) to 1.

We can use this recursively to compute value(n).

n value(n)
------------
1 1
2 1.882862
3 2.755967
4 3.640068
5 4.542981
6 5.467867
7 6.415821
8 7.386923
9 8.380731
10 9.396536
11 10.433498
12 11.490724
13 12.567311
14 13.662373
15 14.775055
16 15.904540
17 17.050054

100 136.900389
1000 1755.195048