Eliot Jacobson sent me the following link:
http://www.ijmp.org/AAP/Loss_Rebate_Theorem.xlsx
He also adds this:
Here are approximate numbers for single deck blackjack with a 35% discount.
The person should quit after winning 66 units or losing 76 units. Scale this so that 76 units = $25000.
Last edited by Norm; 10-06-2019 at 11:16 AM.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
Based on BJ HE = -0.5% and Var = 1.30, my both simulation results and iteration results matched, as below :-
1) loss exit = 29.6 units
2) win exit = 25.5 units
3) average win = 2.442 units
4) expected rounds = 604
5) loss likelihood(%) = 51.45
Meaning you will win 2.44 units after flat bet 604 rounds, average ev(%) = 2.44/604 = +0.404%
Please correct me if anyone have different answers.
Thanks
Last edited by James989; 10-08-2019 at 04:18 AM.
My spreadsheet gives these results (with h/a = -0.5% and var = 1.3):
Win-quit point 25.9967 Loss-quit point 30.0051 Expected net win 2.4344 Probability of win 48.215% Effective edge 0.4052% Expected rounds 600.8
The closed solution assumes differentiable IID random variables. A simulation will always give more accurate results for a discrete game, but of course takes a lot more time and effort.
Last edited by Eliot; 10-08-2019 at 08:25 AM.
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