Apologies if dumb question but in the last section (obtaining EV with real P&L), how do we take into account (in the code) a situation where the bet was a push? I tried a modification but that 2x'd the EV if all other parameters remain the same (N bets, real ROI).
Apologies if dumb question but in the last section (obtaining EV with real P&L), how do we take into account (in the code) a situation where the bet was a push? I tried a modification but that 2x'd the EV if all other parameters remain the same (N bets, real ROI).
Good question.
If there's a small amount of them, would probably just delete prior to analysis. [ROI will be slightly biased here].
If not, a plausible solution would be to compute an estimate of what fraction of bets ends with a push & call this estimated probability q.
Denote prior win prob = 1/ODDS with the letter p.
In your simulation you then update:
win prob to p*(1-q) -> P&L: + stake * (odds-1)
lose prob to (1-p)*(1-q) -> P&L: -stake
push prob to q -> P&L: +-0