And this is probably beating a dead horse but just to complete the circle you can see where that approximation I like to throw around comes from. Not only is a positive EV preferred, but also a positive CE is preferred, because it predicts future bankroll growth instead of bankroll shrinkage. So, take the CE formula, set CE>0, and solve for the bankroll:
CE=EV-Variance/2xBankroll>0
EV>Variance/2xBankroll
2xBankroll>Variance/EV
Bankroll>Variance/2xEV
That's the bleeding edge, it's normal to take at least a 2x safety factor to cover unknown unknowns, and you get:
Bankroll>Variance/EV bets
At that bankroll, CE=50% of EV, at double that bankroll, CE=75% of EV, at 5x that bankroll, CE=90% of EV, for infinite bankroll, CE=EV.
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Posted by: nightoftheiguana2000@yahoo.com
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