Quote from: RHavar on March 03, 2018, 05:49:23 PM

Quote from: Luxo42 on March 03, 2018, 04:25:32 PM

Vice versa. The worst case for casino is low-value-betting on high multipliers, until forced cashout. According to my calculations, max-profit = bankroll * house_edge * (2-house-edge) would be EBG 0+ for any cases.

You sure about that? It looks to me that the worst case is for the casino is low-value betting on high multipliers from the casinos perspective, but this is generated by a player betting a large amount on a low multiplier. (i.e. if a player is betting 1 BTC to try win 10 BTC, from the casinos perspective this is a 10 BTC bet trying to win 1 BTC)

Rechecked again. Sure.
Player: low-value high-multiplier low-win-probability
Casino: high-value low-multiplier high-win-probability
0-EBG at <2 Kelly

Maybe, it's really counterintuitive.
But, for example, casino (HE=1%) may lose 5% of bankroll per bet with high probability (slightly less than 99%). But player's bet is much higher than the whole bankroll. And that's is EBG+ for casino.