the part that I found the most counter-intuitive is that if the casino is over-risking to the point that it expects to lose money, shouldn't it be profitable for a whale to play there?
And...? Don't leave us hanging! How did you resolve this?
I think the way that makes most sense for me, is that the house needs to sort of assume a whale has infinite money. Like if you imagine dragonmaster2's "100% risk" scenario, it's just a matter of time before the infinite angry whale is guaranteed his win.
But if you invert the scenario, it doesn't really make sense to assume you can be a gambler with an infinite bankroll. And with any finite bankroll, all you can achieve is having a very large chance of busting the house -- but you can never turn that into a "profitable" scenario.
So when the house is risking more than a 2x kelly, you have a sort of weird scenario where it's bad for the house (it'll probably go broke) but also bad for the player (it'll still have an expectation to lose)
Tell me RHavar...
What kelly are investors exposed to when they receive 0.75% of the house edge but a single player constantly bets to win 1.5% of the bankroll?
When you minus the dilution fees from the original investment, what does the kelly become greater than?
With this kelly and the house taking 0.25% of the house edge automatically, who are the only people to end up with the money in the end in this model (hint: they're both criminals)?