The other interesting thing about 2x kelly, is that for a binary bet (win all, or lose all) there is 0-EBG (but positive +EV). But actually bustabit (from the houses perspective) isn't a binary bet, it can lose some and win some. So assuming I calculated everything right (which very well might not be the case, as I can't come up with an analytical solution) it's actually quite common for a 2x kelly to be positive expected bankroll growth! (and the worst case is a 2x kelly is 0 EBG)
2x kelly is not 0-ebg for any binary (two-option) bet. It's only for 50% bet.
For bets with low probability 0-EBG point is very slightly less than 2x kelly.
Wolfram alphaSomething like up to 1.9933 Kelly
For bets with high probability 0-EBG point is more than 2x kelly.
Wolfram alpha
Oh wow, brilliant work. I always thought 2x kelly = 0 EBG on a binary bet, but your formula looks correct and it shows that 2x kelly = 0EBG only for the specific case of 2x bet. This actually seems like it's rather good news for investors.
So currently bustabit restricts the per-game limit to 1.5x kelly, but let's assume it used 2x -- the worst behavior could be triggered by a whale max-betting on 200 accounts which would set the forced-point to 1.01x (and stop the game server accepting any new bets). In this kind of insane case, it would only be very slightly negative EBG. But in a more common case of people aiming at higher multiples (especially lottery-style bets), a 2x kelly still leads to very healthy +EBG.
What would be a really cool solution, is that that you dynamically adjusted the limits based on the persons bet multiple. However, I can't really see how to do that cleanly in bustabit without removing the manual-cashout, which would totally suck.
Probably the best thing for bustabit would to never go above 1.99x at the most extreme. That should guarantee that all games are +EBG. Although honestly, I'm not entirely sure that's the best idea. As EBG is only one of the many things that bustabit needs to control for, another thing for instance is controlling variance. Because investing isn't provably fair, if a whale came and won 80% of the bankroll it would look pretty bad even though the site is doing everything correctly.