Quote from: dooglus on February 28, 2018, 07:13:18 PM

What is it that actually goes negative when the house risks over 2x Kelly? It can't be the expected profit per bet, since that is always 1%, hence positive. And it can't be the expected bankroll growth, since that's simply the expected profit per bet summed (or averaged) over all the bets, which therefore is also a constant 1%. So what is it? I can't find a good Kelly resource. They're either too basic, and simply say "expected bankroll growth goes negative" (which I don't think is accurate) or they go far too deep into the math and confuse me.

Your definition of "expected bankroll growth" isn't quite accurate. Have you seen this explanation:
http://www.therxforum.com/showthread.php?t=479974

?

It comes with some worked examples, so it makes it clear. In there he shows an example of betting 1% of your bankroll leading to +EBG and then betting 25% of your bankroll leading to -EGB (even though your EV just goes up 25x).

So to answer your question, it's the actual expected bankroll growth that goes negative if the house risks over 2x kelly (and obviously only for those specific bets). The original paper goes into some detail of why optimizing for expected bankroll growth rather than EV is the correct thing to do. Although it's worth noting that the assumptions the kelly makes are pretty unrealistic for a casino (players have a finite bankroll, will only play a finite amount of games and are attracted by higher limits)