Re: Am I stupid? I can\'t fit these two concepts into any type of harmony.
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"Interesting. If you're playing with an edge and you bet more than 2 times Kelly, your win rate suddenly becomes negative. Maybe you should present that at the next gambling conference of math. They'll probably go for it. I hear you can say anything there."
PairTheBoard
Except that I believe he is right. (But don't confuse that with the statement that the expected value of your bankroll will go down.)
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I was assuming betting at more than twice Kelly, so that you might have to readjust your bets to keep the condition true. Then your bankroll has an expected negative slope=rate. Is there any other "rate" in this case? If you are betting a fixed amount, then your strategy can't be betting "more than twice Kelly".
An extreme example is where you bet your entire bankroll all the time.
The fact alluded to is that (under some assumptions) betting exactly twice Kelly results in an expected rate of bankroll growth of zero.
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