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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 statemnet that the expected value of your bankroll will go down.)
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Ok. I recall now Stanford Wong's treatment
Here where he explains the term "Win Rate" as BillC means it. I don't know who introduced the terminology but it seems an unfortunate one to me since people commonly refer to the Arithmetic Win Rate as the "Win Rate" as well, when they are two different things. I suspect this terminology developed in the gambling world and Not in the Academic world of Mathematics. I think Mathematicians would have come up with a better name.
Basically, the Wong Win Rate for proportional betting defines a Bankroll Growth which the Bankroll will Converge to in Probabilty over the long run. In other words, there will be a high probabilty that the Bankroll will be close to that determined by the Wong Win Rate after a long period of time. Suprisingly, for Kelly betting that limiting curve is where you would be if the return on your actual action was half what your edge says it should be.
However, even though there is a high probabilty your bankroll will be close to the Wong Win Rate Curve, the reality is that your Bankroll remains a random variable whose distribution has enough probabilty spread out into extreme ranges that your Expected Return on Action remains what it should be according to your edge.
BillC was correct when he indicated that the Wong Win Rate becomes negative when your proportional betting exceeds twice Kelly. That's really just a fancy way of saying that in the long run your probablity of being close to zero gets larger and larger. But that's not to say your Arithmetic Win Rate has become negative. Even with the high probabilty of being close to zero, the Expected Value of your Bankroll remains determined by your positive edge and your Action.
I think some qualifying word should be added to the term "Win Rate" when referring to the Win Rate Curve which the Bankroll converges to in probabilty. If Wong introduced the term I'd vote for calling it the "Wong Win Rate". At least Something to distinguish it from the more commonly understood Arithmetic Win Rate, ie. the Win Rate determined by EV.
PairTheBoard