Ed, I absolutely loved Professional No-Limit Hold'em. It's basically my poker bible next to Mathematics of Poker.
Could you comment on the trade-off between rate of bankroll growth and expected hourly rate? I'm actually concerned with the latter but this thread has made me realize that I'm barely rolled for quarter VP when I've been playing dollars all this time. Hourly rate is a function of EV, bet size, and hands/hour, and as many others can probably relate, my time is valuable so the easiest way to immediately maximize hourly rate is to increase bet size. Since this variable is EV neutral, the OP's question on increasing bet size with respect to session bankroll growth could be construed (or misconstrued) as a topic in Kelly betting so a segue into that discussion is not entirely moot. And since the OP confirmed that it was "what he was looking for" I think a few posts on Kelly betting and bankroll growth could add value to some readers. I know in my case it did.
I think my question is a matter of relative utility like you said before, but I just want to confirm it with knowledgeable people such as yourself. If you increase your bet size beyond the optimal Kelly bet (but no more than twice the Kelly bet) you'll experience higher volatility and slower bankroll growth for a given bankroll. Increasing your bet size beyond twice the Kelly bet results in bankroll decline. Similarly, as Jazbo's article points out (http://www.jazbo.com/videopoker/kelly.html), you have a certain bet and if you're bankroll is less than half the Kelly "optimal bankroll" then you should not take the bet. Now the variable of bet size on whether or not you want to increase it beyond Kelly could be a question of "Do I want to increase my hourly rate or preserve my bankroll?" I think therein lies the problem because you can't have both, unless you have an infinite bankroll.
--- In vpFREE@yahoogroups.com, Ed Miller <ed.miller@...> wrote:
>
> Yup, I write about poker.
>
> Again, I think the overwhelming majority of gamblers tend to be much more
> concerned about minimizing their risk of ruin at a given stakes without
> having to move down (or allowing for maybe one or two drops in stakes) than
> they are about optimal bankroll growth rates at infinity. I don't want to
> speak for Bob Dancer, but I'm pretty sure he would forgo optimum exponential
> bankroll growth if it meant he never had to play nickels or hustle coupons
> again.
>
> Now you could call that "fractional Kelly" betting, but I would argue that
> one needn't even know anything about Kelly at all to functionally manage and
> grow a working professional gambling bankroll. Ok, you're betting a fraction
> of Kelly's optimum. So what?
>
> Which brings me full circle back to the original poster's question about
> adding hands as he wins for the day. This question has zero to do with Kelly
> betting. It's not a question about optimizing exponential bankroll growth
> rates, and it's not a question that involves an infinite number of trials.
> So, IMO, the word "Kelly" should never have entered this thread.. and the
> fact that it did, in my view, supports the idea that Kelly is widely
> overused and misused.
>
> Ed
>
