Posted by Bisser on July 15, 1997 at 20:20:09: In Reply to: Re: This is the million dollar question! posted by Pete Moss on July 15, 1997 at 19:23:43:
It seems that we are using the same words for two different things.I call G = lim B(N)/B(0)/N as N --> infinity the "growth rate". Thus E(G) is the "expected growth rate".
The bankroll after N plays is B(N), and so the "expected bankroll" is E(B(N)).
However, E(log B(N)) and E(log G) are maximized when E(log(1+b*R)) is maximized. I call E(log B(N)) the "expected log bankroll" and E(log G) the "expected log growth rate".
What I was trying to say, is that E(G) and E(B(N)) are not maximized when E(log(1+b*R)) is maximized.Bisser