In the real world bet sizing is always discrete, even if it's at the penny level. In the case of FPDW you might have a choice of $2.50, $1.25, $.50, $.25. One of those sizes is more Kelly optimal than the rest for a given bankroll. Multicoin and Multiplay games often provide even more choices of bet size, though not very often for FPDW.
---In vpFREE@yahoogroups.com, <eecounter@...> wrote:
---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote:
Jean wrote: "There is never a zero chance of going broke."
"With the Kelly system there is zero chance of going broke, and a very reduced risk of bankroll depletion....."
Well, not exactly. The Kelly system does promise a zero chance of going broke, but only if you can continually resize your bets downward if you start to lose. Betting strictly according to the Kelly system requires a re-sizing of bets after every change in bankroll size, even down to fractions of a penny bets if you run particularly bad. (All of this assumes you have an advantage. The Kelly bet size for a negative expectation bet is $0.)
In the real world, this kind of bet re-sizing just isn't possible, particularly with VP. If you start out with some fixed amount of money, *and you maintain a fixed bet level*, you definitely have a non-zero chance of going broke, no matter how much money you start out with.
On the positive side, if you start out with a large enough bankroll relative to bet size, and a strong enough advantage, then we might be able to say your chance of going broke is "just about impossible", even if you can't re-size bets downward.
EE
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