You're implying that it's always better to underbet Kelly than to
overbet it.Yes, absolutely, according to the "Kelly System". Betting less than "Kelly optimal" results in less bankroll growth, but less risk, which is a healthy tradeoff.
How is that necessarily healthy?
Betting more than "Kelly optimal" results in less bankroll growth and even negative bankroll growth with more risk, which is reckless gambling. (Reckless to one's bankroll)
I haven't studied Kelly much in video poker, but in simpler games,
such as blackjack, which approximate a 50% chance of winning a bet
that pays even money, one has to bet double Kelly to reduce one's
bankroll growth to 0. I doubt that that's much different at video
poker.
If one's bankroll were $16,000, would it be better to
play 25� or $1?Better to play quarters.
Why?
In fact, if you want my advice, I would not start playing a game unless I had double Kelly, then if I got ground down to Kelly (which works out to about a 10% chance), I would stop and find another game that I had double Kelly for. So, in other words, with $16,000, and if quarter and dollar FPDW are my only choices, I'd play quarter as long as my running bankroll remained above $4250 and below $34,000. At $34,000, I'd switch to dollar FPDW (yes, it's still available but rare, don't ask me were to find it, and there are even better games, don't ask) and play that as long as my running bankroll remained above $17,000. If my bankroll hit $17,000, I'd drop back down to quarters and try to build it back up to $34,000 again. Are you getting the general idea of how the "Kelly System" works? If not I highly recommend Poundstone's "Fortune's Formula" which is written in non-mathematical, everyday English for a general audience. It should be required reading in today's
economy.In summary (of the "Kelly system"), never play a game for which you don't have at least the Kelly bankroll. And stop playing that game if your bankroll drops below the Kelly bankroll. Play any game you want for which you the Kelly bankroll or more. A game that puts you at the Kelly optimal is the hairy edge, you get maximum average bankroll growth, but it's a wild ride, probably wilder than you realize. Most Kelly players back off a bit from the hairy edge, to a position with less risk. You don't have to always bet the exact Kelly optimum to play the "Kelly system". You can underbet for less risk, but you never overbet.
Why not? You've stated that being more conservative than Kelly
indicates is good, but you haven't said why. What other value does
one get that more than compensates for not maximizing one's bankroll
growth? I suspect that you're incorporating factors that the Kelly
Criterion isn't designed to handle, such as living expenses or how
stressed fluctuating makes one feel. I'm too lazy to do the math, but
I'm confident that, in a vacuum, one's bankroll growth would be far
greater by playing $1 FPDW than quarters if one's bankroll were
$16,000.
···
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
>By the way, for information purposes, the approximate kelly number for FPDW is 26/.0077 = about 3400. A while back, myself and others derived the exact number, but I don't recall it at the moment, but it's close. Assuming the 3400 number then:
>
>To play 5 coin nickel FPDW, your running bankroll must always be over $850.
>To play 5 coin quarter FPDW, your running bankroll must always be over $4250.
>To play 5 coin dollar FPDW, your running bankroll must always be over $17,000.