Re: Optimal Betting Question?

Posted by Pete Moss on August 25, 1997 at 17:24:20: In Reply to: Re: Optimal Betting Question? posted by DvBj on August 25, 1997 at 13:02:13:

What is the Kelly bet when the advantage can be two different things to two different people?

The Kelly bet can be two different amounts to the two different people.

Isn't the EV used to determine the Kelly bet just an estimate anyways? And shouldn't you adjust the bet for how
accurate the estimate of EV is?

You say EV is an estimate. I ask, "If so, what is it an estimate of?" The "true" EV? How is that defined?

Statistical or probabilistic calculations like EV are always personal, subjective. They depend on what you know.

A person who has tracked the shuffle has different knowledge than one who has merely counted the observed cards. The two people have different expectations, and the correct Kelly bets for the two people will therefore be different. There is no one "correct" Kelly bet. It depends on what you know.

Card games obscure the subjectiveness of probability somewhat because there is one knowledge-state that we sometimes (incorrectly) consider "perfect", namely knowledge of the exact makeup of the rest of the deck, but not the order. Real perfect knowledge would require that you know the exact sequence of the remaining cards, plus imponderables like whether the dealer is predestined to deal a card out of sequence or drop the deck on the floor. With perfect knowledge, the correct Kelly bet would be to bet all or nothing. The shuffle-tracking example shows that knowledge of the makeup of the rest of the deck is not really perfect. The shuffle-tracker often has knowledge about the next few cards, more exact (less "entropic") than a standard card-counter's knowledge. A player who has gotten a peek at the dealer's hole card has even more knowledge, but it is still incomplete.

Pete

"Probability does not exist." -- Definetti



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