From: jacobs@cs.utah.edu (Steven R Jacobs)
Subject: Re: multi-action BJ
In-reply-to: yung@mcnc.org's message of 15 Sep 92 13:37:47 GMT
Organization: University of Utah CS Dept
Distribution: usa
Date: 15 Sep 92 09:40:43

In article <1992Sep15.133747.19140@mcnc.org> yung@mcnc.org (Edward K. Yung) writes:
>
>When a multi-action BJ table is marked with a minimum bet of $5, does this
>mean that the bet for each spot must be higher than $5 or the total bet for
>all three spots needs to be more than $5?

You must bet $5 on each spot that you play, but you don't *have* to play all
three spots.

>It is claimed by experts in this newsgroup that the same basic strategy
>for regular BJ should be used in this game.  My question is related to
>the bankroll.
>Suppose my bankroll is Y, and the optimal bet size is X.

If the optimal bet size is X, you should bet about X/3 on each of the
three spots.  The "true" optimal bet size will be slightly larger than
this since the bets are not entirely correlated, but this effect is small
enough that it isn't really worth worrying about.

>Now if I am asked to bet 3X in this multi-action BJ game, intuitively it
>doesn't feel right to play the same basic strategy.

Intuition and probability theory often do not mix.  Mathematically, the
multi-action game and the "regular" game are identical from the viewpoint
of basic strategy.  Also, basic strategy has absolutely nothing to do with
bet size -- if you use basic strategy, it will be the same whether you bet
$1 or your entire net worth.  Now if you want to talk about log optimal
playing strategy (nevermind, let's not wake up Bill...)

>I cannot afford to bust and lose 3X in the first hand hoping to win
>X for the first bet.

Then bet smaller, or don't place all 3 bets, or play a better game (i.e.
single deck).  This is like saying that you play at $25 tables but you
never double down because you can't afford it.  Basic strategy doesn't
care about bet size.  Even using a log optimal playing strategy, the only
time you might see a "don't bust because your bet is too big" type of
decision is when you have made a bet that is MUCH larger than the optimal
bet for your bankroll.  In other words, if your bet size is optimal
according to Kelly Criterion, the correct log optimal playing strategy
is almost always the same as basic strategy, unless you are counting cards.
If you are counting cards, then the correct log optimal playing strategy
will usuall be the same as the playing strategy derived from only worrying
about expectation.  It should also be noted that these differences in
playing strategy have absolutely nothing to do with the fact that this
is a multi-action game.

Your action is not just hoping to win X for the *first* bet.  You are hoping
to win X for *all*three* bets.  Any action you take in this game effects all
3 bets simultaneously.  The fact that the dealer plays out the 3 hands
separately is mathematically irrelevant, it is as if all the bets were
lumped together into one.

>Can some experts make a connection between the bankroll and the betting
>strategy issues?

I think I've pretty much covered it above.  If your optimal bet is X,
divide that amount among the 3 spots in whatever way pleases you, but
do NOT bet significantly more than X.
--
Steve Jacobs  ({bellcore,hplabs,uunet}!utah-cs!jacobs, jacobs@cs.utah.edu)
"Be afraid.  Be very afraid.  I have K-10 offsuit...."
Newsgroups: rec.gambling