From: jacobs@cs.utah.edu (Steven R Jacobs)
Subject: Re: VP MATH:  Any analog to the BJ strategy tables?
In-reply-to: hallyb@globbo.enet.dec.com's message of Mon, 17 Aug 1992 14:21:51 GMT
Organization: University of Utah CS Dept
Date: 17 Aug 92 09:50:33

In article <1992Aug17.144608.17115@nntpd.lkg.dec.com> hallyb@globbo.enet.dec.com (John Hallyburton) writes:
>Sorry I won't be at the BARGE this weekend; I'll be doing Dallas.  Ahh, I
>mean, nevermind.
>
>But I do have a VP playing strategy question.  Are there any guidelines for
>how to change playing strategy depending on jackpot size?

There are a few adjustments listed with the strategy in the FAQ, such
as tossing the 9 in KQJT9 straight-flush to go for the royal if the
jackpot is larger than 2282 max bets, and breaking up two high pair
if you have 3/royal.  These adjustments are based purely on expectation,
and would undoubtedly be different for a different utility function (such
as logarithmic).

> Assume you are playing an 8/5 progressive jackpot (for royal flush) machine.
> You are playing MaxBets and are dealt K Q K Q 10, the last 3 cards suited.

Draw to the royal if the jackpot is larger than 2100 max bets.

> It seems obvious to me that one discards the first K/Q and draws 2 to the
> big jackpot.  What about K K K Q 10?  K Q K Q 9?  K K K Q Q?  K K K K Q?

The KQKQ9 is the only one you'd break up to go for the royal flush.  The
expectation when drawing two to a royal is about 2.9 max bets.  Each of
these other hands is guaranteed to pay more than this.

> Isn't it true that for each *winning* pat hand dealt there is a certain 
> jackpot size that makes it worthwhile to pitch the winner and draw to the
> royal flush?

Yes, but in many cases the jackpot would have to be astronomical to make
it worth doing.  For example, four 2s with a 3 kicker or 23456 straight flush
would require you to discard all five cards and give up a substantial win
in order to go for the royal.  Look at it this way: if you stand with say
a full house, you win 8 max bets.  Would you bet 8 max bets to go for the
royal flush?  If so, then you should go for it.  If not, you should stand.
If you break up a pat hand to go for the royal, you are in effect making
an inordinately large bet in order to make the draw.

>Consider getting dealt K K K Q Q.  You can stand pat for a payoff of 8, or
>draw 3 to a suited K Q in hopes of pulling a royal flush.  By my math (not
>always correct) you have 1 chance in C(47,3) = 16215 of getting a royal flush,
>therefore if the jackpot is greater than 16215 * 8 = 129720 MaxBets (unlikely)
>then you should draw to the royal.  Of course one really should consider the
>effect of other draws and payoffs that could happen -- you might draw trips,
>a straight, flush, full house (!) or other hands that pay off, thereby 
>reducing the minimum jackpot required to play for the royal flush.

In terms of expected gain, the full house is worth 8 max bets while drawing
3 to KQ suited is worth only about 0.69 max bets (this data is listed in
the FAQ).  Clearly, you should keep the full house.

>It seems such a strategy table would be a tedious but straightforward job to
>produce.  Ultimately you should be able to use the results to tell you when a
>progressive VP game is positive expectation.  Then you could start work on the
>player's variance and bankroll requirements.  That would be something new! :-)

It would be fairly easy to express the expectation for each hand as a "fixed"
part and a part that depends on the size of the royal flush jackpot,
so that you could determine the correct play for any size jackpot.  As a
practical matter, there are really only a few playing decisions that change
as a function of the jackpot, and the jackpot usually must be huge for
a change in strategy to be correct.
--
Steve Jacobs  ({bellcore,hplabs,uunet}!utah-cs!jacobs, jacobs@cs.utah.edu)
"Never teach a card counter to sing.  It wastes your time and gets the card
 counter barred."
Newsgroups: rec.gambling