From: jacobs@cs.utah.edu (Steven R Jacobs)
Subject: Re: Betting both sides to get Comps
In-reply-to: sethb@fid.morgan.com's message of Thu, 13 Aug 1992 21:45:11 GMT
Organization: University of Utah CS Dept
	<1992Aug13.162035.16529@kronos.arc.nasa.gov>
	<JACOBS.92Aug13113351@cells.cs.utah.edu>
	<1992Aug13.214511.7205@fid.morgan.com>
Date: 13 Aug 92 16:23:36

In article <1992Aug13.214511.7205@fid.morgan.com> sethb@fid.morgan.com (Seth Breidbart) writes:
>
> In article <JACOBS.92Aug13113351@cells.cs.utah.edu> jacobs@cs.utah.edu
> (Steven R Jacobs) writes:
>
>>Yup, but that is a two edged sword.  Variance also increase the risk to
>>the casino (and before anyone says "what risk, the casino has a huge
>>bankroll", I'll say "then why do casinos sometimes go broke?").  If the
>>games had zero variance, the casino wouldn't _need_ a huge bankroll.
>
> Casinos go broke when customers stay away in droves.

Sigh.  That argument obviously applies to any capitalistic enterprise.

>
> I've never heard of a casino going broke because gamblers won too
> much.

I personally know someone who broke the bank at a casino.  OK, so it
was a piddley little place in Scotland, and the bank was only a few
hundred dollars, but....

> For that matter, would anyone care to estimate the log-optimal bet
> size on craps or roulette for the casino?

Easy, for roulette it is about 5% of the casinos bankroll.  For craps,
it ranges from less than 1% to more than 10% depending on the players.
Adjusting this for light bills and pit critter salary might get tricky...

> I doubt that any bet larger than that is often made.

True, but it might be wise for the casinos to use Kelly principles
to optimize income rates, based on overall action at any given time
rather than on any _single_ bet.  Seems to me that this is part of
the reason for table limits.

> Betting less than log-optimal gives a zero risk of ruin.

True but irrelevant.  Any bet size gives a zero risk of ruin if you
simply avoid any situation that would require you to risk your entire
bankroll.  Zero risk of ruin is MUCH different than zero risk of losing
money.  A casino doesn't have to lose the entire fortune of its owner(s)
in order for it to become unprofitable enough to warrant shutting down.

My main point is that given a game with zero variance, a reasonable
house edge, and enough people willing (or braindead enough) to play
the game, the house needs only enough cash on hand to make change for
the players and cash their payroll checks.  Note that this assumes that
"reasonable house edge" and "enough people" means that the house takes
in enough money to at least pay operating expenses and make enough profit
to keep the owner(s) appeased.  Modulo expenses, there is NO risk to the
house in this scenario, and no need for a large bank to absorb flucuations.

> Restaurants have "zero variance" in that they make money on every
> meal, but they still go bankrupt a lot.

How pertinent :-)

Casinos are in the business of separating the player from his/her money,
gently enough to keep the player coming back for more abuse.  This
involves some risk on the part of the casino, with the exception of
CA card rooms which are really in the "poker table rental" business
rather than the gambling business.  Some casinos fail, and I really
don't think it is realistic to blame this on *everything*but* bankroll
management, any more than it would be realistic to always blame it
entirely on bankroll management.
--
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."