From: jacobs@cs.utah.edu (Steven R Jacobs)
Subject: Re: Betting both sides to get Comps
In-reply-to: emmerik@titan.trl.OZ.AU's message of Thu, 13 Aug 1992 08:07:00 GMT
Organization: University of Utah CS Dept
	<1992Aug13.080700.3263@trl.oz.au>
Date: 13 Aug 92 07:45:25

In article <1992Aug13.080700.3263@trl.oz.au> emmerik@titan.trl.OZ.AU (Mike VanEmmerik-ITG Brisbane) writes:

>>[munch]
>>wrong bet.  All betting both sides does is reduces the variance of
>>outcomes without affecting expectation.  I would think that a
>>casino operator that comped 1 unit bets on right or wrong but not
>>1/2 unit bets on both was acting irrationally.  Is there something
>>I'm missing?
>
>Yep. Variance is where the casino makes most of its money, since most
>people have too small a bankroll.

Nonsense.  Expected gain is where the casino makes ALL of its money.
Variance is not the casinos friend, except to the extent that it gives
the players the illusion that they can win.

>Expectation (house percentage) is only
>5.25% for Roulette (ignoring the 5 way bet), but they make 20%-30% due
>to variance and low bankroll.

They hold 20% to 30% because players tend to give enough action to risk
their entire bankroll 5 or 6 times over.  The 5.25% edge at roulette
multiplied by 500% of bankroll equals the 26% (or whatever) that the
house keeps.  Variance has nothing to do with it.

>If they figure on 20% of action as a comp,

They'd quickly go broke with this kind of policy.  Comps for high roller
are MUCH less than 20% of total action.  Think about it.  If Joe Moneybags
is betting $200 a pop on blackjack and playing 50 hands/hr, his total
action is $10,000/hr.  His free room/meals/airfare would be covered in
the first hour of play if they comped at a 20% rate.

>then variance reducing techniques will cost them money. Assuming they
>flash to what is going on, of course. But they would not be acting
>irrationally to be upset by this technique.

Nonsense.  Variance reducing techniques will simply reduce the
probability of completely busting some players, and increase the
amount of time required for the house to reach "the long run".
House take is expectation multiplied by total action.  Hold percentages
give the pit critters something to worry about (besides card counters),
and help them feel like they are doing something important.

In fact, the casinos would be smart to *encourage* variance reducing
techniques by the players.  When you reduce your variance, you reduce
the variance for the house as well.  Simultanously betting red/black
on roulette or pass/don't at craps GUARANTEES that the house cannot
loose money.  This reduces the casinos risk of ruin to ZERO.  They
wouldn't have to keep large sums of cash on hand to pay the winners
if everyone played this way, since there would be no winners.

Moral:  What's good for the goose is good for the gander.  Reducing
player variance, when the house has the edge, simply tends to ensure
that the casino will take your money.  Sure, you can smooth out the
bumps in your bankroll by reducing variance, but when the house has
the advantage this simply smoothes away the fluctuations that sometimes
put the player ahead.

Now, if the casino will comp at a good enough rate to make up for the
"slow leak" that gently robs you of your money, then a minumum variance
approach would be useful.  But, finding a place that gives cash back
after they've paid for RFB (room/food/beverage) and airfare is going to
be tricky.  By the time you've given enough action to qualify for major
comps, you will have paid for those comps several times over with or
without variance.
--
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."