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 Tue, 18 Aug 1992 11:13:00 GMT
Organization: University of Utah CS Dept
	<1992Aug13.080700.3263@trl.oz.au>
	<JACOBS.92Aug13074525@cells.cs.utah.edu>
	<1992Aug18.111300.22804@trl.oz.au>
Date: 18 Aug 92 07:46:47

In article <1992Aug18.111300.22804@trl.oz.au> emmerik@titan.trl.OZ.AU (Mike VanEmmerik) writes:
>
>jacobs@cs.utah.edu (Steven R Jacobs) writes:
>
>>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.
>
>Ok, I looked it up. For 1986 (or possibly 1982-1986 averaged) the
>industry total casino win percentage for Roulette was 24.8%. This is
>averaged over 12 New Jersey casinos for 1 (or more) years figures. This
>is a LONG term figure; Michael Hall would be proud of it :-). So, their
>actual return is 25%, while their expectation is 5% (assuming no
>cheating, and we all know that NJ is clean :=). So you tell me, are they
>making money from expectation, or as a result of variance and the poor
>betting patterns of the average gambler?

This 24.8% is HOLD percentage, and is NOT equivalent to expectation.
Expectation is dollars won divided by dollars of total actioin.  Hold
percentage is dollars won divivded by dollars dropped into the slot in
the table.  These are entirely different concepts.

>In a certain sense, expectation is where they make all their money, but
>I like to think of expectation as a kind of ideal mathematical
>theoretical concept, that can be written as 5.26%.

Fine, expectation is a mathematical concept, and for roulette the expectation
is 5.26 percent.  Variance is also a mathematical concept.

>Sure, variance lets the average player win almost half of the time, but
>typically players just bet it all back again until the next downswing
>wipes it out, and they never get to the theoretical expectation because
>they have insufficient bankroll.

What do you mean?  The theoretical expectation for the player is to lose
5.26% of every dollar BET.  The long you play, the closer you come to
reaching this ideal.  Yor own data suggest that the "typical" player
plays until they lose 24.8% of the money that they brought to the table,
or that 24.8% of the players lose all of their money while the rest
break even, or some mix of these two extremes. This suggests that the
typical player plays long enough to risk their original buy-in about
5 times over, for a total action of 5X the buy-in, losing the expected
25% of that buy-in.  Any way you compute it, the variance isn't a factor.

>>>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.

Yeah, what I said before :-)

>Well, that's sure one way of looking at it. But how can you say that
>variance has *nothing* to do with it?

Go back and read what I said.  I said that variance isn't the casinos
friend EXCEPT to the extent that it gives players the illusions that
they can win.  It is this illusion that keeps them at the tables long
enough to slowly and gently separate them from their money.

>If variance were zero, all players
>would lose very close to 5.26% every sitting, and the figure in Shelly's
>book would read "5.26%".

No.  The figure in Shelly's book is NOT expectation.  It is hold percentage,
although Shelly might not have called it that.  If you were to sit at a
roulette table and keep track of the total amount bet and the total amount
won, and do this for 12 years, you would find the expectation to be very
close to 5.26%.

>>>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.
>
>Hmmm. I'm starting to suspect a misunderstanding of terms.

You're correct.  You do not understand the terms "expectation" and
"variance".  These are mathematical concepts which have a precise
meaning.

>The same
>table quotes "Win" as 9,247 (million $US, I think) and "Drop" as 37,344.

Note the keyword "drop".  Drop has NOTHING to do with expectation.  Go
to a roulette table and give them a crisp new $100 bill, and they will
give you $100 in chips and DROP your $100 bill down the slot.  Expectation
is total won divided by total bet.  Drop isn't even in the equatioin.

>Divide the first by the second, and multiply by 100%: 24.8%. I assume we
>mean the same thing by "Drop" and "total action".

You've just explained how to comput HOLD percentage.  Expectation is an
entirely different concept.

>>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.
>
>Sorry, cant agree. With variance, average player loses 25%. Without, he
>loses 5%. I prefer the latter, especially if the casino will comp me for
>something more than 5% of my action.

In other words, you're willing to give 25% to the casino as long as you
can live with the illusion that you are only giving them 5%.  Any casino
that would comp roulette players for more than 5% of their ACTION is
managed by blithering idiots.  Show me a casino that does this, and I'll
show you a casino that will either go broke (assuming similar comp policy
at other games) or quick fire the dope who set up their comp policy.  They
might comp you for 5% of the DROP, but that is an entirely different thing.

To put it simply, if you play roulette long enough you will lose 100%
of your money.  This in no way changes the fact that the expectation
for roulette is 5.26%.
--
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