


PART
I
Gambling Ramblings: Extra Stuff by P. Griffin 
Mathematicians frequently confuse, and are confused by, casino personnel in
discussions of win rate (or %) for a game like Roulette. The mathematician describes
the house advantage as 5.26% for a color bet in Roulette because for every 38 units
wagered the house expected to win a net of 2018 = 2 units since there are 20 ways for
it to win and only 18 ways for the player 2/38 = .0526 = 5.26% is then the expected
gain per bet made and is the "mathematical percentage."
Casino bosses have, however, evolved a different method of describing the
performance of, for instance, a Roulette table. They might say that "The PC in
Roulette is 20%" or "The Roulette table holds 20%." This figure is an empirical one
necessitated by the type of bookkeeping casinos use to monitor performance and
appears greatly at variance with the mathematicians' 5%. Who's correct?
Well, a better question is "How is the 20% hold figure arrived at in Roulette?" To
illustrate the casino point of view we'll start with the simplest possible example: one
Roulette table and only one gambler. Suppose the player buys in for $100 worth of
chips and plays for exactly one hour. He may occasionally be ahead or possibly be
wiped out within that hour, but let's imagine he terminates his play (either of his own
desire or because the casino closes the table) with $80 worth of chips, which he takes
to the cashier to be redeemed in money. The pit boss analyses the table's
performance by comparing the $100 drop in the cash box with the 80 missing chips in
the money tray. The difference, 10080 = 20, is the amount that this table "held" and
the quotient of "hold" divided by "drop" or 20/100 = 20%, is the casino's hold
percentage.
It's important to realize that the hold percentage is an empirical, even to some extent
sociological, figure. It varies from day to day, year to year, and it especially varies
with the characteristics of the players. The problem is greatly complicated when there
are different ways to play a game such as Craps, which have different mathematical
percentages and when players, as they frequently do, carry chips from table to table or
game to game.
A couple of oversimplified examples may help to illustrate this dependence. First,
suppose our previously described solitary gambler has enormous endurance and is
determined to play forever or until he loses his entire $100 buy in. Since Roulette is
an unfavorable game, this latter eventuality is the assured result. However long it
takes, when our indefatigable gambler has finally lost all his money and the casino
closes the tables, it will be discovered that all of the chips are still there and so too is
the hundred dollar bill in the drop box. Hence the casino won 100% of the drop. A
mathematician keeping score would count, perhaps, the 1900 dollar bets the gambler
made and report the casino win rate as 100/1900 = 5.26%.
Now let's introduce another table and another gambler. Mr. A buys in for $100 at a
table #1, plays for a while, and then walks away a net loser of $20. Mr. B buys in at
table #2 for just one dollar, wins a dollar, and walks to the cashier a net winner. Now
Mr. A walks over to table #2 with the 80 chips he bought at table #1. He plays for an
hour and only loses two chips at table #2. How will the casino hold performance look
for the two tables? As in the very first example, table #1 will show a 20/100 = 20%
win rate. But what about table #2? Mr. B took away two chips, the one he bought
and the one he won. Mr. A left two chips, the ones he lost. Hence the table has as
many chips as it started with and concludes it "held" all the drop (Mr. B's drop
incidentally, and he was a winner), or 100%.
As insusceptible as win/drop is to precise mathematical prediction it does nevertheless
remain a useful method of description for casinos. The empirical percentages derive a
longterm validity because of the large flow of action. Perhaps one exception to this
is the game of Blackjack where education of the players has probably reduced the
casino hold percentage over the years, although not the profits which continue to grow
because of increased volume.






