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 book-keeping 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 in Roulette arrived at?" 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 lets 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 tables performance by comparing the $100 drop in the cash box with the 80 missing chips in the money tray. The difference, 100-80 = 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 realise that hold percentage is an empiracal, even to some extent sociological, figure. It varies from day to day, year to year, and especially it 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.
