Ralph Vince - Portfolio Mathematics

ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0

The Random Process and Gambling Theory 19

Whenit comes to casinogambling, though, the only time you can find a

positive expectancy situationisif you keep track of the cardsin blackjack,

and then onlyif you are a verygood player, and onlyif you bet your money

correctly.There are manygood blackjack books available, so we won’t

delve any furtherinto blackjack here.

Baccarat

If you want togamble at a casino but do not want to learn to play blackjack

correctly, then baccarat has the smallest negative expectancy of any other

casinogame.In other words, you’ll lose your money at a slower rate.Here

are the probabilitiesin baccarat:

Banker wins 45.842% of the time.

Player wins 44.683% of the time.

Atie occurs 9.547% of the time.

Since a tieis treated as a pushin baccarat (no money changes hands, the

net effectis the same asif the hand were never played) the probabilities,

when ties are eliminated become:

Banker wins 50.68% of the time.

Player wins 49.32% of the time.

Now let’s look at the mathematical expectations.For the player side:

ME=(. 4932 ∗1)+((1−.4932)∗(−1))

=(. 4932 ∗1)+(. 5068 ∗(−1))

=. 4932 −. 5068

=−. 0136

In other words, the house advantage over the playeris1.36%.

Now for the banker side, bearinginmind that the banker sideis

charged a 5% commission on wins only, the mathematical expectationis:

ME=(. 5068 ∗.95)+((1−.5068)∗(−1))

=(. 5068 ∗.95)+(. 4932 ∗(−1))

=. 48146 −. 4932

=−. 01174