ANALYSIS

Rules of Play

A bet must be made prior to the dealing of any cards. Each player and the dealer will then receive four cards face down.

If the four cards are four of a kind, then the hand has one of the highest ranks. Otherwise, all players and the dealer should keep the best three of their four cards and discard the one that they do not want. The three cards that are kept will be evaluated as follows:

 

Card and Hand Values

All cards have a point value.  Face cards and Tens count as 0.  Aces count as 1. All other cards count as their face value.

All hands have a point value. With the exceptions that will be shown in the ranking system below, the point value of a hand is calculated by adding all the points of the three cards together. If the sum exceeds 9, then only the rightmost digit of the sum is used. This Modulo-10 point count system is the same as Baccarat. The highest point total is nine. The lowest ranked hand is zero. Some hand examples are given below:

Queen, 5 and 4 makes a hand total of 9 points.

King, Queen and 10 makes a hand total of 0 point.

3, 9 and 10 makes a hand total of 2 points.

 

Ranking System

The ranking system is shown below, from highest to lowest:

4 of a Kind (4 Aces is the highest, 4 Kings the second highest and 4 2’s the lowest)

KKK

QQQ

JJJ

KKQ

KKJ

QQK

QQJ

JJK

JJQ

Three face cards – KQJ

333

9 Points down to 0 point

 

The bet is played against the dealer. The object is to have a higher point value than the dealer.

Whoever has the higher rank wins. The bet pays 1 to 1 less a 5% commission charged on any player winning hand.

Mathematical Analysis

 

There are C_364,4 x C_360,4 = 719,469,751 * 688,235,310 ways to deal four cards to the player and then four cards to the dealer. A computer program was written to determine the probability distribution and the house advantage as follows:

The player and dealer will beat each other 40.13% of the time and tie 19.74% of the time.

 

The house advantage is 40.1278% – 40.1278% x 0.95 = 2.0064%.

Presented By: Stanley Ko
GAMBOLOGY – PO Box 82225 – Las Vegas, NV 89180 – (702) 258-9685
July 17, 2007