Game Theory

Pick X

Pick X is a bet type where the bettor must pick the winners of X amount of nominated races at the same track.
Pick X has different brand names around the world. For example V64, Pick Four, Scoop6, Win5, Pick5 etc.
In this game theory example we are going to be using an pick 4 bet type as a example. So in pick 4 bet type the bettor must pick the winner of 4 nominated races.


The Pick4 is usually played on different systems. For example: the system of one hundred lines is played so that the first race has one selected runner, in the second race four runners andin the last two five runners.
1x4x5x5=100 lines x betsize

The weakness of this system is the single runner in the first race. The chance of hitting the bet depends solely on it.
In general, systems based on a single coupon have weaknesses: its expensive for larger systems, or relies on single runner selected races.
It must also be taken into account that how large the payout can become compared to the total bet amount if too many runners are selected on a single coupon.


Instead of using single coupon system

When creating systems, the runners of the target races can be divided into groups for example A,B and C runners.

In this example A is the favorite, B is the favorite’s threats and C is a potential surprise winner.
Now system is divided into 16 coupons. 

RACE 1 RACE 2 RACE 3 RACE 4 Coupon #
A AB B C 3
A C AB B 5
A B A C 6
A B C A 7
B A C AB 8
B B BC A 11
B C A AB 12
AB C B A 13
C A B AB 14
C AB A B 15
C A AB A 16

The idea is based on raking the system between A, B and C runners.
Usually one A-runner is chosen, which is the favorite. How many runners are selected for groups B and C is based on the number of lines in the desired system.

A-Runners B-Runners C-Runners Number Of Lines
1 1 1 39
1 2 1 137
1 3 1 391
1 4 1 609
1 1 2 63
1 4 3 1089

For example: If one A, B and C runner is selected for each pick4 race, the number of lines in the system is 39.
If there are three B runners and one A and C runner, the number of lines is 391.

The system always requires at least 1 A -runner’s win.
Other races may be won by A or B runner, but a C runner only once.
So the system of a hundred lines in single coupon in the first example above should usually be rejected.
Usually it makes more sense to choose the 39 and 63 line systems instead.

Now for example A runners can be divided between the two systems and now none of the pick4 races is relying on a single runner and your total bet sizing is still ~100 lines.The same ideology can be extended to include more than four races.