Dice tables

Created by Sho Sengoku, 2003

By differentiating 35 and 53 , rolling a set of two dice means that there are 36 possible combinations. A dice table makes this point clear.

Visualizing the dice table is often useful when you count dice numbers you need for a particular situation like "how many numbers out of 36 can hit the blot", "how often one checker can enter from the bar", "in what probability all checkers can bare off at once", or "what numbers can save gammon." You can get exact numbers of dice combinations without counting on your fingers.

Even if you have trouble in this "visualization" process in a live game, the table is still useful when you study backgammon positions because it makes nature of dice number count clearer.

Dice table
B1 B2 B3 B4 B5 B6
R1 r1b1 r1b2 r1b3 r1b4 r1b5 r1b6
R2 r2b1 r2b2 r2b3 r2b4 r2b5 r2b6
R3 r3b1 r3b2 r3b3 r3b4 r3b5 r3b6
R4 r4b1 r4b2 r4b3 r4b4 r4b5 r4b6
R5 r5b1 r5b2 r5b3 r5b4 r5b5 r5b6
R6 r6b1 r6b2 r6b3 r6b4 r6b5 r6b6

Example: Any n (n=1~6)

When you need any particular number, "4" for example, there are 11 numbers out of 36 combinations.
  b1 b2 b3 b4 b5 b6
r1
r2
r3
r4
r5
r6
Any 4 (11 numbers)

Example: Any i or j (i, j=1~6)

  b1 b2 b3 b4 b5 b6
r1
r2
r3
r4
r5
r6
Any 3 or 5 (20 numbers)
By relocating or switching the position of the rows and columns, the total number of "any i or j" becomes clearer. For example:
  b1 b2 b3 b4 b5 b6
r1
r2
r4
r6
r3
r5
Any 3 or 5 (20 numbers)

Example: Any i, j, or k (i, j, k=1~6)

b1 b2 b3 b4 b5 b6
r1
r2
r3
r4
r5
r6
Any 1,2, or 3 (27 numbers)

Last two checker bearing off models

Single Direct Shots

Single Indirect Shots

Double Shots

 

See:     Other articles by Sho Sengoku
Other articles on Probability

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