By differentiating and , 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.
Example: Any n (n=1~6)When you need any particular number, "4" for example, there are 11 numbers out of 36 combinations.
Example: Any i or j (i, j=1~6)
By relocating or switching the position of the rows and columns, the total number of "any i or j" becomes clearer. For example:
Example: Any i, j, or k (i, j, k=1~6)
Last two checker bearing off models
Single Direct Shots
Single Indirect Shots
Other articles by Sho Sengoku
Other articles on Probability
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