Counting shot hitting numbers

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One concept that all backgammon players should understand early on is the probability of hitting numbers. So let's compare the difference between a blot that is 1 space away, to one that is 6 spaces away. Which one has more chance of getting hit? Well, lets count the rolls.

So this image is the standard 6*6 grid that we use to count rolls. There are a total of 36 unique rolls. Even though in backgammon some rolls are the same like 6-5 and 5-6. But we count them as unique for calculation convenience with the 6*6 grid.

So back to our first quiz. What is the difference between a blot 1 away and 6 away? The blot that is 1 away has 11 rolls that hit it.
[1-1] [1-2] [1-3] [1-4] [1-5] [1-6] [2-1] [3-1] [4-1] [5-1] [6-1]

A blot that is 6 away can be wacked 17 kinds of ways.Lets count them.
[6-1] [6-2] [6-3] [6-4] [6-5] [6-6] [1-6] [2-6] [3-6] [4-6] [5-6] the standard 11 direct shots AND [3-3] [4-2] [2-4] [5-1] [1-5] [2-2] for a total of 17 shots. 6 happens to be the most hitting number and it drops off sharply with 7 as it is the first indirect shot. So if you can stay 7 away you are relatively safe. If you want to minimize your chance of getting hit, stay 7 or more away, or if that isn't possible, try to scoot as close as possible to the hitting checker with 1 away the best chance and as the numbers go up so do the hitting chances, up to 6 which is hit 47% of rolls.

How many rolls hit with a 7?
[6-1] [1-6-] [5-2] [2-5] [4-3] [3-4] that's it. Only 6 hitting numbers 16.6%

What about numbers that can't be hit?
Yes we have some of those as well. [13] [14] [17] [19] [21] [22] [23] are all safe from any roll.
Generally once you get to 7, the further away you are the fewer hitting chances.

This page has more info about this subject http://www.paulspages.co.uk/bgvaults/tips/dicerolls.php