Dice Probabilities

Many choices in a backgammon game rely on understanding dice probabilities. There are 36 different outcomes when two dice are thrown, all of them equally likely-six ways of throwing the first die, and for each of them, six ways of throwing the second die. Note that rolls of 1-4 and 4-1 are different outcomes, which means that there are two chances in 36 of throwing a 1 on one die and a 4 on the other.  
 
Let's say you are choosing between two different moves, each of which will expose one of your stones to being hit. One move will expose a stone that's one point away from opposing stone; the other move will expose a stone that's nine points away from an opposing stone. Which move is riskier, and by how much? To answer this question, simply count the number of throws that will allow the opponent to hit you in each situation. When the opponent is one point away from your blot, 11 rolls will allow the opponent to hit you: 1-1, 1-2, 2-1, 1-3, 3-1, 1-4, 4-1, 1-5, 5-1, 1-6, 6-1. That's 11 chances out of 36. If instead your blot is nine points away, the chance of its being hit is only 4 out of 36 (the opponent would need to roll 3-6, 6-3, 4-5, or 5-4).