You don't have to be a math wizard to play backgammon.

In a court decision, backgammon was found to be a game of skill rather than chance, because there is nothing hidden, as there is in card games such as poker. You can see all the checkers and their positions at all times. This also makes backgammon a better game than poker, as far as I’m concerned, because I’m not a good bluffer.

However, there is an element of luck in backgammon because you roll dice. Knowing the odds of getting a specific roll is important in determining your strategy. The following chart shows the chances of hitting or being hit by an opponent’s checker, depending on the number of pips they are apart.

Read the chart like this: 1-11/36 means that if the checkers are 1 pip apart there are 11 chances in 36 of hitting or getting hit as a result of a single roll of the dice.

1-11/36; 2-12/36; 3-14/36; 4-15/36; 5-15/36; 6-17/36; 7-6/36; 8-6/36; 9-5/36; 10-3/36; 11-2/36; 12-3/36; 16-1/36; 20-1/36; 24-1/36.

Memorize this chart. This is important if you want to play a decent game. (You didn’t know there was going to be homework, did you?)

A roll of 2 dice has 36 possible results (that’s where the 36 comes from). Note that the chances of getting hit are greatest if the checkers are 6 or fewer pips from each other. Being 6 pips away from another checker is the most dangerous distance. A checker will hit another checker 6 pips away 17/36 or almost half the time. At the lower end of the scale, being 1 pip away reduces the risk of being hit to 11/36 or less than 1 in 3. This is because you have to roll a 1 on at least 1 of the dice, and there are 11 ways to do this.

Note that if checkers are more than 6 pips apart, the risk of being hit is greatly reduced, from 1/6 times at a distance of 7 or 8 pips to half that or less at a distance of 10 to 12 pips.

There are complicating factors. Let’s say you’re trying to hit a blot 6 pips away from you. You’ve got a good shot at it, right? You’ll hit it 17/36 or almost half the time. However, let’s suppose your opponent has blocks on all 5 of the points between you and the blot. That reduces your chances of hitting it from 17/36 to 11/36.

Here’s why. You can’t land on your opponent’s blocked points. Therefore, you can only hit the blot if you roll a 6 on at least 1 of the dice. As with rolling a 1, there are only 11 ways to do this. If your opponent has fewer than 5 of the points between your checker and his blot blocked, that may or may not reduce the odds of hitting it, depending on how many points are blocked and where they are located.

Here’s another complicating factor. Suppose you leave a blot on a point that is 1 pip away from 1 of your opponent’s checkers and 2 pips away from another of his checkers. What are the chances of getting hit? Add the chances of getting hit by the checker 1 pip away (11/36) to the chances of getting hit by the checker 2 pips away (12/36), for a total of 23/36. Then subtract the duplicate rolls, of which there are three (1-1, 1-2, 2-1). So your chances of getting hit are 20/36, or more than 50 percent. If your opponent has checkers on 2 different points within 6 pips of your blot, your chances of being hit are always greater than 50 percent.

The chances of being hit increase to well above 50 percent if your opponent has checkers on 3 or more points within 6 pips of your blot.

In general, you want to maximize your chances of hitting your opponent’s blots and minimize the chances of being hit. Having said that, you have to take calculated risks to get your pieces around the board and deter your opponent from doing the same.

If you know what the risks and rewards are, you can make intelligent decisions. But watch out for two things.

Don’t think that just because you made one lucky roll you’ll continue to be lucky, so you can ignore the odds. And don’t abandon your basic strategy because your opponent has hit you three times in a row against 11/36 odds. Each roll of the dice is independent from the others. There’s no such thing as a lucky streak or an unlucky streak.