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Backgammon MathLooking at positions with regard to their chances of a winning movement is how you as a player estimate your ability to win games and matches. You estimate that the dice will allow you that much movement, maybe if you play a double it could go against you, so strategising checkers as well as dice play can bring about a reasonable estimate for success. If there is at least a quarter of a chance of winning that is; then go for it.There are some occasions when your ability to estimate isn't required when a precise move comes available, for example you have two checkers on your ace-point and the opposition two pieces on their 5 and 2 points. They double. Which leaves 19 rolls to get both pieces off out of the remaining 36, giving you a 53% chance to win, therefore you take it. .Now suppose they are on the 5 and 1 points. 23 good rolls that's 64%. You still take. But just supposing they're on the 4 and 1 points. Now they have 29 good rolls or 80%, time to drop. That is where the right estimate comes into play, the better you can estimate the more chances you have to win. Now to backgammon real business: When rolling 2 dice, there are 36 possible combinations. 6 of these are doubles, the other 30 are not. A given non-double roll is twice as likely to come up as a double roll. To understand this, pretend the dice are different colors – say, one red and one green. You can roll a 6-5 with a red 6 and a green 5, or a red 5 and a green 6. But you can only roll 6-6 with a red 6 and a green 6. Of the 36 possible rolls, the following are the number that will give a given total: 2 1 3 2 4 3 5 4 6 5 7 6 8 5 9 4 10 3 11 2 12 1 Of the 36 possible rolls, the following are the number that will give you some combination of one or more dice: 1 11 2 12 3 13 4 15 5 15 6 17 7 6 8 6 9 5 10 3 11 2 12 3 15 1 16 1 20 1 24 1 The odds on rolling a particular number, when the following number of numbers are available, (for example, the odds of entering from the bar with the following number of open pips) are: 1 11/36 2 20/36 3 27/36 4 32/36 5 35/36 6 36/36 The point of backgammon is that there are hundreds of different situations that arise, and if a good player gets them all right and you don't, you are giving him a huge advantage over time.
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