Probability in Backgammon
The chances of rolling a particular number (or numbers) with two dice aren't always what they seem. For example, with just two points out of six to aim at, you have a 55% chance of getting back from the bar, while the chances of rolling a 1 are not 1 in 6, as it might appear, but nearly 1 in 3.

Understanding the true probabilities of dice rolls can greatly improve your tactical play, by letting you accurately assess the risk of leaving blots, and the chances of hitting and covering points. It also helps you to play strategically, by telling you how to distribute your pieces around the board in order to make the largest number of potential dice rolls work well for you. Probabilities are the secret of why good players seem to get more 'lucky' rolls than beginners.

Dice probabilities aren't based on complex mathematics, but simply on the number of dice combinations which give a particular result. For example, 15 of the 36 possible combinations allow you to move a piece 4 pips (points) around the board. All 36 combinations are equally likely to occur on each roll, so on any roll there is a 41.66% (15/36) probability of getting a 4-pip move.

Probability and odds for online roulette

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Some fixed odds:

Directly rolling a particular number: 30.55%

Rolling a particular double: 2.77%

Rolling a particular non-double: 5.54%

Rolling any double: 16.66%

Chances of moving n points in a single roll:

Move	Direct Only	Direct & Indirect		Move	Indirect		Move	Indirect		Move	Indirect
1	31%	31%		7	17%		13	-		19	-
2		33%		8	17%		14	-		20	3%
3		39%		9	14%		15	3%		21	-
4		42%		10	8%		16	3%		22	-
5		42%		11	6%		17	-		23	-
6		47%		12	8%		18	3%		24	3%

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