 |
|
||||||
Backgammon Maths
2008-07-08
Baran Gülçiçek
Baran Gülçiçek
This article was sent in by one of our faithful readers, Baran Gulcicek. Thank you Baran, for your support and contribution to this site.
ODDS
In Backgammon, your probability of throwing any dice is calculated as follows;
1/6*1+1*1/6-1/36 = 11/36
In this equation, 1/6 in the beginning is the probability of the first dice thrown as x. The factor 1 represents any value that the second dice might have (after first dice thrown as x, because it is not important what the second dice might be it is calculated as 6/6, meaning 1)
Samewise, after the cumulative (with the first dice being x), when the first factor is 1 the
In these two expressions, because the probability of xx (22) is only once and it is counted two times, in the final cumulative we can reach the goal by substracting one of these probabilities (1/36 of them) from the cumulative proability.
Because the probabilities in backgammon are limited by 36, we will not analyze the probability calculations in detail. We shall analyze the following probabilities by taking this basic formula as a foundation.
1. Hitting Probabilities
Open 1 = 11/36 --- (dices with 1)
Open 2 = 12/36 --- 11/36 (dices with 2) + 11
Open 3 = 14/36 --- 11/36 (dices with 3) + 11,12,21
Open 4 = 15/36 --- 11/36 (dices with 4)+ 11,13,31,22
Open 5 = 15/36 --- 11/36 (dices with 5) + 14,41,23,32
Open 6 = 16/36 --- 11/36 (dices with 6 + 15,51,24,42,33
Open 7 = 6/36 --- 16,61,25,52,34,43
Open 8 = 5/36 --- 26,62,35,53,44
Open 9 = 4/36 --- 36,63,45,54
Open 10=3/36 --- 46,64,55
Open 11=2/36 --- 56,65
Open 12= 1/36 --- 66
As you can see in the table above, your opponent's probability will occur at most when you leave your checker open for the 6 dice. The lowest probability will occur with the 1 dice.
The chances for being hit are equal when you leave open for a 4 or 5 dices.
For the open checkers you leave for numbers higher than 6, the probability of being hit is at most for 7 and at least for 12.
When you leave your checkers vulnerable in your play, if you pay attention to these probabilities your chances for being hit will reduce.
For the second part of this article, stay tuned to PokerNews.
