Backgammon Luck and Skill

Backgammon is a game of chance and skill. The skill generally improves by practice and by becoming familiar with some of the theories and strategies. Many players approach high levels of backgammon skill by use of math and statistics, while others may arrive to more or less the same place by practice. Both will then become the instincts of the player which combined with his/her personality makes up his style and decision making criteria. Backgammon like Luck itself is a strange phenomenon. You can go through periods of abnormal luck where your or your opponents dice rolls deviate greatly from what is normal.



Some useful information:



Statistics for a 1000 rolls with a pair of dice:



The sum of both dice (e.g. 5 and 2) has a statistical norm of 7. The distribution is shown below.



Click below image to see full size






With a large enough sample the above graph should have a distribution that will get normal in the limit x towards infinity, with mean (y+1)*x/2 and the odds you would expect to be something like:



% Chance of rolling any double= 16.67% (For only a 1000 throws expect +/- 3% deviation)



Number of rolls till a double = 6 (For only a 1000 throws expect +/- 1 deviation)



If you or your opponent need a certain combination e.g. 6 and 3, then lets call it a Perfect Roll. This could be a double like 5 and 5 or any one combination. Then:



Number of rolls till Perfect Roll = 36 i.e. (1/6)*(1/6) (For only a 1000 throws expect +/- 3 deviation)



% Chance of a Perfect Roll = 2.78%



Please Note that the above graph is NOT the mathematical odds of sum of rolls. i.e.



Click below image to see full size






The odd of rolling any number or a pair of numbers in backgammon is well publicized and nothing new. The sum of rolls and its significance however gets little attention. This is a very important factor for a winning formula. Don't forget the main objective of the game is to get your stones to your base faster than your opponent, let alone bearing off quicker than him. Both objectives are greatly helped with your larger sum of rolls. From the above graph you may also notice that when you need a sum of rolls of >6 and <12 your odds are clearly favored for 7 down to 11. This could be significant when you want to avoid getting hit.



Remember there are only 21 permutations a pair of dice can possibly give you. That is: 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 33, 34, 35, 36, 44, 45, 46, 55, 56, and 66. Off course in gammon terms, we don't care if the dice are 1 and 2 or, 2 and 1. If you were looking for a number in one dice, lets say 4, then your odds are obviously 1/6. Now, if you had 2 dice and you needed 2 and 1, due to the little fact above, the first dice may be a 1 or a 2 and you're still in with a chance for your 2 and 1. This time your odds of getting your desired number with the first dice are 2/6 or 1/3. The second dice however need to be the other remaining number exactly and the odds of that is 1/6. Hence the odds of non-double perfect rolls being (1/3)*(1/6) while the odds for double perfect rolls are (1/6)*(1/6).



% chance of any doubles = 16.67%



Rolls until a double = 6 (Not any particular double)



Chance of a particular double = 1/36 (e.g. If you need 3 and 3)



Chance of a Perfect non double roll = 1/18 (e.g. 3 and 6 or, 6 and 3) i.e. (1/3)*(1/6)



Chance of a Single number (1-6) = 11/36



Number of Permutations of a perfect roll = 21

 | play65 | Real Money Backgammon | שש בש באינטרנט | Poker
 | Betting Kingdom |