Board & Card Games Stack Exchange is a question and answer site for people who like playing board games, designing board games or modifying the rules of existing board games. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I recently committed to memory the likelihood of "Entering from the Bar" in a game of backgammon. i.e.

1 point defence - 97%
2 point defence - 89%
3 point defence - 75%
4 point defence - 56%
5 point defence - 31%

Besides the usual likelihood of "throwing a number x", what other statistics are there that I can learn to improve my backgammon game?

share|improve this question
2  
Wow...I've only played BG for fun and memorizing stats such as the above never even crossed my mind! – Gryphoenix Jun 14 '12 at 16:29
    
Even wondered why a computer or good human always seems to get the right dice thrown? Knowing the dice probabilities (in context of the board position) starts to remove the luck factor in backgammon and makes it more strategic and fun to play. – ajmccall Jun 15 '12 at 7:48
up vote 5 down vote accepted

These were all more or less directly copied from the source attributed at the bottom of the answer:

  • Directly rolling a particular number (e.g. 2) 30.55%
  • Rolling a particular double (e.g. 3-3) 2.77%
  • Rolling a particular non-double (e.g. 5-1) 5.54%
  • Rolling any double 16.66%

Chance of getting off the bar with one or two pieces and X open points:

Open
Points  1 piece 2 pieces
1       31%     3%
2       55%     11%
3       75%     25%
4       89%     44%
5       97%     69%
6       100%    100%

Chance of moving X points in a single roll: (direct and indirect combined; direct alone is always 31% for 1-6 only).

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

SOURCE (and more stats): http://www.paulspages.co.uk/bgvaults/tips/dicerolls.php More info on observed Backgammon statistics: http://www.bkgm.com/motif/stats.html

share|improve this answer

I'd learn the chances for the roll combinations. There are 36 possible rolls, (let's say of one red and one green die) as follows:

6-6:  1/36
11:   2/36 (two 6-5s)
5-5:  1/36
10:   2/36 (two 6-4s)
9:    4/36 (two 6-3s, two 5-4s)
4-4:  1/36
8:    4/36 (two 6-2s, two 5-3s)
7:    6/36 (two 6-1s, two 5-2s, two 4-3s)
3-3:  1/36
6:    4/36 (two 5-1s, two 4-2s)
5:    4/36 (two 4-1s, two 3-2s)
2-2:  1/36
4:    2/36 (two 3-1s)
3:    2/36 (two 2-1s)
1-1:  1/36
share|improve this answer

The chance of getting a total of x on the two dice is simply (6-|7-x|)/36 where |7-x| is the absolute value of 7-x.

share|improve this answer

You should always accept a double if your winning expectation from the current situation is 25% or more. You should never accept a double when you have less.

share|improve this answer
    
Not true in match play (first-to-N-points wins) - the take/pass point varies with the match score - or in situations where a significant proportion of your losses will be gammons and backgammons. – Julia Hayward Mar 7 at 8:32
    
"Winning expectation" is not the same thing as "expected number of wins". – Nij Mar 7 at 9:14

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.