Backgammon Probability Charts

 Here are a couple of charts that you may find interesting. The first one shows you what your chances are of entering both one man and two men from the bar. A couple of points are worth noting: With just one of you men on the bar, even if your opponent has a full four points closed, you still have better than a 50-50 chance of entering. Only when he has just one point open, (a full five points closed) do the odds favor you not entering. With two of your men on the bar, the situation is drastically different. Here you need a full five points open before you have a better than 50-50 chance of entering both your men. Even with four points open, your odds of entering both men are less than half - just 44%. (This is why it is often correct to send a second checker to the bar, if you get an opportunity to do so.)

 This second chart shows you the percentages of hitting a blot, wherever it may be on the board, assuming that all the points between your man and the blot are open. (And often they aren't.)For example, if your opponent's man is 24 points away, only a roll of double sixes will hit this man... 1 chance out of 36 or about 3%. If a man is 12 points away, there are just three rolls that will hit it. (3-3, 4-4, or 6-6 would do the trick.) Note the big drop-off after your opponent's man is six points away. You have the greatest chance of hitting a blot if your checker is six points away... 47%, almost a 50 - 50 chance. (The 17 rolls that hit are 1-5, 1-6, 2-2, 2-4, 2-6, 3-3, 3-6, 4-2, 4-6, 5-1, 5-6, 6-1, 6-2, 6-3, 6-4, 6-5, 6-6.) However, if this blot is just one further point away, the chances drop to just 17% since now only six rolls of the dice will hit. (1-6, 2-5, 3-4, 4-3, 5-2, 6-1)