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A Bearoff Lesson

It is Double Match Point, and Red to play 3-1.  What's your play?







Answer:

The goal, especially when gammons don't matter, is to clear your checkers off without leaving a shot.  With two of White's checkers on the bar, Red is a strong favorite to win if he does not leave a shot and get hit.  So the goal is to clear from the top, starting with the 6 point.  With this roll, since the 3 gives Red a spare on the 3 point if he plays both checkers off the 6 point, the odds are strong that he will not leave a shot on the next roll.  No matter how you play this roll, there will always be some chance of leaving a shot on the next roll or future rolls, but by clearing from the top, there is also the chance that White will bring his checkers in before a shot is left. 

Now, if Red had rolled a 4-1, clearing from the top would not have put a spare on the 3 point, so the shot-leaving numbers are higher, and therefore the correct play would be to take a checker off the 4 point and move 4 to 3 with the other checker.  With a 5-1, it would be best to take a checker off the 5 point and move 5-4.  So a good rule of thumb if safety first is the only issue (and gammons don't matter) is to clear from the top if you have a spare on the 3, 4, or 5 point or if you can keep your checkers even where there is no chance of leaving a shot on the next roll. 

Rules of thumb are helpful, but they don't apply in all situations.  The best exercise to learn bearoffs in different situations is to put a position like this into ExtremeGammon, or Snowie or GNU or whichever bot you prefer, and keep changing the roll and the number of checkers your opponent has on the bar and the score and the strength of your opponent's inner board and each time, decide what you would do, then see what the bot says it right.  Remember to roll it out if the answer is close, as many times in very close situations the rollout will change and improve the decision of the evaluation.


[Note:  I use and strongly prefer ExtremeGammon for many reasons, but in this case you can hit the xg roller button and get a 3600 mini-rollout in a couple of seconds and it is far more accurate than 3 ply or 2 ply in Snowie or GNU.  Then, if you do need to roll it out, you can do so much faster on ExtremeGammon.   You can buy this software for $50 at www.extremegammon.com and if you do buy it, contact me and I will give you a free tutorial on using it.]



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