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Kill or Let Die?
by Mary Hickey - March 2007
MARY HICKEY
No, it’s not the latest James Bond movie! This problem is another twist on a theme we have been exploring--what to do about a single checker in your board.

Problem 1:

There was a murder-for-hire case in the US a few years ago where an autopsy showed that the victim had advanced heart disease, and arteries that resembled cement culverts.  If the killers had just waited about six months, Nature would have carried out their bad intent for them, and they would have saved themselves from life in prison. 

Backgammon experts wisely admonish us to “respect a five point board”, so Red might feel threatened enough by White’s position to move in for the kill now by switching points with 2/1*(2).  But some five point boards deserve more respect than others, and Red need not show this one any undue deference when he selects his play here.  White’s awkward, split-up, front-loaded position is an accident looking for a place to happen, and Red should consider simply letting Nature take its course.

My opponent’s actual play was 2/1*(2), 13/11.  The good news is that he chose the best of the hitting plays.  The bad news is, it was a horrific .360 blunder!  If errors were actually the Burger King menu items to which they are often compared, this would have been an Enormous Omelette Sandwich.  It’s ironic that the concept he missed was the great value of a five point board, even as he tried to respect mine by trying to give me fewer shots to hit inside it. 

The problem was that he passed up the opportunity to make a five point board of his own.  His would have been of better quality than mine, since it would have consisted of the top five points, with plenty of spares to use for attacking, controlling the outer board, or perhaps completing a full prime by making his bar point.  By doing this, he’s not passively “letting me go”, since if I roll a 6 and run, in most cases he will get at least a single direct shot back at me somewhere.

(A quick note about “board quality”: Sometimes you’d rather have the lower five points in your board instead of the upper five, but that’s when you’re ahead in the race, and here Red isn’t.  The top five is best when you want to trap, block, and attack, which is his best game plan here.)

This play isn’t an “exception” to the concept of attacking a lone back checker.  It’s preparing for a more devastating attack later, perhaps leading to a win with the cube.  To continue our murderous metaphors, you want to load the gun before you fire it.  It’s also allowing the opponent an opportunity to self-destruct, enabling you to win with the cube without firing a shot.  This will happen now with any roll by White that causes him to break his board leaving two blots, such as 5-4 or 5-3. 

Red’s option to duplicate my 4s to hit or escape was a factor here, but not important enough to make the second-best play, 13/10, 13/12, correct.  We can demonstrate that it wasn’t an irrelevant concern by putting my best spare on my 5 point instead of my 6.  A Mini rollout shows that in that case, making the 5 point with 7/5(2) is better than 13/10, 13/12  by a much greater margin than it is in the actual problem.  (.124 versus .054, not a precise comparison since the rollout of the main problem is much stronger, but pretty convincing just the same). 

Duplication is a means to an end, not an end in itself.  We will see an example soon where duplication is the key to the right play, but also another problem where duplication is overridden by other concerns more central to winning the game than just avoiding an immediate hit.

The rollout below shows that a five point board is so important that even plays that make it but leave a blot on the bar point beat out all the hitting options.


Problem 1 with rollout:

 

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