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Posted By: Stick
Date: Tuesday, 10 June 2014, at 11:06 p.m.

In Response To: Advanced Backgammon #155 (Igor)

To double or not to double? First let's take a look at O'Hagan's Law:

• At a normal match score when the cube is centered if you have at least 9 market losing sequences and are doing okay on the rest of your numbers you have a double. If there are any sequences where you're doing particularly bad (eg to be seen in this position) you should subtract those sequences from your overall market losing sequences to arrival at your final number of market losers.

Remember it's a market losing sequence. That's both your roll and the opponent's. A lot of people get stuck on their own good rolls and forget the opponent gets to roll and perhaps achieve something before we get to have that doubling decision again.

O'Hagan's Law is very useful in general because it gets you thinking in the right direction. You're seeing how your numbers play, how your opponent's numbers play in response, and counting up your market losers which are important. The Law itself is often tough to apply to OtB positions because we can't, esp. in a limited amount of time, follow the string of every two roll sequence because too many things can happen. For prime v. prime positions though it is definitely easier to apply. Let's look at this problem for example.

Any 6 clearly loses our market no matter what the opponent throws. We will have escaped a man, have great timing, and now the opponent's board will always collapse on his subsequent turns. This alone is 11 market losers.

Are there any other market losing sequences? Nothing noteworthy. Let's not forget to subtract any truly horrible sequences for the doubler. Do you see any? [33 44] are awful leaving us having to pass a cube. We should subtract these two sequences from our overall number of eleven market losing sequences leaving us with nine. The rest of our rolls play generally okay.

With our final tally of market losers tallying ~9 that means the double should be just there according to O'Hagan's Law. O'Hagan's Law doesn't provide us with any means of knowing whether to take or not but it's pretty obvious if we come up with the bare minimum to make it a cube then the take is crystal clear.

Stick

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