Bill Robertie Challenge #84

Cash game, center cube. Black on roll.

Should Black double? If doubled, should White take, drop, or beaver?

Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.

Proper doubles in the very early stages of the game are somewhat unusual. It takes some time to build an advantage strong enough to turn the cube. Most correct early doubles come from blitz positions, where one side rolls a quick double, makes a couple of inner-board points, and catches his opponent on the bar. Here the attacker gets enough gammon chances to compensate for the fact that he still doesn’t have a big positional edge.

Genuine positional doubles in the very early stage of the game are rare, but they can happen. Problem 84 is one example. Although Black has not yet made a new point in his board, he’s made his bar-point, gained a big lead in the race, and has an impressive collection of builders. Most of his rolls will make either his 4-point or his 5-point next turn, after which he’ll be threatening to make a 5-prime and snuff out resistance. Many players have conditioned themselves not to double unless they’ve made at least one additional home-board point, and mostly that’s a good rule of thumb. Be aware that there are exceptions, however.

At the same time, White has a take. Black’s far from guaranteed to make a quick 5-prime, White has an anchor, and Black still has a checker to escape. That’s enough counterplay to keep White in the game for a while. Doubling when you have just a one-point board is unusual, but passing is really rare indeed.

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A very interesting feature of this position, however, is the status of the blot on White’s 5-point. Is the blot an asset for White, or a liability? It appears to be yet another weakness, and in fact a lot of players in Black’s position might be encouraged to double, combining the presence of the blot with their own priming chances. In fact, the blot is actually a strong asset for White!

We can see this if we look at how Black will play his upcoming fours. With 4-2 and 3-1, he will clearly make a point in his board. With 4-3 and 6-4, he’s indifferent between hitting on his 20-point and making a home board point. Only with 4-1 and 4-5 is he clearly right to hit White’s blot. With so few hitting rolls, the blot is clearly good for White since it allows White to build his board faster. In fact, if we change Problem 84 by moving White’s blot from his 5-point back to his 6-point, Black’s double is even stronger and White has a marginal take/pass decision. It often happens that we can only decide if a feature of the position is an asset or a liability by looking at how the upcoming rolls play.

Solution:

Black should double.
White should take.

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