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4-23-10 Chouette/Answer

As you can see from the ExtremeGammon evaluation below, it is better to make the point than to hit.
Since we played it wrong over the board, I asked an expert, Matt Cohn-Geier to offer his thoughts on this play:

"The basic problem is that the ammunition just isn't there and if you get hit back with a 3 your attack completely fizzles.  If White hits, he will usually anchor anyway and he is also able to strip away a builder and pick up 22 pips in the race.  Looking at how the rolls play, hitting takes away some of White's good rolls like 12 but it gives White some other good rolls like 41, 43, and 44.

After making the 4, on the other hand, the position is more static.  Of course you still really won't like it if White rolls a 3 but you will have a very solid position.  White will have a decently but not perfectly timed anchor/back game, but he won't have equalized the position.  And it should be clear that you prefer making the 4 point if White enters with one man on the ace.

Hitting is better when White fans with both checkers but there are only 9 rolls that do so, and it's not enough to make up for the swing if White is able to hit with a 3.

As you add more ammo/builders the hit goes up in importance.  In that case if you get hit back you may be able to close the rest of your board anyway and if he misses you have a much better chance of making new points.  Since you have relatively few men/builders here the situation calls for a more pure play."