Friday, December 4, 2020

To hit or not to hit?

Recently I came across this position when playing Gnu Backgammon:


 

White to play 65
 

I thought that the big decision is: hit with 13/2* or play it safe with 13/8, 9/3. I hit on the 2, reasoning that I'm only slightly ahead in the race (4 points before the move), I have the stronger board, and gnubg has two blots in his home board, so if it manages to re-enter and hit me it should not be able to consolidate its board. I concluded that I'm well ahead if I hit.

On the other hand, if I play it safe I have no blot, but I risk that after 62, 55, 54, 53, 52, 44 gnubg gets out. That's 10 rolls that make the game even.

So I played the big blunder 13/2* (-0.21 equity compared to 13/8, 9/3, according to XG2's rollout).

Here's the dice distribution of gnubg rolls after my two moves:

Rolls after the best move, 13/8 9/3. Only 55 is dangerous (bringing gnubg's blot to safety)
 

Rolls after my move, 13/2. If gnubg hits me with a 2, XG considers me no longer a favorite.

Seems I overestimated the danger of gnubg escaping when I play safe - only a 55 diminishes my significant lead. I also underestimated my winning chances. I was expecting a small lead like 0.2, not the 0.8 XG assesses. 

My hitting move makes gnubg a favorite if it hits. That's also something I didn't expect. But if you actually look at the positions after every move 2+x, it shows that gnubg can always cover one of the blots and make a three-point board itself, giving us an almost symmetrical position (and costing me 23 pips in the race, obviously).

The basic lesson I learned: with a big roll like 65, don't consider the pipcount before but after the move. I was not 4 pips ahead but 15, which is quite a lead and which suggested a conservative play.


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