Game number 4

GNU 2-ply seems to have a slight preference for 13/11 8/5, slotting the right point but unstacking the wrong one. The game move looks better to my eye, but maybe there are considerations that I missed.

One more difficult cube decision, and of a very different kind from the previous ones since the doubler is now Black, the match leader. Gammons carry less weight (although with as many gammons as this position has they surely can't be completely discarded), but redoubles carry a lot more weight. As we already went through the weighing of gammons, I will do only the redouble math this time.

Our "usual" 40% gammon rate for Black, and a 20% gammon rate for White give us a take point at 36.5%. But in order to consider the redoubles, we also have to compute Black's take point when White redoubles ; this time we can ignore gammons as they count for a lot less with a 4-cube. Here the possible results (from Black's point of view) are 25%, 50% and 100%, for a take point of 25/75 = 33%.

What does that mean ? After White accepts the double, if he could always redouble exactly at Black's take point, that would mean that his redoubles are always optimally efficient, and that getting to 67% of winning chances would be as good as a win for him. So instead of being played in the 0-100% interval, the game would effectively being played in the 0-67% interval. That turns out to shrink White's take point to exactly 67% of the take point we calculated when we didn't take the redoubles into account, that is about 24% (two thirds of 36.5%).

Now this 24% isn't the end figure since we made the assumption that White would always be able to redouble at the perfect time ; this is of course not the case, and White often will have either to redouble while still short of his cash point, either to lose his market (redouble when the opponent has a pass). So White's actual take point lies somewhere between 24% and 36.5%, depending on how efficient his redoubles are. A rule of thumb is to assume a 60%-70% cube efficiency, which means that the take point would be a little closer to 24% than it is to 36.5%.

A take point of 29% would seem to be almost right on the bubble of how many games White can expect to win. So it is a close decision in any case.

I passed because I thought White's wins would be in the high 25%, seeing that he is far from a favourite to make his 21-point anchor, and he might get crushed if he doesn't make it. But at this score White doesn't fear a doubled gammon too much, so he can play his ace-point games and his deep backgames in a more tenacious way, staying back for longer than he would normally do. This must be one of the reasons for which White seems to win rather 29% of games.

Even though 29% seems to be right on the bubble, GNU says it is a pass anyway. To be honest I am not sure whether he doesn't underestimate White's redouble potential ; I could be wrong here, but I think it is usually easier for the trailer to manage an efficient cube, because he doesn't lose too much by doubling early. This could well be a take.