Note that the match score is 5-away for Black, 3-away for White.

XG gives the following numbers for the top two contenders. Since gammons are not possible, I just give the percentage wins for Black followed by the equity reported by XG.

5/Off: 34.8% eq:-0.034
4/3 4/Off: 35.7% eq:-0.068 (-0.034)

Notice that the move with higher percentage of wins (4/3 4/Off) has the lower equity (-0.068). What is the explanation for this? I figure it must have something to do with the cube, but I can't explain it.

(These numbers are for XG under ++, but a rollout doesn't change the basic facts above.)

Experimenting with this position under different conditions in XG:

Money game:
5/Off 34.9% eq=-0.172
4/3 4/Off 35.7% eq=-0.159
Equity is consistent with percentages.

DMP:
5/Off 34.8% eq=-0.304
4/3 4/Off 35.7% eq=-0.285
Equity is consistent with percentages.

So something special is going on at this match score ?!

Yeah, it's due to cube effects. After White's immediate dances, XG thinks the cube is a lot more efficient (in other words, White is closer to the take/pass line) after 5/off than 4/3 4/off.

It's worth giving up cubeless equity sometimes to make your cubes more efficient (or your opponent's less efficient).

My posts in this thread might be helpful:

https://forumserver.twoplustwo.com/1...40/?highlight=

Thanks _Z_, that thread was helpful, especially that example where you compared 8/3* 4/3 vs 8/3*/2.

I will write some more details that helped me understand this. I would appreciate any comments or corrections if anything is wrong.

Let's look at the equities after a dance for both moves in my original position, at both the original score and at DMP. These are from XG's "Dice Distribution" 4-ply.

At the score:
5/off, dance: 0.675
4/3 4/off, dance: 0.362

At DMP:
5/off, dance: 0.184
4/3 4/off, dance: 0.041

At both the score and at DMP, if White dances, then Black is better off having played 5/off than 4/3 4/off. However, at DMP, the risk of getting hit after 5/off makes it the worse play. But at the score, the equity gap between 5/off, dance and 4/3 4/off, dance is much wider, compensating for the risk of getting hit.

(A minor note: The probabilities of dancing in the two cases are equal, making the comparisons valid.)

How is this related to cube efficiency? I like to think of cube efficiency as the additional contribution to equity relative to DMP.

Difference between score equity and DMP equity:
5/off, dance: 0.491
4/3 4/off, dance: 0.321

So the cube after 5/off, dance is more efficient, which compensates for the risk of getting hit.