I had this position on a match on DailyGammon. I really struggled to calculate my take point here, because I couldn't quantify the value of owning a 4 cube. So I passed the double. This is a pass in a cash game and a pass if it were an initial double, at this match score though it's a 0.189 error to pass here. How do I figure out the value of owning the 4 cube in this spot?

If the score was more imbalanced, say if it was 15-9, you should be redoubling to 8 to *extremely* aggressively, so you would assume the game would always end with an 8 cube, calculate your take point based on that (accounting for the fact that you win 16 sometimes), and adjust down a percent or two since always doubling to 8 is a little suboptimal.

But here, you probably won't be doubling to 8 *that* aggressively (though you should still be quite aggressive, say if White dances, you should redouble that, despite the fact that you are losing). You're going to have to guess at how often the game ends at the 4, 8 and 16 levels. The math would look like this --

Equity after passing -- 21%

Equity after taking and losing 8 -- 0%. Equity after taking and losing 4 -- 12%. I'm going to guess that due to gammons and aggressive recubes, 75% of losses are at the 8 level. So that means equity after taking and losing is 75% of the way from 12 to 0. So 3% on average.

Equity after taking an winning 16 -- 100%. Equity after taking and winning 8 -- 75%. Equity after taking and winning 4 -- 50%. When you win, you might win 16 20% of the time, win 8 60% of the time, and win 4 20% of the time, so equity after taking and winning, would be .2 * 100% + .6 * 75% + .2 * 50% or 75%.

So now we have the three relevant match equities -- 21%, 3%, and 75%. You are risking 18 (21-3) to gain 54 (75-21). You're getting 54 to 18 odds, exactly 3 to 1, so you should take if you win this more than 25% of the time, by this analysis, which is probably not particularly accurate, but it shows what you can do.

But I don't know how many players would do that (or some equivalent other method) over the board. Some would, I'm sure. I wouldn't. I could try, but I'd be likely to screw it up somewhere anyways. I might calculate my take point assuming I always redouble to 8, just like in the more imbalanced score position, and if I think I'm within a few percent of that figure, I would take.

Thanks for that, These kind of positions are my biggest weakness. I know how to calculate risk/risk+gain but comparing various equities with deep cube potential can be difficult.

Happy New Year