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Position of the Day 05-03-25

Posted By: John O'Hagan
Date: Wednesday, 18 June 2025, at 5:13 p.m.

In Response To: Position of the Day 05-03-25 (Stick)

If Blue recubes, White will certainly take and win immediately on Blue's 16 non-hitters. Blue rates to win about 19.5 of the 20 hitting numbers so recubing gives Blue 19.5 wins and 16.5 losses.

How many extra wins does Blue need to justify not redoubling? BG author Danny Kleinman answered this in one of his books way back in the 70s or 80s. It uses what he calls "excess 18 arithmetic" where you double the difference from half. Here 19.5 is 1.5 above half so you double that to 3. 18 + 3 is 21.

You can see that this is correct because 4 x (19.5 - 16.5) = +12 points in 36 games. Your equity after not doubling would then be 2 x (21-15) which is also + 12 points in 36 games.

So if Blue can win at least 1.5 of the 16 games where he fails to hit, then not recubing is correct. That's a little less than 10% and I'm pretty sure Blue wins more than 10% after a miss.

The gammon chances figure to be the same regardless if you recube or not. so I think excess 18 arithmetic gives the answer to this problem. NR/T.

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