Quote:
Originally Posted by a_free_lunch
Two questions:
1. Is there a heuristic derivation for this? Or was the 1:5 ratio found by just examining a database of cases?
2. Can you explain whether the rule handles this position correctly?
- Blue will nearly always have a take if they roll double 1, double 2 or double 3 (3 sequences). I *think* that they might also have a take after 13 or 23 (assuming they enter and hit loose on the 22 point). So we might think they have something like 7 taking sequences.
- Multiplying by 5, we get 7 x 5 = 35.
- Meanwhile, White's Gammon chance is 34%, which is basically 35.
- So the rule seems to suggest that the double is optional -- which is the right answer.
hi,
1.
Found by looking at a few hundred cases.
The positions are from real matches where the human player made a too good related error.
2. For this position
XGID=a---BBCBBA--bAa--cce--A-A-:0:0:1:00:0:0:0:7:10
on XG++ it is Too good to double/Pass
+1.036
There are 4.28 taking sequences in this position. You can see this in XG via the Dice Distribution function. This
sheet counts it for you.
Then 4.28 * 5 = 21.4 which is less than the 35.16% gammons, so it's too good according to the rule.
In this position 22 isn't always a take, and 31 is rarely a take
E.g. white rolls 42, and makes the 20 point
blue rolls 22 and no matter what he plays it will be a pass. Even 33 would be a pass.
So your thinking was correct, but it's difficult to accurately estimate the taking sequences. I think practise helps a little - for me, just stopping to consider the possibility has been enough to marginally improve my game.