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Old 06-25-2021, 04:27 AM   #1
NeedsMust
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Join Date: Mar 2014
Posts: 9
Len's Too Good Rule

Here's a calculation you can use to check if you're too good.

You’re too good if your gammon % is more than five times your opponents taking sequences.

A taking sequence is two rolls (one for you and one for your opponent) after which, your opponent will take if you double.

And gammons is the percentage number of gammon wins.


Red estimates 20% gammon wins.

gammon % = 20

For green to take, red must leave a shot (4/36) - the rolls 66, 65, 44. And Red must hit the direct shot (11/36).

So the number of taking sequences is 4/36 * 11/36 ~= 1.3
Five times your opponents taking sequences = 6.5

You’re too good if your gammon % is more than five times your opponents taking sequences.

20 > 6.5.

So this position it too good for red.

More examples.
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Old 07-05-2021, 05:27 AM   #2
a_free_lunch
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Join Date: May 2020
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Re: Len's Too Good Rule

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.

Last edited by a_free_lunch; 07-05-2021 at 05:32 AM. Reason: Fixed mistake!
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Old 07-30-2021, 03:16 PM   #3
NeedsMust
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Join Date: Mar 2014
Posts: 9
Re: Len's Too Good Rule

Quote:
Originally Posted by a_free_lunch View Post
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.
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Old 07-30-2021, 03:43 PM   #4
Robertie
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Join Date: May 2004
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Re: Len's Too Good Rule

Question: Who was (is) Len?

Offhand it seems like a pretty good rule, and one I haven't heard of before.
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Old 07-30-2021, 05:17 PM   #5
NeedsMust
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Join Date: Mar 2014
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Re: Len's Too Good Rule

Quote:
Originally Posted by Robertie View Post
Question: Who was (is) Len?

Offhand it seems like a pretty good rule, and one I haven't heard of before.
I am Len, I named the rule after myself.
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