On "New Ideas in Backgammon"

[ptane...@hotmail.com]

From Heinrich & Woolsey's "New Ideas in Backgammon":

[ Problem #31: X to play 55 ]
Money game

^ ^ O O X O | | ^ O ^ ^ ^ X
O X O | | O X
X O | | ---
| | | 1 |
| | ---
X | | O
X X O X | | X O O
X X X ^ O X | | X ^ ^ O ^ O
_________________________________________________
1 2 3 4 5 6 7 8 9 10 11 12

In the preface to this superb book, the authors elaborate on the selection
criteria, and their method for winnowing out possible solutions, via Jellyfish.
This consisted of a progressive screening through Level 5, Level 6, truncated
roll-outs, then full-game roll-outs. They admit that this process might
occasionally eliminate a valid solution. The above diagram appears to be one
such case.
The authors list several tries, and equities, with {20/15(2), 13/8(2)}
clearly best. My candidate, {20/15(2), 13/3} was not mentioned at all, implying
that it had been screened out earlier, hence inferior to the others. However,
roll-outs indicated it as a dead heat with the top play, although the absolute
equity deviated from the book.
Anybody else care to take a crack at this...?

Paul Tanenbaum

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[David Montgomery]

In article <5lgvu2$g6a$1...@bilbo.reference.com> ptane...@hotmail.com writes:
> From Heinrich & Woolsey's "New Ideas in Backgammon":
> [ Problem #31: X to play 55 ]

> O O X O | | O X

> O X O | | O X
> X O | |
> | |

> X | | O
> X X O X | | X O O

> X X X O X | | X O O

> _________________________________________________
> 1 2 3 4 5 6 7 8 9 10 11 12
>

> The authors list several tries, and equities, with {20/15(2), 13/8(2)}

>clearly best. My candidate, {20/15(2), 13/3} was not mentioned at all [...]

>roll-outs indicated it as a dead heat with the top play, although the absolute
>equity deviated from the book.
>

>Paul Tanenbaum

I rolled your play out, too, along with one other try.
My results, 10368 full games, JF version 2 level 5, cubeless numbers:

15(2), 3: +.079
15, 3, 8: +.114

Which indicates that these plays are inferior to the best play, which
according to the book gets +.200.

----

I've rolled out a few additional candidates for other problems. The only
one on which I got a higher result for the play not in the book was for
23, 3 on problem #9. For this play I got +.041 (same parameters) -- I
don't think this is statistically significant, but my bet is that it is
better than the play in the book. This play was suggested to me for
rolling out by Ed Maslansky (themaz on FIBS).

Bob Koca's (bobk on FIBS) choice for #56 was 17/11 10/9, and he has
done JF v2 L6 rollouts of this and 10/9 8/2, with 11, 9 coming out
better (but statistically tied).

I didn't believe the results for problem 104, so I did a manual interactive
rollout. I don't have my results handy, but I can say this much: now
I'm confident the book is right.

----

I would love to hear about any other results where a play not mentioned
comes out nearly equal to or better than the book's choice -- or any other
rollouts that might indicate an error in this (most excellent) book.

David Montgomery
monty on FIBS
mo...@cs.umd.edu