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## Re: [Bug-gnubg] A simple question about backgammons...

 From: Øystein Johansen Subject: Re: [Bug-gnubg] A simple question about backgammons... Date: Wed, 25 Feb 2009 20:09:02 +0100 User-agent: Thunderbird 2.0.0.19 (Windows/20081209)

```Jonathan Kinsey wrote:
> Øystein Johansen (OJOHANS) wrote:
>>> How often will the player win a backgammon in this position:
>>>
>>> GNU Backgammon Position ID: dhsAaQwfAAAAAA
>>> Match ID : cAkAAAAAAAAA
> +13-14-15-16-17-18------19-20-21-22-23-24-+     O: gnubg
> |                  |   |    O  O  O  O    |     0 points
> |                  |   |    O  O  O  O    |
> |                  |   |          O       |
> |                  |   |                  |
> |                  |   |                  |
>v|                  |BAR|                  |     (Cube: 1)
> |                  |   |                X | XX
> |                  |   |                X | XX
> |                  |   |                X | XX
> |                  |   | O        O     X | XX  On roll
> |          O     O |   | O        O     X | XX  0 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+     X: me

>>> This is such a simple question that I really feel silly
>>> wins and why? (The "and why"-part of the question is important here.)
>>
>> Thinking one more minute, and the answer comes obviously: 0.4350
>
> You didn't give your why part! Anyway I get something like:
>
> X rolls a double in 2 rolls (11/36) and O doesn't escape (32/36) =
> (11*32/36*36)
> = 0.272
> X doesn't roll a double either time (25/36) and O doesn't escape two
> times in a
> row [by either rolls two high numbers either time or one high number
> twice]~(1/4) = (25*1) / (36*4) = .174
>
> So I get a similar number .446 (although who knows if my reasoning is
> correct) -
> if only we had some kind of computer program to work these things out...

The point was that I could not figure out why the backgammon probability
was not the same as a bearoff:

GNU Backgammon  Position ID: YwAA4A8AAAAAAA
Match ID   : cAngAAAAAAAA
+13-14-15-16-17-18------19-20-21-22-23-24-+     O: gnubg
|                  |   |       O        O | OOO 0 points
|                  |   |       O        O | OO
|                  |   |                  | OO
|                  |   |                  | OO
|                  |   |                  | OO
v|                  |BAR|                  |     (Cube: 1)
|                  |   |                7 | X
|                  |   |                X | X
|                  |   |                X | XX
|                  |   |                X | XX  On roll
|                  |   |                X | XX  0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+     X: Øystein

Go figure... why is the backgammon probabilities in the first position,
the same as the winning probability in the bearoff position? Think for a

it's because 2s and 3s can make the important crossover in the
backgammon position, however 2s and 3s can not be used to bear off in
the bearoff position. Quite obvious....

-Øystein

```

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