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

[Jonathan Kinsey]

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
>> asking. Can someone answer how many backgammons the player
>> 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...

Jon

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