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Backgammon» Forums » Strategy

Subject: Probability question rss

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Raymond G
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Here is an example I found in a comprehensive backgammon website I came across.

Black is leading Red 3-2 in a 5-point match, and Black has two pips on his two point while Red has two pips in his own one point. It is black's turn.

If Black doubles and Red takes, what is Red's probability for winning the match. The website has it at 23% but I'm not so sure that is correct. Does anyone know how to compute this probability?


 
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Badger
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Black will bear off with any result except a 2-1, 3-1, 4-1, 5-1, or 6-1. So that's 10 results from a possible 36, giving just over 72% success, just under 28% fail. So if red accepts the double and wins, they go in to the next round 4-3 up, with the Crawford rule in effect, so black has to win two games in a row. So that 28% is then adjusted by whatever the odds are of black winning two in a row, which I would guess are 25% if everything else is equal. I make that 20.83%.
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Raymond G
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Badger, thanks for your quick reply.

Black doesn't necessarily have to win two games in a row. In the Crawford game, he can win the match with a gammon.
 
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Badger
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Good point, but I have no idea how likely that is to be honest.
 
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Christopher Dearlove
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SoRCon 8 27 Feb - 1 Mar 2015 Basildon UK http://www.sorcon.co.uk Essex Games 27 Jul '15
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wins0904 wrote:
Badger, thanks for your quick reply.

Black doesn't necessarily have to win two games in a row. In the Crawford game, he can win the match with a gammon.


But the probability of that can't be determined.
 
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Raymond G
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According to equity tables found all around the internet, the probability of black winning when it is 2-away vs red 1-away is 30%.

What I don't get is how website gets 23% in the scenario described above.
 
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Russ Williams
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wins0904 wrote:
According to equity tables found all around the internet, the probability of black winning when it is 2-away vs red 1-away is 30%.

What I don't get is how website gets 23% in the scenario described above.

The probability of winning this particular game is different from the probability of winning the entire 5-game match (of which this game is just one part of).
 
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Raymond G
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I compute the probability of winning the match at (10/36) * 70% = 19%

Is this not correct?
 
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Klim Chugunkin
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Can you post the link to where you found this? 19% seems right. If red takes, then black wins the match immediately on 26 rolls. On the 10 missing rolls, red redoubles and black passes. The score becomes -1C-2 and red has 68% to win the match (using the currently most accurate XG MET). So, red's overall chances are 10/36*68/100, which is about 19%.

On the other hand, if red passes the score becomes -3-1C, which gives red about 25% chances for the match. So, this is a huge pass.
 
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Klim Chugunkin
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Dearlove wrote:
wins0904 wrote:
Black doesn't necessarily have to win two games in a row. In the Crawford game, he can win the match with a gammon.


But the probability of that can't be determined.


It can and has been determined (assuming "perfect" play, of course), and that's why we have METs showing match winning probabilities between two "perfect" players depending on the match score.
 
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Raymond G
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Sharikov wrote:
Can you post the link to where you found this? 19% seems right. If red takes, then black wins the match immediately on 26 rolls. On the 10 missing rolls, red redoubles and black passes. The score becomes -1C-2 and red has 68% to win the match (using the currently most accurate XG MET). So, red's overall chances are 10/36*68/100, which is about 19%.

On the other hand, if red passes the score becomes -3-1C, which gives red about 25% chances for the match. So, this is a huge pass.


I found this at gammonempire under the "Money vs Match Strategies" section of the navigation menu.
 
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Klim Chugunkin
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Oh, this is just an online gaming platform. I wouldn't consider it a good source of backgammon strategy. You may want to take a look at Backgammon Galore:

http://www.bkgm.com/

Also, there is a backgammon federation in US:

http://usbgf.org/

And I'm pretty sure few people are aware that one can get titles of master/grandmaster in backgammon now:

http://bgmastersab.com/
 
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Raymond G
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Sharikov wrote:
Oh, this is just an online gaming platform. I wouldn't consider it a good source of backgammon strategy. You may want to take a look at Backgammon Galore:

http://www.bkgm.com/

Also, there is a backgammon federation in US:

http://usbgf.org/

And I'm pretty sure few people are aware that one can get titles of master/grandmaster in backgammon now:

http://bgmastersab.com/


Thank you for the resources. I'll assume it is a calculation error then.
 
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