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So You Think Backgammon is Easy?

by Phil Simborg
29 July 2008

Phil Simborg

Here's a good example of how complex this game can be.

There are two positions below where Black holds a 2-cube and is on roll.

See if you can guess the proper cube action for both positions.

Scroll down and see what the answers are:

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Subject: Re: So You Think Backgammon is Easy?
From: Lee Wood
Date: 31 Jul 2008 18:51 EST

Assuming this is a money game and white can redouble to 8. I disagree with the analysis as black fails to take 2 off 44.5% of the time and then white will redouble to 8 in either position. So if black redoubles they lose some of there winning chances by allowing white to redouble to 8 and not risk rolling bad numbers.

Subject: Re: So You Think Backgammon is Easy?
From: RichMunitz   
Date: 05 Aug 2008 20:42 EST

This is an example of the Jacoby Paradox. The "paradox" comes from the fact that a decrease in black's cubeless winning chances turns the position from no-redouble into a redouble.

This principle repeats frequently in more complex positions. Sometimes you'll come across positions during bot analysis where the correct play is the one that wins fewer games and fewer gammons and gammon losses are about the same, and you'll be trying to figure out how the heck that can be so. The answer is that the seemingly inferior position results in an efficient double the following turn (i.e. take equal to cash) in exchange for no risk, while the play that wins more does so by trading big market losses when things go well in exchange for small immediate risk of loss. It helps to think of the object of the game of backgammon as not being the first to take your checkers off, but to be able to give an efficient double. An efficient double is the same as a win.

Subject: Re: So You Think Backgammon is Easy?
Date: 06 Aug 2008 04:26 EST

Can somebody explain the math, as if you're explaining it to a third grader please? Much appreciated.

Kamyar (cubed2death)

Subject: Re: So You Think Backgammon is Easy?
From: Coolrey
Date: 06 Aug 2008 09:04 EST

It is quite normal for Kamyar to ask someone else to do the work for him. Before, I might have explained it to him, but now his free lessons are over.

Subject: Re: So You Think Backgammon is Easy?
Date: 09 Aug 2008 15:01 EST

Thank you for the non-math explanation Phil.

Its normal for Ray to be needlessly insulting, so I forgive him; he can't help it.

If I knew how to do the math I would. Last I checked, online forums were for sharing ideas and learning from eachother, no?

I teach people what I know on a daily basis, without asking for anything in return. If everyone did the same, the game would flourish.

Kamyar (cubed2death)

Subject: Re: So You Think Backgammon is Easy?
Date: 11 Aug 2008 21:29 EST


Thank you for the math! Much more clear now.


P.S. My above comment was directed at Coolrey, not you, but I'm sure you figured that out. =)

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Celebrating 15 years in backgammon games