Backgammon Cube Handling

Cube Handling

When to double

From:   Kit Woolsey
Address:   kwoolsey@netcom.com
Date:   29 November 1994
Subject:   Re: doubling
Forum:   rec.games.backgammon
Google:   kwoolseyD00ABz.MEH@netcom.com

Craig Connell wrote: > I find the most difficult part of the game is the doubling cube. I read a > book and have the following question. > > The author said that you should accept a double if your odds of winning > are 25% or more. His logic is that if you played 100 games in which your > odds of > > winning were 25% and you conceded them all, you would lose 100 points. > If you accepted them all you would lose 150 points (75 X 2) and win 50 > (25 X 2) for a net loss of 100 points. Therefore, 25% is the break even > point. Makes sense to me. > > He next says that you should offer to double when your odds of winning > are 66% or greater. He does not explain his logic and I do not > understand this. If I apply the same logic as above, 50% would be the > break even point and at 51% I should double. > > I am guessing that the higher winning percentage is required to offer to > double because you turn control of the cube over to your opponent. But > it seems to me that this disadvantage is less important as the game goes > on. > > Can someone explain why such a high percentage is required to offer to > double. You've got the right idea, Craig. If it were the last roll of the game (i.e. if you didn't double now you would never have a chance to double), then it would be correct to double with a 51% advantage. The reason it may not be right to double with an advantage greater than 50% is that you relinquish the opportunity to double later (if you already own the cube then there is even more cost to doubling, since in addition to losing the chance to double later you are giving your opponent the opportunity to double which he did not have). So, why should we double now when we can double later? The answer, of course, is that after the next exchange of rolls (that is we roll, he rolls) we may shoot over the 75% mark so our opponent will have a proper pass. This is called losing our market. If this happens, clearly we wish we had doubled. So, our motivation for doubling depends not only on our chances of winning from the given position but on the volatility of the position. If the position is a very static position (such as a holding game or a long race) it is not likely we will lose our market by much, so we would want to be near the 75% mark before we turned the cube. On the other hand if the shit is about to hit the fan on the next roll we would need much less in winning chances, since if things go our way we would lose our market by a lot. Naturally the last roll of the game is the most volatile position of all. The 66% figure you read does not have any mathematical validity. It is simply the author's estimate of when on average it would be correct to turn the cube. As I have shown, the real question is how volatile the position is -- that is just as important as the winning chances. Hope this helps to answer the question -- it is really a very complex subject and there has not been any adequate written material on doubling. Kit

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