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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### Cube Handling

Against a weaker opponent  (Kit Woolsey, July 1994)
Closed board cube decisions  (Dan Pelton+, Jan 2009)
Cube concepts  (Peter Bell, Aug 1995)
Early game blitzes  (kruidenbuiltje, Jan 2011)
Early-late ratio  (Tom Keith, Sept 2003)
Endgame close out: Michael's 432 rule  (Michael Bo Hansen+, Feb 1998)
Endgame close out: Spleischft formula  (Simon Larsen, Sept 1999)
Endgame closeout: win percentages  (David Rubin+, Oct 2010)
Evaluating the position  (Daniel Murphy, Feb 2001)
Evaluating the position  (Daniel Murphy, Mar 2000)
How does rake affect cube actions?  (Paul Epstein+, Sept 2005)
How to use the doubling cube  (Michael J. Zehr, Nov 1993)
Liveliness of the cube  (Kit Woolsey, Apr 1997)
PRAT--Position, Race, and Threats  (Alan Webb, Feb 2001)
Playing your opponent  (Morris Pearl+, Jan 2002)
References  (Chuck Bower, Nov 1997)
Robertie's rule  (Chuck Bower, Sept 2006)
Rough guidelines  (Michael J. Zehr, Dec 1993)
Tells  (Tad Bright+, Nov 2003)
The take/pass decision  (Otis+, Aug 2007)
Too good to double  (Michael J. Zehr, May 1997)
Too good to double--Janowski's formula  (Chuck Bower, Jan 1997)
Value of an ace-point game  (Raccoon+, June 2006)
Value of an ace-point game  (Øystein Johansen, Aug 2000)
Volatility  (Chuck Bower, Oct 1998)
Volatility  (Kit Woolsey, Sept 1996)
When to accept a double  (Daniel Murphy+, Feb 2001)
When to beaver  (Walter Trice, Aug 1999)
When to double  (Kit Woolsey, Nov 1994)
With the Jacoby rule  (KL Gerber+, Nov 2002)
With the Jacoby rule  (Gary Wong, Dec 1997)
Woolsey's law  (PersianLord+, Mar 2008)
Woolsey's law  (Kit Woolsey, Sept 1996)
Words of wisdom  (Chris C., Dec 2003)

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