Cube Handling

 When to beaver

 From: Walter Trice Address: wgt@world.std.com Date: 30 August 1999 Subject: Re: When to beaver Forum: rec.games.backgammon Google: FHADG3.F26@world.std.com

> So my buddy Jimmy and I like to have a drink or two when we play BG,
> and we tend to get a little loosey-goosey with the old doubling cube at
> times.  Beavers, raccoons, ardvarks,... we've seen them all, and then
> some.
> Well, before I let Jimmy take any more of my money, I thought I'd try
> to ascertain the break point for when to beaver.  Obviously, it must be
> somewhere between 25% and 50%.  Since there is equity in owning the
> cube, I would not think I need to be all the way to 50%, but where is
> the break point?
> And while we're at it, any thoughts about when to raccoon?

For bear-offs, there is a theoretical minimum beaver point of 37.5%. This
corresponds to the analogous minimum take-point of 18.75%. The minimum take
is realized in the position where each player has one man on the 6-point.
As far as I know, the minimum beaver doesn't come up in a real position.
However, in the following position you can beaver with a cpw of 39.6%: your
opponent (doubling) has 2 men on the 3-point and you (beavering) have one
man on the 6.

The "continuous model" gives a take-point of 20%, and a corresponding
beaver-point of 40%. Just as you usually need more than 20% to take, you
usually need more than 40% to beaver. In a short race it depends a lot on
what effect the specific position has on your cube efficiency. It is very
commonly correct to beaver with a 44% or greater cubeless chance of
winning. In a long race the beaver point approaches the theoretical 40%.

Of course it's a bit more complex with gammons.

For raccoons, it is usually true that you should raccoon if your opponent
shouldn't have beavered. But there is a class of exceptions -- consisting
of the Kauder Paradox positions. The sequence double/beaver/raccoon may be
correct (rarely!) And, finally, there are positions which you should beaver
if and only if your opponent can't (or won't) raccoon.

--Walter Trice

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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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