Cube Handling

Forum Archive : Cube Handling

How to use the doubling cube

From:   Michael J. Zehr
Address:   tada@ATHENA.MIT.EDU
Date:   18 November 1993
Subject:   Re: Doubling Cube
Google:   2cg278$897@senator-bedfellow.MIT.EDU

How to use the cube?

The cube lets one play offer to double the stakes of the game.
Initially either player can offer to double, but after the initial
double the player who most recently accepted a double "owns" the cube
and only that player may offer a double.

After one player doubles, the other may accept the double, and play
continues at the doubled stakes, or the double can be declined, in which
case the declining player resigns the game at the current stakes.

When to use the cube?

This is a very complicated subject.  Entire books have been written
about the topic.  Here's my attempt at an introduction though.

[First, a brief glossary.  Equity is the expected winnings from a game.
If a player has a 65% chance of winning the game (worth one point) and a
35% chance of losing the game (worth negative one points), the equity is
.65 - .35 or .30.  The other player's equity would be -.30.]

Suppose it's the last roll of the game and you have the opportunity to
double.  If your equity is positive (or your chance of winning greater
than 50%) you should double.  But should your opponent accept?

Well, the opponent can drop for an equity of -1, or accept for an equity
of twice the previous equity.  So if before the double the equity of the
person being doubled was greater than -.5, s/he should accept.  This
represents a 25% chance of winning.

This is the key to roughly determining whether you should take or drop a
cube.  Look at the 36 possible rolls by the doubler, consider how many
of those 36 variations you think you can win, and accept if there are 9
or more of them.

So, why don't people normally double as soon as they get a slight edge
in the game?  Because what I said above is only true on the LASST roll
of the game.  Remember that by doubling you give up the opportunity to
double later, thus you give up a bit of value.  Here's an example:

1 2 3 4

1 2 3 4
X on roll, cube action?

X wins outright 26/36 rolls (any roll that doesn't have a 1 plus 11) and
has a big double.

Should O take?  O wins when X misses and O rolls one of 26 rolls, so
it's 10/36 * 26/30 or 20%.  Looks like a drop, right?  But if O takes, O
has a chance of redoubling, and in fact should redouble if X doesn't win
immediately.  This gives O enough equity to accept the cube.  (I'll let
you work out the math yourself.)

In this case, the value of being able to redouble is worth around 5%
equity to O, changing the situation from a big drop to a close take.

In general you can count on cube ownership being worth around 5%,
possibly more.

Some other things to keep in mind about doubling.

A "market loser" is a roll (more generally a roll by you and a roll by
your opponent) after which he will drop a double (provided on this turn
your opponent will take the double).  If you have no market losers, then
it cannot be correct to double.  Even after your best sequence your
opponent will still take, so there's no point in doubling.

(It's hard to have zero market losers.  Most positions would have a
variation in which one side rolls a double, hitting and making an inner
board point, and the other side fans, leading to a double/drop

In a match situation, the value of each game to the players varies with
the score, and this changes the basic 25% drop value.  The decision then
depends on what's known as match equities.  See Kit Woolsey's "How to
Play Tournament Backgammon" for a good introduction to match play.
(It's available from Gammon Press -- see the FAQ for more information.)

What is the purpose of the cube?
"purpose" sounds philosophical.  It's affect on the game is to make
things more interesting, speed play, add a new level of complexity, etc.

As I said, entire books are devoted to cube handling.  It's probably the
most important aspect of the game.  The gain or loss from perfect or
poor cube handling is far greater than gains or losses from checker
play.   I hope this provides enough information to get you sstarted and
give you an idea on what else to study.

-michael j zehr
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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)  [Long message]
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)  [Recommended reading]
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)  [GammOnLine forum]
References  (Chuck Bower, Nov 1997) 
Robertie's rule  (Chuck Bower, Sept 2006)  [GammOnLine forum]
Rough guidelines  (Michael J. Zehr, Dec 1993) 
Tells  (Tad Bright+, Nov 2003)  [GammOnLine forum]
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)  [GammOnLine forum]
Value of an ace-point game  (Øystein Johansen, Aug 2000) 
Volatility  (Chuck Bower, Oct 1998)  [Long message]
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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