Cube Handling

Forum Archive : Cube Handling

Too good to double

From:   Michael J. Zehr
Date:   19 May 1997
Subject:   Re: "unlosing" your market
Google:   5lqjt7$i68@senator-bedfellow.MIT.EDU writes:
> I unneccsarily complicated the example by refferring to playing on for
> gammon (I had a particular situation in mind). I agree one can
> increase equity by casing, but sometimes by a lot less than having a
> double accepted. In theory, if the take point is not too far below, it
> pays to 'go back' and pick up the extra eqity. I was just wondering if
> it was practical at all.
> Suppose your opponents take point is 22% and you're at 80%. By cashing
> you gain 0.2 points. If you were back at 75% you could double for an
> expected 1.5 points and gain 0.7 points instead.

In a *money* game, until you turn the cube, your maximum equity against
a perfect opponent is 1.0, regardless of how much of that comes from
doubling.  Whether your expected equity with no cube is .6 or .9, a
double/drop gives you +1.0.  A double and *correct* take gives you an
equity < 1.0.  So if your cubeless equity is .6, you could gain .4 by a
double/drop, or you could make a poor play, drop your cubeless equity
to, say, .5, then double, and gain .45 equity to be at .95.  Sure, you
"picked up" an extra .05 from your double, but you basically lost .1
from your bad play, giving a net loss of .05.

The key to remember is that if it is a correct take for your opponent,
your equity is less than if it's a correct drop for your opponent.

Let's extend this concept further -- suppose you're holding the cube, so
it might actually be correct to play on for a gammon.  If so, your
equity from playing on *must* be greater than or equal to 1.0 times the
cube value.  So if you try to get to a position in which it is a correct
take for your opponent, you must reduce your equity to below 1.0 times
the cube value.  Since this represents a net loss, the equity you gave
up to reach that position must be more than the extra equity you
'gained' at the moment of turning the cube.  (This might be where some
of the confusion somes from.  You don't really gain that equity by
turning the cube -- it's already yours if you have access to the cube,
it's just a matter of whether you're going to make the optimal play to
get that equity or not.)

There are also positions in which it's correct to cash, i.e. you don't
have enough gammon threat to have an equity greater than 1.0 times the
cube value.

But of course, we don't always play against perfect opponents.  (I
mentioned this in my earlier posting on this topic... in fact, much of
this is a rehash, but the fact that the question was raised again makes
me wonder if my article made it everywhere.)

Suppose you have the choice between two positions:

A. Cubeless equity .6, equity for double/take 1.1, chance your opponent
will incorrectly take = 10%.

B. Cubeless equity .7, equity for double/take 1.3, chance your opponent
will incorrectly take = 0%.

Obviously your equity against that opponent is higher for 1.1.  So you
might have a position in which the correct move against that opponent
when you hold the cube is different than the correct move against that
opponent when you don't hold the cube, and might even be different than
the correct move against a different opponent.

But without knowing *exactly* how your opponent will make mistakes, we
can't really answer this question.

-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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