Cube Handling

 Early-late ratio

 From: Tom Keith Address: tom@bkgm.com Date: 25 September 2003 Subject: Re: Early/Late Cost Ratio Forum: rec.games.backgammon Google: 3F732BC8.6C977F8@ETEbkgm.com

```Hi Martin.

First a brief history of the terminology.  The "early/late cost ratio"
is a term I used the 1996 article you are referring to
(http://www.bkgm.com/articles/mpd.html).  When the computer program
Snowie came out (1998), it included the ability to report this ratio
for a given match score.  Snowie called it the "early-late ratio."

Douglas Zare has written a column on early-late ratio in the July 2002
issue of GammonVillage (http://www.gammonvillage.com/), which explains
the concept very nicely.  (GammonVillage is available only by
subscription, but you'll find the \$20 for 3 months well worth your
money.  A subscription gives you access to past articles.)

One way to view the doubling decision in backgammon is that it depends
on four things:

1.  Your current game-winning changes (GWC).

2.  Opponent's take point (the point at which his equally well of
taking or dropping your double).

3.  The volatility of the position (how much can change between now
and your next turn).

4.  The early-late ratio.

Your goal is to double as close to the opponent's take point as
possible.  A double made at exactly the opponent's take point is said
to be an "efficient" double.  Early doubles (where opponent has a
clear take) and late doubles (where the opponent has a clear pass) are
"inefficient."  But inefficiency is not equal on both sides of the
take/drop line.  That's the purpose of the early-late ratio, to
compare the inefficiency of doubling early to the inefficiency of
doubling late.

For example, in money play it turns out that the early-late ratio of
an INITIAL DOUBLE (when the cube is centered) is 0.5 -- an early
double is only half as inefficient as a late double.  If opponent's
take point is, say, 75%, then doubling at 74% GWC is half as
inefficient as doubling at 76% GWC.  Or, another way of looking at it,
doubling 2% early is just as good as doubling 1% late, and vice versa.

For a REDOUBLE (when you own the cube), the early-late ratio is 1.0.
An early redouble is just as inefficient as a late redouble.  You are
equally well off redoubling 1% early as you are redoubling 1% late.

Why the difference?  The reason is that owning the cube has value; as
long as you hold the cube your opponent can't use it.  This fact has
recognized by players for a long time; the early-late ratio just puts
a number to it.

In match play things are more complicated.  The early-late ratio
depends on not only on who owns the cube, but also on the score of the
match, the level of the cube, and the fraction of wins in the current
game that will be gammons.  These are a lot of factors, and
unfortunately a single table doesn't encompass them all, so here are a
few tables for various match situations.

Early/Late Cost Ratio, Cube at 1, No Gammons

-2    -3    -4    -5    -6    -7    -8    -9   -10
----- ----- ----- ----- ----- ----- ----- ----- -----
-2:  0.00  0.84  1.72  1.35  0.89  1.02  1.04  1.05  0.93
-3:  0.29  0.85  1.42  0.94  0.76  0.77  0.83  0.79  0.77
-4:  0.36  0.74  1.06  0.88  0.71  0.72  0.74  0.74  0.72
-5:  0.35  0.51  0.76  0.64  0.61  0.62  0.65  0.65  0.65
-6:  0.22  0.37  0.56  0.56  0.56  0.58  0.61  0.62  0.63
-7:  0.27  0.33  0.48  0.47  0.50  0.52  0.56  0.57  0.58
-8:  0.22  0.29  0.40  0.42  0.45  0.48  0.51  0.53  0.55
-9:  0.25  0.28  0.39  0.40  0.43  0.46  0.49  0.50  0.52
-10:  0.19  0.26  0.36  0.38  0.42  0.44  0.47  0.49  0.50

Early/Late Cost Ratio, Cube at 1, 25% Gammons

-2    -3    -4    -5    -6    -7    -8    -9   -10
----- ----- ----- ----- ----- ----- ----- ----- -----
-2:  0.00  0.57  1.03  1.14  1.14  1.56  1.83  1.70  1.43
-3:  0.22  0.64  0.96  0.84  0.89  1.06  1.30  1.14  1.09
-4:  0.27  0.58  0.80  0.76  0.77  0.90  1.06  1.03  0.96
-5:  0.32  0.41  0.56  0.54  0.61  0.71  0.83  0.82  0.82
-6:  0.26  0.34  0.43  0.46  0.52  0.61  0.71  0.74  0.76
-7:  0.35  0.32  0.39  0.40  0.47  0.53  0.61  0.64  0.67
-8:  0.30  0.31  0.36  0.36  0.42  0.47  0.54  0.58  0.61
-9:  0.33  0.28  0.34  0.34  0.39  0.43  0.49  0.52  0.56
-10:  0.24  0.25  0.30  0.31  0.36  0.40  0.46  0.49  0.53

Early/Late Cost Ratio, Cube at 2, No Gammons

-3    -4    -5    -6    -7    -8    -9   -10
----- ----- ----- ----- ----- ----- ----- -----
-3:  0.48  0.94  1.41  1.79  2.48  3.21  2.83  2.62
-4:  0.39  0.91  1.29  1.63  2.15  2.75  2.60  2.38
-5:  0.41  0.78  1.04  1.32  1.70  2.18  2.06  2.07
-6:  0.30  0.63  0.85  1.06  1.37  1.75  1.79  1.81
-7:  0.31  0.58  0.75  0.92  1.17  1.47  1.52  1.59
-8:  0.25  0.51  0.67  0.82  1.02  1.27  1.37  1.43
-9:  0.25  0.47  0.59  0.72  0.89  1.10  1.19  1.28
-10:  0.20  0.41  0.53  0.64  0.78  0.96  1.06  1.15

Early/Late Cost Ratio, Cube at 2, 25% Gammons

-3    -4    -5    -6    -7    -8    -9   -10
----- ----- ----- ----- ----- ----- ----- -----
-3:  0.32  0.57  1.05  1.46  2.04  2.64  2.60  2.72
-4:  0.27  0.56  0.92  1.30  1.75  2.25  2.30  2.35
-5:  0.28  0.49  0.77  1.05  1.40  1.80  1.84  1.98
-6:  0.21  0.41  0.62  0.84  1.13  1.45  1.57  1.69
-7:  0.22  0.38  0.56  0.73  0.97  1.24  1.34  1.47
-8:  0.17  0.34  0.49  0.65  0.85  1.07  1.20  1.31
-9:  0.18  0.31  0.44  0.56  0.73  0.92  1.03  1.15
-10:  0.15  0.28  0.38  0.49  0.63  0.79  0.91  1.02

Anyway, to your question:

> Lets say I'm 2 away and opponent is 8 away. When there are no gammon
> chances I would like to have 83% to double.
> Now the Cost ratio says at this score a number of 1.7.
> How do I manage this number now?

The table presented in the article your refer to assumes that 20% of
the wins in the current game are gammons, so we can't use that here.
Instead refer to the first table above (initial double, no gammons).

This table says that the early-late ratio is 1.04.  1.04 is higher
than normal (normal being 0.5) and reflects the fact that you are
ahead in the match and will have to be more careful than usual about
letting the cube go too high.  An early-late ratio of 1.04 is actually
about the same as for a REDOUBLE in money play.

Going back to factors that influence the doubling decision, the
primary indicators are your current game-winning chances (GWC) and the
opponent's takepoint (TP).  You've computed your opponent's TP as 83%.

As long as you have no market losers (no chance that before your next
turn your GWC will exceed opponent's TP), then you have no decision to
make and can leave the cube alone.  But once you have market losers,
you have to decide (a) how many there are, (b) how big they are, and
(c) how costly they are.

How big your market losers are depends on how close you are to
opponent's TP.  It also depends on the volatility of the position.  If
you are getting close to opponent's TP and the position is volatile,
then you will certainly have some big market losers.  High volatility
argues for doubling early.

How costly your market losers are depends on the early-late ratio.  If
you have a low E/L ratio, then losing your market is more costly than
normal and you want to be extra sure to double while your opponent is
still willing to take.

Notes

The Snowie definition of early-late ratio is not quite the same as my
definition.  If A is the cost of doubling early and B is the cost of
doubling late, then my early-late ratios are reported as A/B.  Snowie
early-late ratios are A/(A+B).  Either method works; in both cases a
low number means you should double earlier than usual.

In his article on early-late ratio, Douglas Zare offers the following
suggestion for how you can relate the early-late ratio to actual play.
"The [Snowie] early-late ratio tells you roughly what fraction of
doubles should be passed in nongammonish positions.  That is, roughly
1/3 of initial doubles should be passed, while 1/2 of the redoubles
should be passed."  Perhaps this is a good argument for using the
Snowie definition of early-late ratio, since it gives you something to
relate to actual play.

Tom
```

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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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