Match Play

 2-away/3-away: playing for gammon

 From: Tom Keith Address: takeith@io.org Date: 27 February 1996 Subject: Re: Leader doubling at -2:-3? Forum: rec.games.backgammon

```Stephen Turner wrote:
> Someone -- Michael Zehr I think -- talked the other day about when the
> trailer could double at -2:-3; basically with a slight edge combined
> with some gammon threats. I wondered when the leader can double. In a
> racing position the trailer's takepoint is at 25%, but I'm not
> confident about handling the cube in midgame positions. Presumably a
> slight gammon threat is enough to put the leader off doubling?
>
> And what sort of game should the leader aim for? An ungammonish one to
> thwart the trailer's doubling strategy?
>

To get a sense of the effect that gammon potential has on
simplifying assumptions:

1. Trailer's gammon chances are zero.
2. Trailer will be able to make an efficient double
if he goes on to win.

Now let x be Leader's probability of winning the present game.

Trailer will double at x=.28 because that's when Leader's
match equity in a doubled game will be the same as his match
equity if he drops.  Leader's match equity at x=.28 is 50%.

If Leader wins but never doubles, his match equity will be
either 75% (single win) or 100% (gammon).  So Leader's
match equity at x=1.00 is (1-GR).75 + (GR)1.00, where GR is
the fraction wins which are gammons.

of never doubling is

neverdouble(x) = .4 - .1 GR + .35 x - .35 GR x

Otherwise, any time Leader doubles and Trailer takes
(and redoubles), Leader's equity will be

doubletake(x) = x

will be

doubledrop(x) = .75

So, at any point x, Leader does better playing on for
gammon if:

neverdouble(x) > doubletake(x)
or
neverdouble(x) > doubledrop(x)

Let's see what this means in practice.  We'll say that
a player can make an "effective" double any time he is
better off doubling now than never doubling.  As Leader's
gammon potential increases, the window of opportunity for
making an effective double narrows:

Leader's Gammon Rate       Range of Effective Double
.25                        .67 - .86
.30                        .68 - .84
.35                        .69 - .81
.40                        .71 - .80
.45                        .72 - .78
.50                        .74 - .76
>.538                         (none)

Different assumptions will change these numbers slightly,
but I think this gives a good picture of the situation.

enough to put the leader off doubling?

I would say no -- with only a slight gammon threat,
the leader can still expect to make an effective double.
So a slight gammon threat is really no gammon threat
because the leader is planning to double anyway.
Only when there is a significant gammon potential
(perhaps above 40%), giving the leader a reduced chance
to make an effective double, do gammons begin to help.

As a general rule at this match score, it seems that the
leader should tend away from gammonish positions since
gammons are likely to help only the opponent.

Tom
```

### Match Play

1-away/1-away: advice from Bernhard Kaiser  (Darse Billings, July 1995)
1-away/1-away: advice from Stick  (Stick+, Mar 2007)
1-away/1-away: and similar scores  (Lou Poppler, Aug 1995)
2-away/3-away: playing for gammon  (Tom Keith, Feb 1996)
2-away/4-away: Neil's rule of 80  (Neil Kazaross, June 2004)
2-away/4-away: cube strategy  (Tom Keith, Dec 1996)
2-away/4-away: practical issues  (Mark Damish, Jan 1996)
2-away/4-away: trailer's initial double  (Kit Woolsey, Jan 1996)
3-away/4-away: opponent's recube  (William C. Bitting+, Feb 1997)
3-away/4-away: racing cube  (Bill Calton+, Nov 2012)
3-away/4-away: tricky cube decision  (Kit Woolsey+, July 1994)
3-away/4-away: what's the correct equity?  (Tom Keith, Sept 1997)
4-away/4-away: take/drop point  (Gary Wong, Oct 1997)
5-away/11-away: redouble to 8  (Gavin Anderson, Oct 1998)
7-away/11-away: volatile recube decision  (Kit Woolsey, May 1997)
Both too good and not good enough to double  (Paul Epstein+, Sept 2007)
Comparing 2-away/3-away and 2-away/4-away  (Douglas Zare, Mar 2002)
Crawford rule  (Chuck Bower, May 1998)
Crawford rule  (Kit Woolsey, Mar 1997)
Crawford rule--Why just one game?  (Walter Trice, Jan 2000)
Crawford rule--history  (Michael Strato, Jan 2001)
Delayed mandatory double  (tem_sat+, Oct 2010)
Delayed mandatory double  (Donald Kahn+, Dec 1997)
Doubling when facing a gammon loss  (Kit Woolsey, Jan 1999)
Doubling when opponent is 2-away  (David Montgomery, Dec 1997)
Doubling when you're an underdog  (Stein Kulseth, Dec 1997)
Doubling window with gammons  (Jason Lee+, Jan 2009)
Free drop  (Ian Shaw, May 1999)
Free drop  (Willis Elias+, Oct 1994)
Gammonless takepoint formula  (Adam Stocks, June 2002)
Going for gammon when opp has free drop  (Kit Woolsey, Jan 1998)
Going for gammon when opp has free drop  (Kit Woolsey, Apr 1995)
Holland rule  (Neil Kazaross, Apr 2010)
Holland rule  (Kit Woolsey, Dec 1994)
Leading 2-away with good gammon chances  (Douglas Zare, Feb 2004)
Match play 101  (Max Urban+, Oct 2009)
Matches to a set number of games  (Tom Keith+, Oct 1998)
Playing when opponent has free drop  (Gilles Baudrillard+, Dec 1996)
Post-crawford doubling  (Scott Steiner+, Feb 2004)
Post-crawford doubling  (Maik Stiebler+, Dec 2002)
Post-crawford doubling  (Gus+, Sept 2002)
Post-crawford mistakes  (Rob Adams, Sept 2007)
Post-crawford/2-away: too good to double  (Robert-Jan Veldhuizen, July 2004)
Slotting when opponent has free drop  (onur alan+, Apr 2013)
Take points  (fiore+, Feb 2005)
Tips to improve cube handling  (Lucky Jim+, Jan 2010)
When to free drop  (Dan Pelton+, Oct 2006)
When to free drop  (Tom Keith+, July 2005)
When to free drop  (Gregg Cattanach, Dec 2004)
When to free drop  (Kit Woolsey, Feb 1998)
When to free drop  (Chuck Bower, Jan 1998)
Which format most favors the favorite?  (Daniel Murphy+, Jan 2006)