Match Play

Forum Archive : Match Play

Post-crawford doubling

From:   Scott Steiner
Date:   29 February 2004
Subject:   Optional doubles at odd-away post crawford

Let's say we have a 7 point match and score is 6-4 post crawford.

If the trailer doesn't decide to double on his first opportunity, when
is the right time to double?  And when should the leader take?


Michael Sullivan  writes:

The leader should take up to the point where wins plus gammons equal or
top 100%.  If there are no gammons, the leader should take anything that
is not absolutely gin.  This is on the assumption that trailer will know
enough to double immediately next round after a drop.  That's why this
is known as a forced take.

With equity greater than 1, it may be a drop

The advantage of the trailer not doubling immediately is that it's very
difficult to lose one's market, so if the opponent doesn't understand
the match score, you can often pick up drops when you double at 80%
wins, 10% gammons, or some such, gaining some equity from opponent's
mistakes.  Obviously, threading the needle looking for mistakes from an
opponent who understands the score is not worth it.  But you can usually
get to a money drop or close take without ever facing a serious threat
to lose your actual market at this score.  If you wait until such a
time, it's easy to sucker your opponent into a mistake and you haven't
risked much.

Jørn Thyssen  writes:

Ah, this reminds me of a recent online match of mine:

    GNU Backgammon  Position ID: vn4CABC2zYQALA
                    Match ID   : cAmgAEAAEAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+  O: opponent
  O | X  O  O  O     O |   |             X    |  4 points
    | X  O     O       |   |                  |
    |    O     O       |   |                  |
    |    O     O       |   |                  |
    |    O     6       |   |                  |
    |                  |BAR|                  |v 5 pt match (Cube:1)
    |                  |   |                  |
    |                  |   |                  |
    |                  |   |                  |
    |       X  X  X  X |   |    X             |  On roll
    | O     X  X  X  X | X |    X     X       |  2 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: Jørn Thyssen

This is a huuuuuuuuuge take since O has one chequer off, so he can
never lose a gammon, hence he can take any non-gin position. Although
X is a big favourite it's certainly not a gin.

My opponent passed giving up more than 6% MWC.

Douglas Zare  writes:

I wrote an article on this for Bibafax last year. I think it was in
the March issue.

The leader should take any immediate double, but it gets tricky at
post-Crawford 3-away, and very tricky at post-Crawford 5-away
or more. The trailer gains if the leader makes a bad pass. The
trailer does not gain if the leader makes a bad take. So, to save
energy, the leader can simply take everything, which is like forcing
the trailer to double immediately.

The take point is very low, perhaps 3% at pC 3-away and 5% at
pC 5-away. Gammons are very valuable at pC 3-away, and not
nearly so valuable at pC 5-away. Backgammons are extremely
valuable at pC 5-away. The leader can take with about

3% + gammon losses, at pC 3-away.
5% + 3/5 gammon losses + 8/5 backgammon losses, at pC 5-away.

Many players will pass huge takes at both scores. You might
want to double when your opponent just rolled an awkward
number that increased the gammons a lot or the first possibility
of a market loser.

Michael Sullivan  writes:

How do you derive those numbers for the win percentage?

I would have figured that the gammonless take point is equivalent to the
value of the free drop, and I have a hard time believing that's as much
as 3%.

I'm also having a hard time figuring out how the take point at -5 would
be higher, because you can only use one free drop.  I guess the idea is
that you don't drop a marginal disadvantage at your first opportunity,
so you have two tries to get a significant boost from the free drop
because of a good roll by the opponent.  It still seems like 2% is a lot
for that.

Douglas Zare  writes:

> How do you derive those numbers for the win percentage?

Educated guesses and rollouts. The important part is that
the racing take point is extremely low, and that the gammon
price is 1 at pC 3-away but much lower than 1 at pC 5-away.
If you are much more comfortable using a value of 2.5% for
the racing take point at pC 3-away, go ahead, but it won't
make much of a difference.

> I would have figured that the gammonless take point is equivalent to the
> value of the free drop, and I have a hard time believing that's as much
> as 3%.

A 3.0% racing take point is consistent with pC 2-away
being worth 51.5% for the leader. The risk:reward ratio of
taking is 1.5:48.5 = 3.0:97.0.

> I'm also having a hard time figuring out how the take point at -5 would
> be higher, because you can only use one free drop.

First, you can either use the free drop, or possibly retain the
option of using the free drop later.

Second, pC 4-away is more volatile than pC 2-away, since
in addition to variations of winning chances, gammon
chances also vary. I believe that would make the free drop
worth significantly more in relative terms even without the
ability to use the free drop later if you take now.

At both pC 2-away and pC 4-away, the trailer can play on
for the gammon after some good sequences. It is not clear
how much this is worth, but it decreases the value of the
free drop slightly.
Did you find the information in this article useful?          

Do you have any comments you'd like to add?     


Match Play

1-away/1-away: advice from Bernhard Kaiser  (Darse Billings, July 1995)  [Long message] [Recommended reading]
1-away/1-away: advice from Stick  (Stick+, Mar 2007)  [GammOnLine forum]
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)  [GammOnLine forum]
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)  [Long message]
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)  [Recommended reading]
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)  [GammOnLine forum]
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)  [GammOnLine forum]
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)  [GammOnLine forum]
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)  [GammOnLine forum]
When to free drop  (Gregg Cattanach, Dec 2004)  [GammOnLine forum]
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)  [GammOnLine forum]

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