Match Play

Forum Archive : Match Play

Doubling window with gammons

From:   Jason Lee
Date:   3 January 2009
Subject:   Computing where the doubling window opens -- WITH gammons
Forum: Forums

How does one compute where the doubling window opens -- assuming we have
information about gammon rates? I realize that this is very difficult to
actually apply over the board -- so this question is just theoretical.


John O'Hagan  writes:

First compute the minimum doubling point ignoring gammons, which is
risk/risk + gain.

For example, 0-1 to 5: Don't double and lose makes the score 0-2 with about
35% match equity (ME).  Do double and lose makes it 0-3 with about 25% ME.
The risk from doubling is therefore 10% ME.

Don't double and win makes the score 1-1 with 50% ME, do double and win
makes it 2-1 with about 57.5% ME. The gain from doubling is therefore 7.5%
ME. This makes the gammonless minimum doubling point 10%/10% + 7.5%, about

Next compute the 2-cube gammon prices for both players: The 2-cube single
game swings are from 25% ME to 57.5% ME. A gammon win makes it 4-1 Crawford
with about 82% ME, a gammon loss loses the match with 0% ME. The gammon
price when you win a gammon is therefore 24.5%/32.5% (about 75%) vs.
25%/32.5% (about 77%) when you lose one.

The minimum doubling point including gammons is then: 57% - (75% * gammon
wins) + (77% * gammon losses). So if you win/lose 20%/10% gammonss, your
minimum doubling point becomes 49.7%.

The absolute lowest your gammon-included minimum doubling point could be at
this score occurs where all of your wins are gammons and none of your
losses are. The risk from doubling in this situation is still 10% but the
gain from doubling is 24.5%, making your minimum dbling point 10%/34.5%,
about 29%.

At a moneylike score (say 0-0 to 25), the lowest possible gammon-included
minimum doubling point is 1/3.


Another way to figure this out would be to use Kit Woolsey's blended
average approach. The idea here is to include the gammon wins/losses into
the risk/reward ratio.  Here's how it works (using the same 0-1 score to

You need to first estimate 2 figures: your gammon wins/your total wins and
your gammon losses/your total losses. Let's use 40% and 20% for these two

If you don't double and lose this game, 80% of the time you'll be down 0-2
with 35% ME and 20% of the time you'll be down 0-3 with 25% ME.

(80% * 35%) + (20% * 25%) = 33%.

Do double and lose, 80% of the time you're down 0-3 with 25% ME and 20% of
the time you lose the match with 0% ME. 80% * 25% = 20%. The risk from
doubling is then 13%.

Now the reward side. Don't double and win, 60% of the time you're tied 1-1
with 50% ME and 40% of the time you're up 2-1 with 57.5% ME.

(60% * 50%) + (40% * 57.5%) = 53%.

Do double and win, 60% of the time you're up 2-1 with 57.5% ME and 40%
you're up 4-1 Crawford with 82% ME.

(60% * 57.5%) + (40% * 82%) = 67.3%.

This makes the gain from doubling 14.3%.

The min doubling point is therefore 13%/27.3%, about 47.6%.

Bob Koca  writes:

Rew asks:

> Do you also have to consider gammon prices on 4 cubes?

That makes it much more difficult, rew.  Then you would also need to
consider the rerecubes etc.

The minimum window point is done ignoring the future cube value and is same
as answer to, "Suppose you had the choice of doubling right now or having
the cube be frozen for the rest of the game at its current value, how good
do you need to be to double?"

Note that it is possible for a cube to be correct even though one is below
this window and occurs because it is possible that an opponent has less
cube power holding a 2 cube than he does having access to a centered cube.
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]

[GammOnLine forum]  From GammOnLine       [Long message]  Long message       [Recommended reading]  Recommended reading       [Recent addition]  Recent addition

  Book Suggestions
Computer Dice
Cube Handling
Cube Handling in Races
Extreme Gammon
Fun and frustration
GNU Backgammon
Luck versus Skill
Magazines & E-zines
Match Archives
Match Equities
Match Play
Match Play at 2-away/2-away
Opening Rolls
Pip Counting
Play Sites
Probability and Statistics
Source Code
Strategy--Bearing Off
Strategy--Checker play


Return to:  Backgammon Galore : Forum Archive Main Page