Match Play

Forum Archive : Match Play

Which format most favors the favorite?

From:   Daniel Murphy
Date:   26 January 2006
Subject:   Longer matches favor the favorite, right?
Forum:   GammOnLine

Which of these four formats is most favorable to the better player:

1. One match to 21 points
2. Best of 3 matches to 7 points each
3. Best of 7 matches to 3 points each
4. Best of 21 matches to 1 point each

Ian Dunstan  writes:

One might suspect that three 7pt matches is best for the superior
player. There will be plenty of score based problems for the weaker
player to overcome as well as needing to win several games to reach 7pts
and win a match. E.g., the now defunct World Cup was 3 matches to 11pts,
and I believe that was a highly regarded test of skill for our top

OTOH, working on the basis that the stronger player likes to utilise his
skill over as many games as possible, twenty-one 1pt matches is probably
best. On the basis that chequer play is harder than cube play, I think
that forgetting about match score nuances and playing as many games as
possible is most likely to find the best player. However, it's not very
satisfying to have a tournament based on 1pt matches.

Maik Stiebler  writes:

The easy part of the question is: What does it mean to play 'best-of-N-

If one of the players wins a single match with probability p=0.5+eps and
eps is smallish, then he will win

best-of-three with p* approximately 0.5+1.5*eps-2.0*eps^3;
best-of-five with p* approximately 0.5+1.875*eps-5.0*eps^3;
best-of-seven with p* approximately 0.5+2.19*eps-8.75*eps^3;
best-of-21 with p* approximately 0.5+3.70*eps-49.0*eps^3;

The difficult question is how eps depends on the match length. This is
discussed by Tom Keith (

One method is to believe the FIBS formula, which says eps is
approximately sqrt(matchlength) * beta, where beta represents skill
difference in a one-pointer.

I prefer the 'MET method', which however, in the version described by
Tom, assumes that there is no skill in cube play, so as a third method I
propose a MET method based on the Jacobs-Trice-050 table.

According to the FIBS method and ignoring the eps^3-terms, we get a
'skill factor' of

1.0*sqrt(21)=4.58 for a single 21-pointer,
1.5*sqrt(7)=3.96 for best-of-three 7-pointers,
2.19*sqrt(3)=3.79 for best-of-seven 3-pointers,
3.70 for best-of-21 one-pointers.

The MET-method says

1.0*2.51=2.51 for a single 21-pointer,
1.5*1.62=2.43 for best-of-three 7-pointers,
2.19*1.24=2.72 for best-of-seven 3-pointers,
3.70 for best-of-21 one-pointers.

JT say

1.0*6.5=6.5 for a single 21-pointer,
1.5*3.7=5.55 for best-of-three 7-pointers,
2.19*2.3=5.04 for best-of-seven 3-pointers,
3.70 for best-of-21 one-pointers.

Hmm, if I extracted the data from the JT-50 correctly, they appreciated
the skill in a one-pointer even less than the FIBS formula - can that be

I think that best-of-21 one-pointers is usually the most skill-intensive
variant, albeit a bit boring. So, what do you think which match length
offers the best match play fun? Isn't a 21-point match mostly like a
money session, until the score is so lopsided that there is not much at
stake anymore? Or are things like offering sharp four-cubes at 20 away -
17 away something you wouldn't want to miss?

Chris Yep  writes:

I think that Bill Robertie discussed this subject (maybe only briefly)
in an issue of Inside Backgammon. His conclusion was that the stronger
player was more likely to win a longer match (e.g. a 21-point match
instead of a best-of-3 set of 7-point matches). This intuitively makes
sense to me -- my intuition says that an extra layer of luck is added by
having another hierarchical level of results. A player who loses the
series 7-6, 0-7, 7-6 probably outplayed his opponent.

Casper van der Tak  writes:

It depends on what makes the better player better. If it is skills at
adapting to match scores, then I believe the 7 3-point matches would
have most to offer (more scores that really change your playing strategy
that one 21-point match or 3 7-points matches). Best of five 5-point
matches would be even a better format.

The 21-point match format would favour a better player who is also the
better player for money, and who has experience in playing matches this
long (I would run out of MET knowledge myself).

Personally, if I'd need to maximize chances against a weaker player, I
would prefer best of five 5-point matches, best of 7 3-point matches,
best of 3 7-point matches, 21-point match, and best of 21 1-point
matches in that order.

Maybe the 21 1-pointers would be better for me than indicated here, but
the absence of any cube action makes me wonder.

Robert-Jan Veldhuizen  writes:

Cubeless play, such as in 1pt matches, has the advantage that all games
are played to conclusion. That gives the worse player a lot more moves
to go wrong. So there is at least some compensation.
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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