Match Play

 Matches to a set number of games

 From: Tom Keith Address: tom@bkgm.com Date: 26 October 1998 Subject: Re: Set-number-of-game matches Forum: rec.games.backgammon Google: 3634B92C.D7330A04@bkgm.com

```BobSMan wrote:
> Andrew Bokelman writes:
> > One variation I've come up with is as follows:
> >
> > 1. A match consists of a decided-upon number of games.
> > 2. When that number of games is played, whoever has more points wins.
> > 3. If there is a tie, one more game is played to break the tie.
> >
> > But I guess that this can have its problems too.  For example, if it is
> > near the end of the match the trailer can start doing automatic
> > doubles.  But for some reason the above method strikes me as better.
>
>     But remember, if the trailer starts doubling early there will now be
> a price to pay.  Once a player needs more than three points per game
> remaining, the match is over.  If he doubles, the double will be refused,
> and winning an undoubled backgammon in every game will not be enough to
> save him.  If a player begins making early doubles before this point (in
> an effort to avoid this situation) the price will be an increased
> probability of reaching this point even earlier.
>     In fact, I've thought of this type of match myself, and it has always
> seemed a good solution to the problem, IMO.  A player who is behind will
> never be able to double automatically in an effort to catch up, because
> of the probable benefit to the opponent.  And once a player becomes
> sufficiently far behind, any attempt to use the cube at all will result
> in the loss of the match.  The structure of the match itself removes the
> need for any artificial controls on the cube.
>
> Bob Sisselman

Gary Wong did a nice critique of this type of match a week or so ago.
Here are a few observations about what happens if you run matches this
way:

1.  Near the end of the match, the match equities are not very evenly
distributed -- especially at 1-game-to-go, where there is no real
difference between being ahead by one point, being tied, or being
behind by one point.  Besides appearing somewhat unfair, this
skews the take points in the 2-to-go game.

2.  Some match scores leave the trailer with only a very remote chance
of turning things around.  For example, when you are behind by 4
with 2 games to go, you must win two consecutive gammons and then
a tie-breaker to win the match -- that's less than a one percent
chance.  Playing with so little at stake would not be very
enjoyable for many players.  (Behind by 6 with 3 games to go is
even worse.)

3.  At certain match scores, such as down-3 with 2-to-go, you've lost
must be to play for a gammon, and then only if things go badly
will you double.  (This isn't bad, necessarily -- just different
than normal match play.)

Some match equities:

Games left:     0     1     2     3     4     5     6     7     8     9    10
Lead  10:  1.000 1.000 1.000 1.000 1.000 1.000  .999  .986  .953  .939  .921
Lead   9:  1.000 1.000 1.000 1.000 1.000 1.000  .990  .954  .932  .912  .893
Lead   8:  1.000 1.000 1.000 1.000 1.000  .993  .956  .922  .902  .880  .863
Lead   7:  1.000 1.000 1.000 1.000  .997  .960  .910  .890  .864  .845  .827
Lead   6:  1.000 1.000 1.000  .999  .969  .894  .874  .845  .824  .805  .789
Lead   5:  1.000 1.000 1.000  .980  .876  .855  .821  .798  .778  .761  .747
Lead   4:  1.000 1.000  .992  .877  .830  .792  .765  .745  .727  .714  .701
Lead   3:  1.000 1.000  .891  .793  .756  .724  .705  .687  .674  .663  .653
Lead   2:  1.000  .938  .695  .718  .669  .658  .636  .628  .618  .610  .603
Lead   1:  1.000  .500  .678  .584  .598  .573  .572  .564  .559  .555  .552
Lead   0:   .500  .500  .500  .500  .500  .500  .500  .500  .500  .500  .500
Lead  -1:   .000  .500  .322  .416  .402  .427  .428  .436  .441  .445  .448
Lead  -2:   .000  .062  .305  .282  .331  .342  .364  .372  .382  .390  .397
Lead  -3:   .000  .000  .109  .207  .244  .276  .295  .313  .326  .337  .347
Lead  -4:   .000  .000  .008  .123  .170  .208  .235  .255  .273  .286  .299
Lead  -5:   .000  .000  .000  .020  .124  .145  .179  .202  .222  .239  .253
Lead  -6:   .000  .000  .000  .001  .031  .106  .126  .155  .176  .195  .211
Lead  -7:   .000  .000  .000  .000  .003  .040  .090  .110  .136  .155  .173
Lead  -8:   .000  .000  .000  .000  .000  .007  .044  .078  .098  .120  .137
Lead  -9:   .000  .000  .000  .000  .000  .000  .010  .046  .068  .088  .107
Lead -10:   .000  .000  .000  .000  .000  .000  .001  .014  .047  .061  .079

(Assumptions: 25% gammon rate, 0% backgammon rate, efficient doubles,
free drop ignored.)

Tom Keith
```

 Johan Richter  writes: ```Andrew Bokelman writes: > > One variation I've come up with is as follows: > > > > 1. A match consists of a decided-upon number of games. > > 2. When that number of games is played, whoever has more points wins. > > 3. If there is a tie, one more game is played to break the tie. In tournament play of the Backgammon variation "Swedish tables" that is the format used. However the tiebreaker is different. If the score is tied after the predetermined number of games you look at who won the most points in their highest scoring game. If that doesn't decide the winner you look at the second highest scoring game and so on. Eg, if player A scored at 4 points in his highest scoring game and player B scored 3 in his, player A would win. If player B had also scored 4 points in his highest scoring game you would look at the second highest scoring game. If player A had won two games with 4 points and player B one, player A would obviously win assuming these were the highest scoring games in the match. As long as you play an odd number of games this tiebreaker is guaranteed to generate a winner. The proof, which works for any two-player game where draws aren't allowed, is left as an exercise for the reader. ```

### 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)