Variations

 Freeze-out match

 From: Dave Brotherton Address: dbroth02@aol.com Date: 4 July 1998 Subject: "Freeze out" match strategy Forum: rec.games.backgammon Google: 1998070405080100.BAA08683@ladder01.news.aol.com

```I was recently introduced to the idea of a "freeze out" match, and am

For those unfamiliar (as I was) with the rules for a "freeze out" match, I
will reproduce the rules that I saw posted for a side event in the Michigan
Summer Backgammon Championships, directed by Carol Joy Cole:

<START rules>

1.  All matches will be played to a 5 point differential.  That is, a
winner is declared when s/he is 5 or more points ahead of his/her opponent.
Examples: If a player has just won a game making the score 8 to 3, then
s/he has won the match and will advance to the next run.  If a player wins
a game and the score is 7 to 3, then another game must be played, until one
player has achieved a 5 or more point lead over his/her opponent.

2.  Doubling cube.  The cube will start at "One" for the first five games.
The cube will start at "2" for the second five games.  The cube will start
at "4" for the third five games.  If need be, the cube will start at "8"
the next five games.

3.  Standard tournament rules apply except the Crawford, Holland and Jacoby
rules are NOT in affect.

This event is designed to provide a new challenge to tournament style play.
All participants are encouraged to relax and enjoy this format and to
exercise patience if any idiosyncrasies or problems arise as a result of
this format. Thank you and good luck.

<END rules>

I'm relatively new to the world of regular backgammon match strategy, but
have a math/stat background.  After reading Woolsey's "How to play
Tournament Backgammon", I can grasp the general ideas behind equity tables
and their usage in a regular backgammon match.  Some of the same ideas must
apply to the "freeze out" format, but clearly many of the particulars would
change.

In general, it seems that the longer a "freeze out" match lasts, the less
important having a lead becomes - the cube escalation feature certainly
gives the trailer more than the usual chances to come back.  In fact, match
equity seems to be a function of what game it is as well as the score.

For a simple example of this, your match equity (under the usual
assumptions) for the 16th game of the described "freeze out" match (the
first one where the cube is on "8") would be 50% at ANY match score.  If
either player trailed by 4 points, then they would double to "16" at the
first opportunity (no Crawford rule), so the match will go to the winner of
this game.  If the match is closer, the match will go to the winner of this
game without the cube being turned.

I don't know what your match equity (under the usual assumptions) is with a
4 point lead entering game 2 of the described "freeze out" match.  It is
clearly larger that 50%, and I conjecture that a 4 point lead would be less
valuable in each subsequent game, with relatively small drops between games
when the cube doesn't escalate, and relatively large drops when it does
(entering the 6th, 11th, and 16th games).

I further conjecture that the match equity with a 4 point lead entering
game 2 of the described "freeze out" match is less that of a (-5,-1)
Crawford game in a regular match (85% in Woolsey's table) and also less
than that of a (-5, -1) post Crawford game in a regular match (Woolsey
gives no post Crawford match equities, presumably since there are no
post-Crawford decisions based on them, but it would have to be at least a
couple percent less than the same score during the Crawford game, with no
free drop available to the leader, so say 83% as an upper bound?).

Perhaps those with experience in "freeze out" matches can provide some
further insight into appropriate strategy (and/or amusing war stories!).

Dave Brotherton
```

### Variations

Acey-deucy  (J. Nagel, Dec 2004)
Acey-deucy  (Steve Ewert, June 1998)
Acey-deucy  (Lee+, Jan 1997)
Acey-deucy  (John David Galt+, Dec 1995)
Acey-deucy  (James Eibisch, Apr 1995)
Backwards play  (Colin Bell+, Feb 1996)
Best-of-n variant of match play  (Tim Chow+, Feb 2009)
Bluff Cube  (Timothy Chow+, Dec 2012)
BluffGammon  (Christian Munk-Christensen, June 2009)
Cancelgammon  (Ilia Guzei+, Mar 2004)
Domino backgammon  (Laury Chizlett, Sept 1999)
Duodecagammon  (David Moeser, Dec 2000)
Duplicate backgammon  (Dean Gay+, Jan 1997)
Duplicate backgammon  (Albert Steg, Feb 1996)
Exact bearoff  (Chris Moellering+, Dec 2002)
Fevga  (George, Sept 2004)
Fevga (or Moultezim)  (Igor Sheyn+, May 1995)
Freeze-out match  (Dave Brotherton, July 1998)
Gabgammon  (jckz, Oct 2005)
Greek backgammon  (Alexandre Charitopoulos, Aug 2003)
Greek backgammon  (Alexandros Chatzipetros, June 1997)
Greek backgammon  (Marc Jacobs+, Feb 1994)
Hit man  (Matt Reklaitis, Jan 2004)
Hyper backgammon  (Gregg Cattanach+, Dec 2000)
Hyper backgammon  (Michael A Urban, Oct 1993)
International backgammon  (Bob Lancaster+, Oct 2002)
Jacquet  (Mark Driver, June 2001)
Joker cube  (Joe Russell+, May 2011)
Khachapuri  (Michael Petch+, Sept 2010)
Kleinman's tandem backgammon  (Fabrice Liardet+, May 2010)
LongRun  (Bill Hickey, Mar 2010)
Longgammon  (Michael Strato, Dec 2000)
Low number first, fixed dice, others.  (Walter Trice, Jan 1997)
Mexican  (Tom Henry, Apr 1997)
Middle Eastern backgammon  (Alan Cairns, Mar 2002)
Misere (backgammon to lose)  (Jason Lee+, July 2004)
Misere (backgammon to lose)  (Jason Lee+, Apr 1995)
Misere, Chase, Skewed dice  (Stein Kulseth, Jan 1997)
Nackgammon  (Ken Arnold, July 1996)
Nackgammon Shuffle  (Stick, Sept 2011)
Nackgammon opening moves  (Warwick+, Feb 2002)
Narde  (narde, Nov 2006)
Nardi  (KL Gerber+, Nov 2002)
No hit  (RedTop+, May 2004)
Nuclear backgammon  (Walt Swan, Apr 1997)
Old English  (Nick Wedd+, Feb 1996)
One roll lookahead  (Stephen Turner, Mar 1997)
Opening slot rule  (Gregg Cattanach, June 2006)
Other variations  (Douglas Zare, Feb 2000)
Plakoto  (Ed Dengler+, May 1995)
Plakoto  (Pasteel M., Feb 1994)
Plakoto express  (Athansios Vagias, Feb 2005)
Portes  (George, Sept 2004)
Roll-over  (Edward D. Collins, Oct 1997)
Russian backgammon  (Daavid Turnbull, Aug 1991)
SassanGammon  (Chiva Tafazzoli+, June 2009)
Shesh Besh  (G.S., May 2003)
Simborg Rule  (Scott+, Feb 2005)
Slot backgammon  (Fabrice Liardet+, Aug 2008)
Sudden death, Woodpecker, Gerhardsen  (Fredrik Dahl, Jan 1997)
Tablestakes betting  (TrueMoneygames, June 2002)
Takhteh  (Bruce Scott+, Mar 2003)
Tandem Backgammon  (Mislav Kovacic, Feb 2012)
Tavla  (Arda Findikoglu, Nov 2004)
Tavla  (ucc02cx+, Feb 1997)
Tavli (Portes, Plakoto, and Fevga)  (Jens Larsen, July 1997)
Tavli question  (Brus+, Apr 2011)
Tracy turn around  (Michael J. Zehr, Feb 1996)
Tri-gammon  (Gregg Cattanach, Sept 2000)
Trictrac  (David Levy+, May 1998)
Trigammon  (James Eibisch, Jan 1997)