Forum Archive : Variations

Freeze-out match

From:   Dave Brotherton
Date:   4 July 1998
Subject:   "Freeze out" match strategy

I was recently introduced to the idea of a "freeze out" match, and am
curious about appropriate match strategy.

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

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
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