Match Play

 4-away/4-away: take/drop point

 From: Gary Wong Address: gary@cs.auckland.ac.nz Date: 21 October 1997 Subject: Re: Take? Forum: rec.games.backgammon Google: ieyhgab6ezi.fsf@cs20.cs.auckland.ac.nz

```MJR writes:
>
> 13 14 15 16 17 18       19 20 21 22 23 24
>    +------------------------------------------+ X: Jellyfish - score: 5
>    | X           X  X |   |  X  X  X  X  X    |
>    |             X    |   |  X  X  X          |
>    |                  |   |  X                |
>    |                  |   |  X                |
>    |                  |   |                   |
>   v|                  |BAR|                   |    9-point match
>    |                  |   |                   |
>    |             O    |   |                   |
>    |             O    |   |  O  O  O          |
>    |             O    |   |  O  O  O  O       |
>    | X           O    |   |  O  O  O  O       |
>    +------------------------------------------+ O: Me - score: 5
>     12 11 10  9  8  7        6  5  4  3  2  1

(You don't show the cube; I assume it's centred at 1.  If you were holding
a 2 cube, it would be a clear redouble/drop).

> Pipcount O:83 X:95
>
> JF3.0 Level 7 Evaluation:
>
>       Wins
> JF    19.7
> Me    80.3
>
> Equity Me:    0.605
> Volatility:   0.189
> Cube Action:  Double/Take
>
> I guess I am bit confused over this.  How can this be a take with such
> slim winning chances?

At 4-away, 4-away, the take (of a 2 cube) is a little bit easier because of
the excellent recube vig at this score -- Jellyfish can redouble you later
and give you a dead cube.  Admittedly with only 19.7% winning probability
the take looks pretty borderline regardless, but here's the maths:

If Jellyfish drops, it ends up at 4-away, 3-away with match equity of 42%
(depending whose tables you use).  If it takes, it should redouble to kill
the cube the moment its game equity is greater than its match equity if it
plays without doubling (to bring the game to 4-away, 2-away with match
equity 68% to the leader).  Since its redoubles won't be perfectly
efficient, let's assume it's forced to redouble when it has 2:1 odds for
winning, to keep the maths simple.  In that case, since it has 19.7%
winning chances, we can assume it reaches its redoubling point in 29.6% of
the games.  The results then are expected to be 70.4% losses; 9.9%
redoubled losses; and 19.7% redoubled wins.  So its total match equity is:

Takes and loses:            match equity 0.32 x 0.704   = 0.225
Takes, redoubles and loses: match equity 0.00 x 0.099   = 0.000
Takes, redoubles and wins:  match equity 1.00 x 0.197   = 0.197

For a total match equity of 42%... exactly the same as if it had dropped!
Oh well...

(In practice the match equities will vary somewhat depending on the gammon
rate you assume, the relative strengths of the players, etc., and also the
probability of "takes, redoubles and loses" will depend on how efficiently
Jellyfish can redouble.  But when it comes down to it, the situation is a
very close take/drop with little equity lost either way).  So (assuming
Jellyfish's evaluation of the game equity is reasonable), it's a clear
double, and borderline take/drop.

Cheers,
Gary (GaryW on FIBS).
--
Gary Wong, Computer Science Department, University of Auckland, New
Zealand
gary@cs.auckland.ac.nz        http://www.cs.auckland.ac.nz/~gary/
```

### 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)