Match Play

 3-away/4-away: what's the correct equity?

 From: Tom Keith Address: tom@bkgm.com Date: 21 September 1997 Subject: Re: Is this a double? Revisited. Jury is out? Forum: rec.games.backgammon Google: 34257847.641@bkgm.com

```I wrote:

: Leader's drop point at 3-away, 5-away is quite sensitive
: to the match equity you assume for 3-away, 4-away.
: The higher the value of Trailer's equity at 3-away, 4-away,
: the more reluctant Leader will be to give up one point when
: the score is 3-away, 5-away.
:
: Kit Woolsey's table lists Trailer's 3-away, 4-away match
: equity at 41%.  But there are other tables (e.g., Norman
: Zadeh's) which place the value for this score as high as 43%.
: Each one point increase in the assumed value of Trailer's
: equity at 3-away, 4-away produces a two or three point rise
: in Leader's drop point at 3-away, 5-away.
:
: So, as much as anything else, the position of Leader's drop
: point at 3-away, 5-away depends on which match equity table
: you use.

Kit Woolsey wrote:

> Good point, Tom.  Let's see what this means if we use Zadeh's 43%.  I
> don't know what his figure is for 1 away, 5 away Crawford, so let's
> assume it is the same as mine (85% for the leader).  Now, let's look at
> the leader's drop point, assuming no gammons:
>
> Leader passes:  He is ahead 4 away, 3 away for 57% equity.
> Leader takes and wins:  He is ahead 1 away, 5 away for 85% equity.
> Leader takes and loses:  He is even, for 50% equity.
>
> Thus he would be risking 7% to gain 28%, so he would be getting 4 to 1
> odds on his take.  Therefore, he could take with 20% winning chances,
> ignoring possible recube vig.
>
> This just doesn't feel right, does it?  All our intuition tells us that
> the leader should be more cautious in taking the cube than he should be
> in money (except possibly where the double puts him out exactly), but
> these figures say he can take positions which are clear money passes.
> To me, this indicates that Zadeh's 43% figure has to be off.

Maybe not.  There is an "odd-even" effect on match scores that can
produce surprising results.  Since points in backgammon often come
in twos and fours, the opponent's match-winning chances take a big
step forward when he goes from 5-away to 4-away.  At 4-away he can
win the match with one doubled gammon or two 2-point games.

Because a one-point loss is so expensive when the opponent is 5-away,
and a two-point loss not that much worse, the leader is more willing
than usual to try turning the game around rather than give up exactly
one point.

> When I constructed my match equity table, one of the things I did was to
> introduce smoothing effects so anomalies such as the one above would be
> avoided.  Thus I believe my table will lead to more practical results in
> one's match equity calculations.

Here's an interesting question:  Which is better, leading a match at
at 3-away/4-away or leading at 4-away/5-away?

Tom
```

### 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)