Match Play

 7-away/11-away: volatile recube decision

 From: Kit Woolsey Address: kwoolsey@netcom.com Date: 2 May 1997 Subject: Re: Justifying my double in Las Vegas Forum: rec.games.backgammon Google: kwoolseyE9JB9F.L69@netcom.com

```zzyzx97@earthlink.net wrote:

+13-14-15-16-17-18-+---+19-20-21-22-23-24-+
|       O     X    |   |    O  O  O  O  O |
|             X    |   |    O  O  O  O  O |
|                  |   |          O  O  O |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |             X  X |
|                  |   |    X  X  X  X  X |
|       O        X |   |    X  X  X  X  X |[2]
+12-11-10--9--8--7-+---+-6--5--4--3--2--1-+

> Here are the rest of the facts:
>
> Abe is X and he leads 10-6 in the 17 point match. I am O and I have
> the cube on 2. It is my roll. Abe has 61 pips to go and I have 74. My
> doubling window opens at 45.6% (.456). His take point is .277. So I
> passed the window test.  But its not often you should double toward
> the short end of the window. So let's look at what is likely to
> happen.In a non contact race with these pips, I only win 31%. However,
> there is contact. He has 2 blots and I have 16 shots. I let Jellyfish
> play 1296 games on level 5, and left the settlement value at .550.
>
> If I hold the cube I win 57.6% and we both get 1.3% gammons for a
> positive equity of .153

This is a very complex problem, due to the potential of doubling later if
you hold the cube.  Here is how I would work it out at the table, using
as much simplifying assumptions as possible.

First:  Using Neil's numbers (which give a close approximation of my
match equity table):

6-14:  10% equity
6-12:  20% equity
8-10:  39% equity
10-10:  50% equity

So if it were a now or never situation you would be getting 11 to 10 odds
on the double.  However it isn't a now or never situation -- if you hold
the cube, you may get to double later and win some games which might
have been lost if you had to play them to conclusion.

First simplifying assumption:  I assume that O will never redouble to 8
(since he can't redouble except as a huge favorite, this isn't far off).

Let's suppose that X hits a shot.  If he doesn't double, I assume he
always wins the game, since unless O rolls a joker X will be able to
claim with the cube next turn.  This doesn't take O's jokers into
account, but they are somewhat counterbalanced by the potential of X
playing for, and getting, a gammon when O flunks.
If X does double and hits a shot, he has to play to conclusion.  I
estimate that X will win 88% of the time when this happens (actually I
think it is a bit lower, but to compensate X will win a few gammons).

Let's suppose that X misses.  He is a clear underdog, but has some racing
and some hitting chances.  Also, he will clearly win more often if he
hangs onto the cube, since he may get an efficient double later and not
have to play to conclusion a game he might lose.  I will guess that X
will win 35% of the time if he let's the cube go, and 40% of the time if
he hangs onto the cube.

So, what does all this mean?  Roughly speaking, it looks like about 1/8
of the games X would win if he hangs onto the cube will turn into losses
if he doubles.

How does this figure into the match equities?  If X loses a game he would
have won if he hadn't doubled, this costs him 29% equity (difference
between 39% and 10%).  Thus, of the games X would have won if he hadn't
doubled, he gains 11% 7/8 of the time and costs 29% 1/8 of the time.
This comes to an average gain of about 6%.  As we have seen, X loses 10%
if he doubles and is wrong.  Thus, when we take the cube value into
account it looks like X is actually giving 10 to 6 odds with his
redouble.  He clearly isn't close to being worth this in this position.
So, if you accept my estimates, the redouble is incorrect.  Of course my
estimates may well be quite wrong, and different estimates might lead to
a different conclusion.

Kit
```

### 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)