Forum Archive : Cube Handling

Too good to double--Janowski's formula From:   Chuck Bower Address:   bower@bigbang.astro.indiana.edu Date:   5 January 1997 Subject:   Re: Two positions and an Intro Forum:   rec.games.backgammon Google:   5aoqas$q05@dismay.ucs.indiana.edu Klaus G Wagner wrote: > From two recent FIBS matches: > > X to play 51. > > +-1--2--3--4--5--6--------7--8--9-10-11-12-+ O: OOOOO - score: 2 > | X O | | X O O X | > | X O | | O X | > | O | | O X | > | O | | O X | > | O | | | > | |BAR| |v 7-point match > | | | | > | X | | O | > | X | | X O | > | X | | X O | > | X O X | | X O | > +24-23-22-21-20-19-------18-17-16-15-14-13-+ X: kgw - score: 2 > BAR: O-0 X-0 OFF: O-0 X-0 Cube: 2 (owned by kgw) > > > I played 1-2-7, thinking of nothing else ... > gepard (my 9 year old son Gerhard) would prefer 17-22*-23. > Which one is best? Or is it something else? ( surprise! :) Jellyfish level-7 evaluation agrees with Gebhard: 17/22*/23 is better than 1/7 by 0.10 units (cubeless money equity) which is quite a bit, BTW. Good news is that you and the lad found the two best plays. (Note that the match score doesn't alter the "correct play" in this case.) > (snip) > > The second position: > > X on roll. Cube Action? > > +13-14-15-16-17-18-------19-20-21-22-23-24-+ X: XXX - score: 2 > | O X X X | X | X O | > | O X X | | X | > | O X | | X | > | | | X | > | | | X | > v| |BAR| | 5-point match > | | | | > | | | | > | | | O | > | X O | | O O O | > | X O O | | O O X O O | > +12-11-10--9--8--7--------6--5--4--3--2--1-+ O: kgw - score: 2 > > BAR: O-0 X-1 OFF: O-0 X-0 Cube: 1 turn: kgw > > I doubled (after a dance by X), XXX dropped (and went on to win > the match by a narrow margin). > > Afterwards, I wondered about whether playing on for the gammon would > have been better. There are 15/36 chances to make the 4 point, and most > other rolls are constructive too (except maybe 65). On the other hand, > X surely is not finished yet. > > What do you think? You really want to know? OK, but you asked for it.... Actually, knowing when to cash and when to play on for gammon is one of the least discussed (and therefore, quite possibly one of the least understood) areas of the game. Fortunately for us (well, you and me, anyway), Rick Janowski wrote an excellent series of articles a couple years ago in "Hoosier BG Newsletter". FOR MONEY PLAY, he gives the following formula for the "TOO GOOD (to redouble) POINT", assuming "typical" cube ownership equity: L + 1 If game winning chances greater than: ------------- W + L + 0.333 then play on for the gammon. L and W are (respectively) the average losing and winning expectations (cubeless) for the player making the decision (O in this case). These can easily be calculated from JF rollout (or evaluation) results as illustrated below. JF rollout (108 trials on level-6 cubeless) gave the following results: simple g+bg bg O wins 75.9 50.6 1.4 X wins 24.1 5.0 0.4 (cubeless equity = 0.983, std. dev. = 0.024, equiv. to 3107 games). From O's point of view, W = (75.9 + 50.6 + 1.4)/75.9 = 1.685 and L = (24.1 + 5.0 + 0.4)/24.1 = 1.224 So, the cutoff point for playing on for the gammon is: (1.224 + 1) / (1.685 + 1.224 + 0.333) = 68.6% And since JF sez O wins 75.9% (which is more than 68.6%), O should play on for the gammon at money play. As far as this particular match score, I did the math (but save the reader the multiple lines here) which shows the following (assuming the gammon fractions indicated by the rollout): X's drop point for money: 36.5% X's drop point at this match score: 40% As you can see, X should be MORE LIKELY to drop this position at this match score (assuming the large gammon fraction indicated by the rollout) so playing on for the gammon is even more likely to work than at money play. (As always, there is some argument for doubling IF you think your opponent might take. In this case taking looks rather foolish.) One final note: Rick's formula appears to diverge from "reality" when gammons chances go to zero, since then you would expect the formula to give 1.00, which it doesn't. Maybe he can comment on this. Chuck bower@bigbang.astro.indiana.edu c_ray on FIBS   Did you find the information in this article useful?           Do you have any comments you'd like to add?

 

Cube Handling

Against a weaker opponent  (Kit Woolsey, July 1994) 

Closed board cube decisions  (Dan Pelton+, Jan 2009) 

Cube concepts  (Peter Bell, Aug 1995) 

Early game blitzes  (kruidenbuiltje, Jan 2011) 

Early-late ratio  (Tom Keith, Sept 2003) 

Endgame close out: Michael's 432 rule  (Michael Bo Hansen+, Feb 1998) 

Endgame close out: Spleischft formula  (Simon Larsen, Sept 1999) 

Endgame closeout: win percentages  (David Rubin+, Oct 2010) 

Evaluating the position  (Daniel Murphy, Feb 2001) 

Evaluating the position  (Daniel Murphy, Mar 2000) 

How does rake affect cube actions?  (Paul Epstein+, Sept 2005) 

How to use the doubling cube  (Michael J. Zehr, Nov 1993) 

Liveliness of the cube  (Kit Woolsey, Apr 1997) 

PRAT--Position, Race, and Threats  (Alan Webb, Feb 2001) 

Playing your opponent  (Morris Pearl+, Jan 2002) 

References  (Chuck Bower, Nov 1997) 

Robertie's rule  (Chuck Bower, Sept 2006) 

Rough guidelines  (Michael J. Zehr, Dec 1993) 

Tells  (Tad Bright+, Nov 2003) 

The take/pass decision  (Otis+, Aug 2007) 

Too good to double  (Michael J. Zehr, May 1997) 

Too good to double--Janowski's formula  (Chuck Bower, Jan 1997) 

Value of an ace-point game  (Raccoon+, June 2006) 

Value of an ace-point game  (Øystein Johansen, Aug 2000) 

Volatility  (Chuck Bower, Oct 1998) 

Volatility  (Kit Woolsey, Sept 1996) 

When to accept a double  (Daniel Murphy+, Feb 2001) 

When to beaver  (Walter Trice, Aug 1999) 

When to double  (Kit Woolsey, Nov 1994) 

With the Jacoby rule  (KL Gerber+, Nov 2002) 

With the Jacoby rule  (Gary Wong, Dec 1997) 

Woolsey's law  (PersianLord+, Mar 2008) 

Woolsey's law  (Kit Woolsey, Sept 1996) 

Words of wisdom  (Chris C., Dec 2003) 

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