Cube Handling in Races

Forum Archive : Cube Handling in Races

Near end of game

From:   Ron Karr
Date:   22 February 1997
Subject:   Re: Over the Board Bearoff Analysis

Dean Gay wrote:
>   +24-23-22-21-20-19-+---+18-17-16-15-14-13-+
> 13|          X  X    |   |                  |
>  X|                  |   |                  |
>  X|                  |   |                  |
>  X|                  |   |                  |
>  X|                  |   |                  |
>  X|                  |   |                  |
>  O|                  |   |                  |
>  O|                  |   |                  |
>  O|                  |   |                  |
>  O|                  |   |                  |
>  O|             O    |   |                  |
> 12|    O        O    |   |                  |
>   +-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
> O on roll.
> Should O double?
> This position came up in a game I played today on FIBS.  I started to
> think it through and quickly became overwhelmed.  I know that an exact
> calculation can be done on this type of position, and I feel that,
> given enough time, and the aid of a calculator, I could *eventually*
> come to the correct decision here.  But during a game there is a
> practical limit to how much can be done.  I'm wondering, what is the
> thought process that a good player goes through *over the board* to
> figure out these type of decisions?  Assume whatever score and cube
> ownership you like -- or pick a more interesting position if this one
> is too easy -- but "think out loud" for me if you will.  I'm sure that
> your incites would be valuable.

There are several ways to look at these positions.  What I usually do
(and I'm not a bearoff expert by any means) is quickly run through a few
of them to see if one leads to a decisive result; if none of them do, I
may have to do a more detailed analysis (if I feel like it :-)).

1. Pip count.  Often this is too crude in short bearoffs, but sometimes
it can quickly point to the right result.  Here, for example, O has 12
pips, X has 9.  Being on roll in a race is generally considered to be
worth 4 pips; therefore the pip count alone would indicate that O is a
very slight favorite, unlikely to be strong enough to double.

Then I'd look at factors that would tend to require adjustments to the
pip count.  There are formulas, such as Thorp's, that attempt to do this
quantitatively, but in many positions you don't need to get real exact
to know what the correct decision is.  Here, for example, O has one
extra checker, which is a minus.  And he has 2 checkers on the same
point, which tends to produce less flexibility.  Both players have gaps,
but X's are less harmful since all numbers that miss can play
efficiently.  So these factors, if anything, would tend to make O's
equity worse, reinforcing the idea that he shouldn't double.

2. Another reasonable rule of thumb, which is attributed to Bill
Robertie, is: if I roll an above-average number (not my best) and my
opponent rolls a below-average number (not his worst), will I then
regret not having doubled?   Here, it may not be so clear:  if O rolls
5-4 or better and X doesn't bear off both checkers, then he'll lose his
market.  But 6-3 or 5-3 leave O in a position of having a very efficient
double next time (still a take, X has 28% winning chances), which would
tend to make me think O shouldn't double now.

3. Beyond these, you may need to look at how likely each side is to bear
off in a given number of rolls.  For a short position like this, it
shouldn't be too hard.  X has 10 numbers to get off in 1 roll
(combinations of 6,5,4, plus 33).  And he'll be off in 2 unless he rolls
very small numbers twice.  O, on the other hand, has only 2 numbers to
get off in 1, and has a quite reasonable chance of needing 3 rolls.
This would tend to indicate that he should wait a roll.

(Incidentally, Jellyfish Level 7 says O wins 52.3%, which seems quite
consistent with the above reasoning.  If it were the last shake, O would
double as the favorite, but not here.)

Match scores make a big difference.  If the cube will be dead after you
turn it, it's often correct to double with ANY market losers. Or it may
be correct to wait much longer than for money.  It depends on the
doubling window, which varies wildly for different scores.  That's a
whole separate discussion.

Did you find the information in this article useful?          

Do you have any comments you'd like to add?     


Cube Handling in Races

Bower's modified Thorp count  (Chuck Bower, July 1997) 
Calculating winning chances  (Raccoon, Jan 2007) 
Calculating winning chances  (OpenWheel+, Nov 2005)  [GammOnLine forum]
Doubling formulas  (Michael J. Zehr, Jan 1995) 
Doubling in a long race  (Brian Sheppard, Feb 1998) 
EPC example  (adambulldog+, Jan 2011) 
EPC example: stack and straggler  (neilkaz+, Jan 2009) 
EPC examples: stack and straggler  (Carlo Melzi+, Dec 2008) 
Effective pipcount  (Douglas Zare, Sept 2003)  [GammOnLine forum]
Effective pipcount and type of position  (Douglas Zare, Jan 2004)  [GammOnLine forum]
Kleinman count  (Øystein Johansen+, Feb 2001) 
Kleinman count  (André Nicoulin, Sept 1998) 
Kleinman count  (Chuck Bower, Mar 1998)  [Recommended reading]
Lamford's race forumla  (Michael Schell, Aug 2001) 
N-roll vs n-roll bearoff  (David Rubin+, July 2008) 
N-roll vs n-roll bearoff  (Gregg Cattanach, Nov 2002) 
N-roll vs n-roll bearoff  (Chuck Bower+, Dec 1997) 
Near end of game  (Daniel Murphy, Mar 1997) 
Near end of game  (David Montgomery, Feb 1997) 
Near end of game  (Ron Karr, Feb 1997) 
One checker model  (Kit Woolsey+, Feb 1998) 
Pip count percentage  (Jeff Mogath+, Feb 2001) 
Pip-count formulas  (Tom Keith+, June 2004)  [GammOnLine forum]
Thorp count  (Chuck Bower, Jan 1997) 
Thorp count  (Simon Woodhead, Sept 1991) 
Thorp count questions  (Chuck Bower, Sept 1999) 
Value of a pip  (Tom Keith, June 2004) 
Ward's racing formula  (Marty Storer, Jan 1992) 
What's your favorite formula?  (Timothy Chow+, Aug 2012) 

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