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Thorpe Count

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John Greenwood

Jun 30, 1997, 3:00:00 AM6/30/97
to (FLMaster39) wrote:

>I know that there is something called a "Thorpe Count" involving pip
>count, checkers on the ace point, and open points. But I know I saw a
>much more sophisticated Thorpe Count. It involved crossovers, useless
>gaps, and checkers off, and maybe something else, and purported to convert
>to a winning percentage. Does anyone know the exact formula?


A Leader's and Trailer's adjusted pip count, L & T, are calculated as
<L=(pipcount) + (2*number of men) + (number of men on 1 point) -
(number of home points covered).
<L is further increased, if the above total is greater than 30, by 10%
(rounded down).
T is calculated as for the first stage for L but no further increase
is ever applied.
<The Thorpe metric decides double/take decision according to the
following criteria:

L should double if L <= T+2.
L should redouble if L <= T+1.
T should pass if T >= L+2.


John Greenwood


Jul 1, 1997, 3:00:00 AM7/1/97

Chuck Bower

Jul 8, 1997, 3:00:00 AM7/8/97

In article <>,

FLMaster39 <> wrote:

In Hoosier Backgammon Newsletter about 3 or 4 years ago, the virtually
unknown (and definitely unsuccessful) Chuck Bower presented a "Modified
Thorp Count" (Note the CORRECT spelling of Edward Thorp's name--no -E-!).
Here is a reproduction of that method.

NOTE: you absolutely must keep track of the sign in this calculation!
For example, if you subtract two positive numbers giving a negative number,
you MUST keep track of the minus sign.

1) Subtract roller's pip count from non-roller's. Multiply by two.
2) From this, subtract 1/4 of roller's pip count.
3) Subtract number of non-roller's covered home board points from number of
roller's covered home board points. Multiply by 2 and add to result of
step 2.
4) Compare crossovers. Excess crossovers by non-roller are worth 5 each.
Add to result of step 3. (NOTE: excess crossovers for roller are
subsequently worth -5 each.)
5) A missing home board point is a "useless gap" if:
a) all checkers have been born in (that is, no outfield ckrs remain),
b) at least one higher point is occupied, and
c) a roll of THAT gap's number will not fill a lower gap.
(For example: 1, 3, and 5 points are occupied but the 2,4, and 6 are empty,
the 4-point is a useless gap--4's can't take a checker off and cannot fill
an unoccupied point.)
Add 4 for every useless gap for non-roller on the 3-point or higher.
Subtract 4 for every useless gap of roller's on his/her 3-point or higher.
Subtract 2 for every checker on any of roller's points in excess of 4.
Add 2 for every checker of non-roller in excess of 4 on a point. OBSOLETE!
7) Add result of these steps to 74. That is roller's cubeless game winning
chances in percent.

Let's look at an example:

1 2 3 4 5 6
x x x x
x x x x
x x
x x

o o o
o o o o
o o o o o
1 2 3 4 5 6

Assume O is on roll.
1) O leads 40-52. Two times the difference is +24 for roller.
2) 1/4 of 40 is 10. Subtract this from 24 giving 14.
3) O has five points covered to only four by X. Net of one point
covered; multiply by 2 and add to 14, giving 16.
4) O needs 14 crossovers to X's 12. Net two, worth -5 each: 16 - 10 = 6.
5) O has a USELESS GAP on the five point. (A five is wasted by being
forced 6/1--stacking a point already covered.) Subtract 4: 6 - 4 = 2.
6) (OBSOLETE--skip).
7) Add the result to 74, giving O 76% winning chances. (Actual cubeless
chances are 71.7% according to Larry Strommen's BPA.)

Here are some "accouting tricks". You are working out roller's winning
chances. "Good things" for roller are positive (bad are negative). Bad
things for NON-roller are positive (good are negative). So the sign of
each term, by step, goes like this:

1) Race lead--good.
2) Race is long--bad. (Advanced readers please note: this is consistent with
original Thorp Count but not used directly in Kleinman Count.)
3) Points covered--good.
4) Crossovers--bad.
5) Useless gaps on 3-point or higher--bad.
6) OBSOLETE! Stacks are bad.

Note that the example chosen (from a real game) missed by about 4%.
That's not too good. (At least you know I didn't "cherry-pick"!) The
method isn't much better than the "Percentage Thorp Count" that I've
written up in this newsgroup previously. Both pale when compared to the
FULL Kleinman Count (which includes gaps and crossover differences as
well). If you REALLY want to nail these positions, that is the way to
go. I'm working on an article which will compare the various methods.
Stay tuned...

One final comment. Suppose X were on roll. This method calculates
49% cubeless game winning chances (BPA says 54.9%). In a match where O
is closing in on victory (with a sizable lead), knowing this could be
valuable. Here the original (money play only) Thorp method is virtually

c_ray on FIBS


Jul 10, 1997, 3:00:00 AM7/10/97

Robertie's classic "Advanced Backgammon" lists a count method attributed
to Thorpe. I don't have it in front of me but it seems it was simpler than
that. I no longer play much but if I ever get more leisure I will
certainly try method listed in Hoosier Backgammon.


Chuck Bower

Jul 13, 1997, 3:00:00 AM7/13/97

In article <>,
Strctbil <> wrote:

You are right, the standard Thorp(e) Count (best publicized in Robertie's
book) is simpler than the "modified" version I wrote up in HBC Newsletter.
I was attempting two things: 1) make Thorp more accurate, and 2) modify
it for match play. I certainly succeeded on point 2, but point 1 is
marginal at best, and probably not worth the extra (complicated) steps.
Since I also have done 2) for the standard Thorp Count, my method is even
less valuable. BTW, here is how to convert Thorp Count to winning chances
(and thus make it applicable for match play):

Winning chance for player on roll (W) in percent for a Thorp Count (T) is

W = 74 + 2*T

Works pretty well for the range -10 < T < 5 ( 54 < W < 84)
which covers a lot of match play situations.

Finally, I'm becoming convinced that the author or the Thorp Count
(also author of the blackjack book "Beat the Dealer") should have his
name legally changed to Thorpe!

Kevin O'Bryant

Jul 13, 1997, 3:00:00 AM7/13/97

Chuck Bower (c_ray on FIBS) wrote:
...a detailed description of the "Modified Thorp count".

Can anyone post a similarly detailed description
of the Kleinman Count?

Kevin O'Bryant

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