Thorpe counts Kleinman counts

[agerson]

How important is Thorpe counts Kleinman counts to most people. In fact, what are they?

[don]

Both counts are for dealing with the cube in races.  Edward Thorpe, the original blackjack card counter, invented the Thorpe count, Danny Kleinman the Kleinman count.  Click on the URLs for details.

How important are they?  I'd say you need to be pretty deep into the game to memorize either of these.  At least as far as I'm concerned, there's a lot of room for improvement in other areas before I do.  For race positions, a little common sense on distribution of checkers combined with pip count is quite close.  For example:  In a short race (60 points) double at 7 pips ahead, reject at 10 behind.  Make it 10-13 for a long race.  These are money game considerations, and do not take cube equity into the picture.

[tryout]

Most importantly you should think twice before implementing them into a FIBS client. At least for people who know what they are and how to use them it's an edge over people who use other clients. To my knowledge only MacFIBS has implemented them (and imho probably shouldn't).
For comparison look at the pip count. In online play it's become a standard, but then there is a setting on FIBS which prohibits (well, if the clients comply) to show it for _both_ players. With every automatic aid you're moving away from the original game.

[wyzzz]

Thanks Don for the links on this topic.

The simple formulae will be fun to try



Wyzzz

[Shades]

Thanks Don for the links on this topic.

The simple formulae will be fun to try



Wyzzz

... and otherwise, there is always  adamosad who surely will tell u the fine rules of it... :LOOOL:  

[NIHILIST]

More precisely, Thorp and Klienman are formulas for ADJUSTING pip counts. The idea is to give a more accurate count after things like gaps and stacks are factored in.

As an example, bearing off, I have 2 checkers on my 6 point, you have 12 checkers on your one point. We each have a pipcount of 12. However, this is far from an even race; if you're on roll you certainly aren't doubling, and if I'm on roll, and I double, you certainly aren't taking.

Without going thru the entire formula, Thorp adjusts for this by adding or subtracting from the count. Typically, you might add 2 pips to the count for each checker on your 1 point. Using the example, you'd now have an adjusted count of 36 for your 12 checkers on the 1 point.

12 vs 36 is a much more accurate representation of the position than the basic 12 vs 12.

How valuable is it ? Who knows or cares ? I can tell you I've never used Thorp or Kleinman once in 23 years of play. Be aware of extreme positions like the example, make mental adjustments of 1-2 pips per checker in a big stack, and you won't be far off.


NIHI

[MND]

I cut this from a letter from a reader in gammonline. Jan 2000 issue
Its surely interesting to hear what Kit Woolsey say about it.





There are a few formulae that I have come across that are used to establish correct cube actions in bearoff positions. The Thorpe, Ward and Kleinman formulae are the ones I know of and you surely must know of them too. My question is how come no one seems to use them? Is it because they are inaccurate or because they are impractical? Perhaps it is too complicated and time consuming to use these formulae.

Do most top players make their cube decisions in bearoff positions based on benchmark positions and general experience as opposed to using a formula? I notice you never use any formulae in your annotations so I presume you do not use them when you play.Though you have probably experimented with them, if you have, what were your impressions?

Tony Moutzouris

Everybody does his own thing. Some players use a formula, some rely more on seat of the pants judgment. I couldn't say what most top players do.

Personally, I have never learned any of the formulas you mention, so I don't have any real experience with them. Not to say that they aren't valuable. I'm just lazy, I guess. In practice I take a pipcount, make whatever adjustments I believe I should make depending on men off and bearoff structure, and go from there. The formulas attempt to do the same thing but in a more rigorous manner. They will all work well in some positions, badly in others.

Several years ago I did develop a method of evaluating races which is based on shifting checkers to an "optimal" bearoff, and evaluating the effect of the shifts. This approach was very accurate almost regardless of the position. I wrote it up in an Inside Backgammon article. The problem with it is that it is very complicated; too much so for me to use at the table. In practice I just rely on my judgment, and try to save my mental energy for more important things. If I midjudge and am off by a couple of percent, it's not the end of the world.

Kit Woolsey

[don]

Thanks for that post, MND.  It's interesting to see that an expert player like Kit Woolsey has reached the same conclusion a humble player like me has reached.

The basis of all counts is the pipcount, and from there you just kinda move the checkers around in your mind in some mystical and experienced fashion to come up with how many rolls it'll take you and your opponent to bear off.  I DO know that the actual calculation of the odds in a race MAY defy even the BEST computer algorithms except in very simple situations.

As NIHI pointed out, an equal pipcount may not be equal.  I offer this suggestion:  If you can make a right-triangle, high on your six point, you are in an ideal bear-off situation.

x
xx
xxx
xxxx
xxxxx
654321

In this position you will waste the fewest pips bearing off.  I believe that the 7-10, 10-13 rule I mentioned previously, coupled with common sense AND position AND experience will yeild a race strategy that is more or less equal to using these counts if you can recall 'em and calculate 'em.

If you want to take the time, and you have some saved matches floating around, I can see value in reviewing the matches and applying the Thorpe or Kleinman counts after the fact.  You may modify your view of races.  For actual play, unless you are an idiot-savant, I still say there are other areas of play to improve on and pay attention to.

At least for me!

[amarganth]

Tom Keith wrote an excellent article Cube Handling In Noncontact Positions. He compares several known formulas (f.i. Thorp, Ward, Lamford) and created a better one.

I think, the positions came from motif, his bot.

amarganth

[adamosad]

Thx for the site Amarganth.

I know that a lot of people believe that these formulas are useless, but if anyone want to use some of them, he must choose to use Keith or Ward count.

According to statistical and econometrician methods the estimator who minimize the sum of squares error under some assumptions is the best estimator.

Gauss-Markov Theorem says that: under some assumptions (linearity, strict exogeneity, no multicollinearity and spherical error variance) this kind of estimator (Ordinary Least Squares) is efficient in the class of linear unbiased estimators. For more info see "Fumio Hayashi Econometrics Princeton University Press" or any other good statistical or econometrical book.

With simple words the best method is the one than minimize a general average error. In this site we can see that we must use the ward count in short races and keith count in midlength and long races.

I agree with a lot of people here that this methods are useless but "between blind people there is always a guy with one eye that rules the kingdom"  In this case, two "guys" Keith and Ward counts!!!  

[dorbel]

To say that these formulae are "useless" seems absurd to me. Learning and applying a formula for races that gives you a useful answer must be productive. Without it you are reduced to guessing. Of course a pip count adjusted in the light of experience is good enough for Kit Woolsey, but for players not actually in the top 20 in the world, something a little more mechanical may be a good idea. We are not all Kit, indeed 95% of players are not as good as NIHI, the great majority not even as good as don, depressing though that may be, so formulae that require no skill, just some mechanical number twiddling will pay off for most of us. The Thorp count is very powerful given its simplicity and can be twiddled by more experienced players, notably in adjusting for gaps, the Ward count is slightly better, though harder to operate and the new Keith count seems to best of all, if Tom's stats are to be believed. Those who can't or won't do pip counts, apply a formula and act accordingly are conceding a big advantage in simple positions to those who can.

[Shades]

does none of you stop and think - maybe - that a lot of people just play for the fun of it???  

[adamosad]

Dorbel my last reply was made in order to inform people about the best methods in statistical terms.If some guys believe that these formulas are useful or not this is another story....

Maybe i used a bad word at the beginning of my reply....

[socksey]

I agree with a lot of people here that this methods are useless but "between blind people there is always a guy with one eye that rules the kingdom" In this case, two "guys" Keith and Ward counts!!!

LOL........I agree with you on this statement, Adamosad, and I think you meant it in the most humorous way, for when terms such as "linearity, strict exogeneity, no multicollinearity, spherical error variance, linear unbiased estimators", my brain then goes into tilt mode and I go very blank.    

If dorbel can explain these methods in more lay terms, and he could do it, I feel certain, perhaps I might give it a try, provided I want to spend that much time on a move and provided whoever I am playing allows me.    

does none of you stop and think - maybe - that a lot of people just play for the fun of it???

Yes!  Shades, many of us do, probably most of the time, but sometimes we get serious and want to win a tourney, too, so thanks to all of you who teach us the finer points of the game.  

socksey



"Science may have found a cure for most evils; but it has found no remedy for the worst of them all- the apathy of human beings." - Helen Keller

[jonesyjt]

So much to learn and so few brain cells left.

jonesyjt

[Tomawaky]

I think that jus going to know about these formulas can improve your game if you try to understand them one time and never think about them while playing.
There will be always interesting points to know about that game....

[dorbel]

Yes Shades. a lot of people do play bg "for fun", i.e. just pushing the pieces around the board without caring whether one play is better than another. That's fine, but we can surely assume that they have no interest in formulae or in commenting on them can't we? Perhaps you are one of them.
Sorry adamosad, your last reply actually informed nobody, so nothing new there then.

[adamosad]

There is something new Dorbel, the way of thinking of a statistical and econometrician person. You must study a lot to understand how these methods works. You said that
``new Keith count seems to best of all, if Tom's stats are to be believedÃ,´Ã,´ I have explained in that post how this stat was invented and under what assumptions.
So i said something new that you did not know. I also wrote a referee you can use to understand more if you want......

[dorbel]

Thank you adamosad. "Explaining" involves elucidating your thoughts for the benefit of others, not using a lot of obscure words that are not understood by most people, or indeed I suspect by you. I wasn't casting any doubts on Tom Keith's results which appear impressive to me, rather meaning to imply that I hadn't subjected them to any form of inspection. No doubt you have. If you draw any conclusions from them that are of interest, do let us know.

[diane]

if you try to understand them one time and never think about them while playing.

Not sure I understand that - if you are going to take any time with any of these formulas - perhaps even picking one that helps - surely the point is to have them in mind while playing??