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Cubeful equities: how to derive from cubeless?

Posted By: Matt Ryder
Date: Friday, 8 January 2010, at 5:07 a.m.

In Response To: Cubeful equities: how to derive from cubeless? (NJ)

You made 3 posts with similar questions, and I'll give you all my answers in one post.

I'm impressed NJ! This was a superb, detailed response to my various abstruse questions and was exactly what I needed. Thanks to your clear explanation, I've managed to construct a spreadsheet that ostensibly converts cubeless to cubeful (money, cube centered, contact position, 0-ply). I say 'ostensibly' because it's not giving me the same answer as GNU 0-ply yet... but I'm working on it :-)

(I love this forum; it's amazing what specialist skills are to be found here!)

2) The Janowski method seems to involve a lot of guesswork, especially in the estimation of the cube efficiency (x). Isn't there a better method?

If you actually took some positions and varied x, you would see that it doesn't change the cubeful evaluation by too much.

It seems to matter for 0-ply evaluation quite a bit (which is what I'm looking at), but it makes sense that the effect is increasingly diffused with higher-ply look-aheads, given your explanation that Janowski only applies to the last ply. I didn't understand that, so thanks for putting me straight.

If I had to take a guess as to why, I'd have to say it's because GNU is notoriously bad at estimating absolute equities. It suffers from an strong even-odd effect that causes it to systematically misevaluate positions.

What is the root cause of this "odd-even effect"? I've read about it here, but I've never really understood what might be the bot's malaise...

Let me first say that if you've read "Take Points in Money Games" by Janowski, that it appears to be either incomplete or wrong at places. For example, the formula for cube centered equity doesn't make sense. If you use the formula for a game in which neither side can gammon, it says that you can be too good to double. I ended up deriving my own formulas that didn't have those problems.

Maybe this is why my spreadsheet differs from GNU's outcomes? Care to post your formulae? Or are they proprietary?

The equity graph is now composed of three connected line segments. This is similar to what you read in the GNU manual.

Your explanation is much more lucid! It should be added to the GNU manual.

Anyways, this is where my own theory diverges from Janowski (and maybe everyone else). My personal theory is that the equity graph has seven line segments with the following eight points: certain loss, opponent's too good to double point, take point, opponent's initial doubling point, your initial doubling point, cash point, your too good to double point, and certain win. I also have my own formulas for calculating all these points, that derive somewhat from Janowski's ideas.

Your work here makes sense to me. I'd guess that your cubeful equities are more precise as a result. Have you contacted Janowski? He is apparently active on the GNU mailing list.

Thanks again for a stellar post! Much appreciated.

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