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Add Beavers, stir well, bake using HyperGammon - Undefined equities

Posted By: MK
Date: Sunday, 25 October 2026, at 5:26 a.m.

In Response To: Undefined equities (Timothy Chow)

> I'm of course aware of the earlier r.g.b. discussions, having participated in them.

In turn, I, of course, knew that you participated in them. My referring to them wasn't for you but for others, thinking that it may help them understand your theorem better (or worse :).

Also, I wonder if and how much you were compelled to prove your theorem by arguments made in such RGB discussions in general and, of course, more specifically by any of my arguments. Any chance of even some partial admissions...?

> The new article contains insights not contained in those previous discussions.

Perhaps but it also ignores other elements of those discussions such as "Beavers".

You had said "Ruling out the possibility that the correct cube action is ND/T is the trickiest part of the argument."

What about ruling out the possibility that the correct cube action is ND/Beaver?

Equities get much messier, muddier when critters like Beavers, Raccoons, etc. are allowed. That's why second-rate bots like BGBuzzzt can't handle them. Axel had proposed that not allowing Beavers would help with not ending up in St. Patersburg.

Do you want to keep pointlessly chasing your tail by expanding your theorem to also include Beavers or would you rather just play fetch? ;)

> What it does prove is that if equities do always exist, then at least some of the XG rollouts that I reported in the article are off by a lot.

When you put it in these words, it sound much better to me. I had often said in the past that time was on my side and would eventually vindicate me and that you were most likely to be the first among bg mathematicians to convert over to my side and maybe even support some of my arguments beyond simply giving me credit for them. Could this the be the day one of my wishes/dreams comes true..?

Regardless, thanks for stimulating my brain anyway. Your above words prompted me to post an article on the subject of bots' equity calculations being "off" by comparing HyperGammon and regular GambleGammon equities for some exact same positions. See:

https://www.bgonline.org/forums/webbbs_config.pl?read=222024

MK

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