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Undefined equities

Posted By: Timothy Chow
Date: Thursday, 15 October 2026, at 3:37 a.m.

Since at least 1982, it has been suspected that some money-game positions have an undefined equity. The topic has been discussed on BGOnline before, and of course I put in my two cents.

Recently, I asked ChatGPT to analyze my BGOnline posts on this topic, and in the process of doing so, I became aware of two things: (1) there was a flaw in my reasoning, and (2) Doug Zare's article on the topic had some insights that I had missed. Combining these two realizations with some analysis by ChatGPT, I was able to write an article that comes about as close as one can get to a mathematical proof that there are positions with undefined equities.

You can find my article on my website.

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