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Scottish Verdict?

Posted By: Timothy Chow
Date: Monday, 29 April 2013, at 9:58 p.m.

In Response To: Scottish Verdict? (David Rennie)

David Rennie asked:

Are there occasions where no definitive answer can be found or does on just continue the rollout until 100% confidence is reached?

Certainly there are cases where no "definitive" answer can be found.

1. A position that the bot doesn't understand. I'll ignore this because I don't think that's what you meant by "definitive."

2. A position where the equity is undefined. The position below may be an example.

Money Game
Blue on roll. Cube action?
White117

Blue115
GNUBg Id: 2zYgikDbNiCFQA:cAkAAAAAAAAA
XGID=aBBBBBa--aa-AaAA---AbbbbbA:0:0:1:00:0:0:0:0:10

3. A position where more than one choice has exactly the same equity. You can roll out the position below until kingdom come and it won't tell you "definitively" whether to take or to pass.

Money Game
Blue on roll. Cube action?
White1

Blue6
GNUBg Id: AQAAgAAAAAAAAA:cAkAAAAAAAAA
XGID=------A-----------------a-:0:0:1:00:0:0:0:0:10

4. A position where the equity difference is extremely small. This is an interesting question that I don't think I've seen posed explicitly before, probably because the answer is difficult: What is the smallest possible nonzero equity difference between two checker plays in a legal backgammon position? It has to be very small. I guess a start on this question could be made using one of the non-contact racing databases.

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