Losing your market at 2a2a
Posted By: Timothy Chow
Date: Monday, 15 September 2014, at 5:05 p.m.
The clearest explanation I've seen of optimal play at 2a2a is Bob Koca's analysis.
Dmitriy's recent inquiries have made me wonder about the following question. Is it necessarily true that if you lose your market then you have played sub-optimally? This seems intuitively true but I can't quite see how to prove it using only the assumption that Bob made in his proof.
A natural way to try to prove this is to begin by observing that doubling on the previous roll was optimal, and if you lose your market then you've just experienced a sequence in which you regret not doubling. To balance this there must be a sequence in which you're glad you didn't double. At first this doesn't seem possible, but couldn't there be a sequence that leaves you too good to double?
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