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Herlock Sholmes: Hmm... I'll have to admit that it was those 'technicalities' that caught my interest, though - I've never played games for the money, so I was responding to a situation where the game is a part of a match, rather than a single game with a stake. In that case, I suppose the stronger player should double - and the weaker player shouldn't have made the bet in the first place.
Off the top of my head, I'd say the draw problem could perhaps be solved by counting draws as 0 points instead of 0.5. Wouldn't that cancel all speculations about doubling in a drawn position?
pedestrian: of course, who would like to play for stakes with grand masters ... but you and me, we can try to play pretending we use doubling cube ... want to try one game and find these situations for doubling ? Let's play for funny $100 ... would you ?