Steve, I couldn’t possibly comment on whether the races were fixed but I did notice that the tote board always changed dramatically just before the off. I subsequently looked at what went on at the booths, and noticed that a lot of shifty-looking guys in camel hair coats regularly waged enormous cash sums just before betting closed. It wouldn’t surprise me if these people are now university Vice-chancellors.

Peter

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Anton: I can’t remember where I first saw the Dutch Book argument in this form. It might have been de Finetti that first wrote it up, but I don’t think that’s where I found it. It probably appeals more to people like me who misspent their youth. Although I’ve now stopped going to the dogs in a literal sense, the phrase is probably still apt as a metaphor.

Ben: Thanks for that. I wasn’t aware of that terminology. Of course there’s nothing unfair about the bookmaker doing this so he can’t be foxed by a multiple bet. He has to make a living! There is similar thing with the Tote: the system takes a slice of all the bets before calculating the returns.

Peter

]]>It is fairly intuitive that you can always win if the odds that a bookie quotes correspond to “probabilities” that sum over all dogs to less than one, as in your example where they sum to 95%. I expect there is an elegant proof of that by construction of the optimal strategy.

Anton

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