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You could definitively answer how much he should have bet using what's known as the 'Kelly criterion.' Basically you need to consider the total wealth of the in
by Tycho 12y ago
You could definitively answer how much he should have bet using what's known as the 'Kelly criterion.' Basically you need to consider the total wealth of the individual and the edge they believe they have (ie. bookies offer odds at 4/1 while the gambler reckons it's longer).
http://en.wikipedia.org/wiki/Kelly_criterion http://en.wikipedia.org/wiki/Kelly_criterion
Whether this was a rational bet depends on how good he thought is edge was (perhaps allowing for some margin of error) and how rich he already is.
- eru 12y agoThe Kelly criterion applies for repeated bets. It optimizes the logarithmic expected winnings. I am not sure how it applies for a single bet. I guess it depends on one's like or dislike of risk.
- Tycho 12y agoI was wondering about that but I don't see how it wouldn't apply. In a series of bets it guarantees you wont go bust and will maximise your long term winnings (I'm probably missing some subtleties here so corrections welcome). But the whole concept can be traced back to a letter/essay by one of the Bernoulli family, in which the example was a one off bet. One other thing: it has always bothered me that people should have a 'like or dislike of risk.' Something about the concept doesn't sit right with me, unless we're talking about having an adrenaline rush. That's why I liked the Kelly criterion - it takes all notion of personal preference out of the picture and gives you a universal formula.
- eru 12y agoThe Kelly criterion is actually pretty simple. So it can actually be derived from a few different optimization criteria. Risk aversion is just something we see in practice. (And sometimes risk loving; like when people play the lottery and even take a negative expected value in exchange for a very small probability of a huge win.)
- thanatropism 12y agoIt's not that there's a like or dislike of risk. Preference orderings are either (locally) convex or concave. Risk aversion is just that, a preference ordering over mean/variance bundles. There was an econ textbook that gave a memorable example of a (qualified) exception to convexity: ice-cream and olives. Usually I'll want to have ice cream and olives in my fridge, but I don't want them at once! - so pure ice-cream would be prefered to a mix of them at my plate, right now. Risk aversion does not imply, on its own, that you don't want risk at all. It implies that you want some mix of risky and non-risky assets; while concavity towards risk would imply you want either one or the other. The problem with making risk aversion/convexity work with lotteries and such is that the price you're supposed to pay for lotteries is off your utility surface. But: since lottery tickets and small bets are relatively small in the context of your budget, one can figure that the mispricing in your overall mean/variance bundle is small, and that the emotion of betting may be the case of not wanting to optimize for a grey wall, an optimal mixture. Finally, re: universal formulae, I think you'd profit from reading Elie Ayache's _The Blank Swan_.
- Tycho 12y agoBut... why should anyone have a different 'preference' from another person? Thanks for the book recommendation.
- danieltillett 12y agoUnless this bet is the last one the author ever makes then the Kelly criterion will still apply.