We all know there is no guaranteed way of beating the bank in a casino or predicting the tossing of a coin. Well maybe. Perhaps a little more thought and a large dose of mathematics could help optimise our strategies.
Oxford Mathematicians Jan Obloj and colleagues looked at the optimal strategy of a gambler with cumulative prospect theory (CPT) preferences. CPT preferences capture, in particular, the empirically observed human tendency for being risk averse while winning but being risk seeking when losing. Their research showed that the performance, even of complex betting strategies, can be strictly improved by looking at past betting patterns and by tossing an independent coin. This improvement results from the lack of quasi-convexity of CPT preferences: given two choices we may prefer a mixture of them to either of them individually.
Even better news for gamblers is that if they go through a series of hypothetical choices to determine their particular risk appetites (and hence a numerical CPT representation of their preferences), Jan and colleagues can provide an algorithmic way to compute the bias of the coins which ought to be tossed by the gambler to optimally decide when to stop playing in the casino.