  Prompted by a recent experiment by Victor Haghani and Richard Dewey, this
note generalises the Kelly strategy (optimal for simple investment games with
log utility) to a large class of practical utility functions and including the
effect of extraneous wealth.
  A counterintuitive result is proved : for any continuous, concave,
differentiable utility function, the optimal choice at every point depends only
on the probability of reaching that point.
  The practical calculation of the optimal action at every stage is made
possible through use of the binomial expansion, reducing the problem size from
exponential to quadratic.
  Applications include (better) automatic investing and risk taking under
uncertainty.
