Yes, but there’s an additional thing I’d point out here, which is that at any finite timestep, Kelly does not dominate. There’s always a non-zero probability that you’ve lost every bet so far.
When you extend the limit to infinity, you run into the problem “probability zero events can’t necessarily be discounted” (though in some situations it’s fine to), which is the one you point out; but you also run into the problem “the limit of the probability distributions given by Kelly betting is not itself a probability distribution”.
Yes, but there’s an additional thing I’d point out here, which is that at any finite timestep, Kelly does not dominate. There’s always a non-zero probability that you’ve lost every bet so far.
When you extend the limit to infinity, you run into the problem “probability zero events can’t necessarily be discounted” (though in some situations it’s fine to), which is the one you point out; but you also run into the problem “the limit of the probability distributions given by Kelly betting is not itself a probability distribution”.