May 25, 2009. Working paper. 20 pages. Paper also available at http://ssrn.com/abstract=1409843.
Proebsting's Paradox is an argument that appears to show that the betting rule known as the Kelly criterion can lead a bettor to risk an arbitrarily high proportion of his wealth on the outcome of a single event. In this paper I show that a large class of betting criteria, including fractional Kelly, also suffer from the same shortcoming and use standard tools from microeconomic theory to explain why this is so. I also derive a new criterion, dubbed the doubly conservative criterion, that is immune to the problem identified above. Immunity stems from the bettor's attitudes towards capital preservation and from him becoming rapidly pessimistic about his chances of winning the better odds he is offered.