Applied Ultrafinitism OR Amending a Forgotten Parameter
December 14, 2011 11:33 PM Subscribe
posted by jeffburdges (3 comments total)
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, E. Georgiadis, D. Zeilberger
. "How to Gamble If You're In a Hurry." arXiv:1112.1645v1
), 7 Dec 2011."The beautiful theory of statistical gambling, started by Dubins and Savage and continued by Kelly and Breiman has mostly been studied under the unrealistic assumption that we live in a continuous world, that money is indefinitely divisible, and that our life is indefinitely long. Here we study these fascinating problems from a purely discrete, finitistic, and computational viewpoint, using both symbol-crunching and number-crunching."
In short, Georgiadis and Zeilberger amend the Kelly criterion
with a bound on the time spent in the casino, providing a dynamical programming algorithm for computing optimal bets, but designing this algorithm gets tricky.
If you aren't up for the mathematics, you might still find the differing conclusion on page six of the article's pdf
amusing, ditto Zeilberger's opinions
A few paradoxes to which Zeilberger
alludes in the BBC Horizon excerpt
include the Borel–Kolmogorov paradox
, the Banach–Tarski paradox
, the Hausdorff paradox
, or really any
modern paradoxes. All these paradoxes have infinitary resolutions considered satisfactory by virtually all mathematicians, but that doesn't preclude stranger resolutions, such as simply rejecting them through finitism.