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First of all, Kelly had a betting scenario in mind when he came up with his fixed fraction betting idea. In betting you can lose no more than how much you bet. In the betting scenario, if you use the Kelly criterion correctly you cannot blow up. This is how it works: You define an initial...

Here's a writeup I did some time ago: http://mayer.pro/documents, have a look at the section "Gambles that are offered with lower frequency" of the online document "The Kelly criterion and fixed fraction betting". The way I looked at it back then was to assume a 'betting frequency', i.e. per...