Optimal betting

#1
For Kelly betting in blackjack we can define the optimal size of our unit bet as fB where B is our bankroll and f = (advantage of the game) / (variance of the game).

But, if f is a fraction, how can it be that we get it dividing "units of bet" (advantage) by "units of bet" squared (variance)? If so, the unit of f should be 1/"units of bet" but it happens that f is a fraction.

Can anyone explain this?

Thanks,

BJFan
 
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