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]]>Both of these are fairly complicated but here goes….
The Kelly Criterion arose from the work of John Kelly at AT&T’s Bell Labs in 1956. His original formulas dealt with long-distance telephone transmission signal noise. But the gambling community quickly understood that the same approach may help them to calculate the optimal amount to bet on a horse and the best way to take advantage of overlays and underlays, maximizing the growth of your bankroll over the long term. Nowadays, Kelly Criterion is a recognized money management system and whenever the question of optimal betting size pops up in handicapping or money management books you always see Kelly formula mentioned.
The Kelly’s formula is : Kelly % = W – (1-W)/R
where:
* Kelly% = percentage of capital to be put into a single trade
* W = Historical winning percentage of a trading system
* R = Historical Average Win/Loss ratio
The math behind the system is pretty complicated. Kelly’s original paper is all but unreadable to non math majors.
For more in-depth information about using Kelly’s value in stock trading and long term investing please read the following literature (free ebooks):
http://www.bjmath.com/bjmath/thorp/tog.htm
http://www.bjmath.com/bjmath/thorp/paper.htm
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Mathematical expecation explained (using a Roulette wheel example)
On the roulette wheel there are 36 numbers, double zero, and the blank. That makes 38 spaces to bet on. Each bet costs $1 to play. The winner pays $35. To calculate the mathematical expectation of the roulette wheel you do the following:
Multiply the probability of winning by what you win when you win. And from that, you subtract the probability of losing by the cost of each bet. The difference is the mathematical expectation. If it’s positive, it’s a fair bet. If it’s negative, you don’t play.
[(1/38) x (35)] – [(37/38) x (1)] = mathematical expectation of playing roulette.
(35/38) – (37/38) = (-2/38) or (-1/19).
So in the case of the Roulette wheel, the best bet is not to play
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