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The Kelly Criterion is the most well-known, simple and practical formula in the world the gambling and speculation. It determines the most optimal bet size according to the win-loss and reward-risk ratios of a betting system. The formula is given by:
K = W - (1 - W) / R
Where:
W = winning probability
R = reward-to-risk in each trade
For example, if your system risks one dollar to win every two dollar, and your hit rate is 40%, then you should bet:
K = 40% x 60%/2 = 12%
So, you should risk 12% of your stake each time you bet.
Here is a tabulated result of different W and R:
To determine how many contracts or shares to trade, simply calculate it by:
Position Size = P x K / L
Where:
P = Principal amount
K = Kelly %
L = Stop loss distance
Round down the answer to the nearest integer / contract size.
In addition, if you substitute K with 0, then:
0 = W - (1 - W) / R
W = 1/R - W/R
(1 + 1/R) W = 1/R
W = 1/[R(1 + 1/R)] = 1/(R+1)
This is the minimum win rate given a particular ratio. For instance, if you have a system of risking one dollar to win two, which is the minimum win rate required to break even?
W = 1 / (2+1) = 33.33%
So, you system must win as least 33% of the time.
Here is another tabulated result of the minimum win rate:
By the way, if you want to go one step further, you can visit this page to see the more complicated to determine the Kelly criterion when there is more than one outcome.
K = W - (1 - W) / R
Where:
W = winning probability
R = reward-to-risk in each trade
For example, if your system risks one dollar to win every two dollar, and your hit rate is 40%, then you should bet:
K = 40% x 60%/2 = 12%
So, you should risk 12% of your stake each time you bet.
Here is a tabulated result of different W and R:
To determine how many contracts or shares to trade, simply calculate it by:
Position Size = P x K / L
Where:
P = Principal amount
K = Kelly %
L = Stop loss distance
Round down the answer to the nearest integer / contract size.
In addition, if you substitute K with 0, then:
0 = W - (1 - W) / R
W = 1/R - W/R
(1 + 1/R) W = 1/R
W = 1/[R(1 + 1/R)] = 1/(R+1)
This is the minimum win rate given a particular ratio. For instance, if you have a system of risking one dollar to win two, which is the minimum win rate required to break even?
W = 1 / (2+1) = 33.33%
So, you system must win as least 33% of the time.
Here is another tabulated result of the minimum win rate:
| R | W-min |
| 1.5 | 40.00% |
| 2.0 | 33.3% |
| 2.5 | 28.57% |
| 3.0 | 25.00% |
| 3.5 | 22.22% |
| 4.0 | 20.00% |
| 4.5 | 18.18% |
| 5.0 | 16.67% |
| 5.5 | 15.38% |
By the way, if you want to go one step further, you can visit this page to see the more complicated to determine the Kelly criterion when there is more than one outcome.