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====== Forex - Probability ======

Trading is thinking in probabilities and finding setups that make money.

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===== Positive Expectancy =====

  * You may not make money on the trade right now, or even the next one, but if it makes money over the long run (has positive expectancy).

  * You could have a system which is 35% accurate which still makes money (and a lot of it) over time.

  * Get comfortable with uncertainty, and comfortable with losses (which are inevitable), then you will find yourself making good decisions more often than not.

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===== Probability =====


<code>
                Profitable Trades
probability =  -------------------
                 Total Trades 
</code>

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===== Example =====

Suppose that you have made nine trades, six of which turned out to be profitable. 

<code>
                 6
probability =  -----  =  67
                 9
</code>

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What is the probability of winning for a future trade? 

  * The denominator of the fraction will increase by one for any outcome. 
  * But with the numerator, two options are possible - a future transaction may turn out to be either profitable, or unprofitable. 
    * In other words, we have two possible options:

<code>
                (6+1)            6
probability =  -------   or   -------
                (9+1)          (9+1)
</code>


Using the average of these values, has the estimate of the probability of winning as follows:

<code>
                 6 + 0.5
probability =  ----------  =  0.65
                  9 + 1
</code>


<WRAP info>
**NOTE**: This is slightly less than the original value of 6/9.

  * This method is called Laplace smoothing. 

</WRAP>


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===== Smoothing using Weights =====

<code c++>
double value=price[i+center], // Price value at the center.
       max=_Point;            // Maximum deviation.

for(int j=0; j<period; j++)   //Calculate price deviations from the central one and the max deviation.
{
  weight[j]=MathAbs(value-price[i+j]);
  max=MathMax(max, weight[j]);
}

double width=(period+1)*max/period,  // Correct the maximum deviation from the center so that there are no zeros at the ends.
sum=0,
denom=0;

for(int j=0; j<period; j++)  // Calculate weight ratios for each price.
{
  if (Smoothing==Linear)  // Linear smoothing.
    weight[j]=1-weight[j]/width;

  if (Smoothing==Quadratic)  // Quadratic smoothing.
    weight[j]=1-MathPow(weight[j]/width, 2);
 
  if (Smoothing==Exponential)  // Exponential smoothing.
    weight[j]=MathExp(-weight[j]/width);

  sum=sum+weight[j]*price[i+j];
  denom=denom+weight[j];
}

buffer[i]=sum/denom;  // Indicator value.
</code>

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===== References =====

https://www.mql5.com/en/articles/11627