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Let's create a basic model for Pick 3's positional filters that considers frequency at each position, with a weighting that combines linear and logarithmic aspects of frequency.
### Step 1: Collect Historical Positional Frequency
Assume that for each position (1st, 2nd, 3rd) we have the frequency of occurrence of each number (0-9). Example:
| Number | Freq. Pos. 1 | Freq. Pos. 2 | Freq. Pos. 3 |
|--------|--------------|--------------|--------------|
| 0 | 12% | 9% | 10% |
| 1 | 8% | 11% | 7% |
| … | … | … | … |
| 9 | 10% | 12% | 15% |
### Step 2: Define Frequency Transformation
Let's combine linear and logarithmic transformations as follows:
$$
F_{adjusted} = \alpha \times F_{linear} + (1 - \alpha) \times \log(1 + F_{linear})
$$
- $$F_{linear}$$ = raw frequency (as a decimal, e.g., 0.12)
- $$\log$$ is the natural logarithm (base $$e$$)
- $$\alpha$$ is a weight between 0 and 1 that regulates how linear (closer to 1) or logarithmic (closer to 0) the filter is.
### Step 3: Create Filter
- Define an acceptable range for $$F_{adjusted}$$ (minimum and maximum).
- When generating combinations, for each number in the position, check if the adjusted function ($$F_{ajustada}$$) of the number in that position is within this range.
- Only accept combinations where all numbers in their positions respect these limits.
Practical Example (pseudocode)
```
alpha = 0.5 # intermediate weight
min_freq = 0.05
max_freq = 0.20
for each number pos in (1,2,3):
for each number n in (0..9):
f_linear = freq_pos[n][pos]
f_adjusted = alpha * f_linear + (1 - alpha) * ln(1 + f_linear)
store f_adjusted in freq_adjusted[n][pos]
for each combination (x,y,z) in 000..999:
if freq_adjusted[x][1] between min_freq and max_freq AND
freq_adjusted[y][2] between min_freq and max_freq AND
freq_adjusted[z][3] between min_freq and max_freq:
accept combination
otherwise:
reject combination
``