# Some formulas

– $$\vartheta$$ is the random rotation
– $$a_i$$ is a picked value around a shared variable. The randomizer must give an uniform repartition.
– $$n$$ is an ad hoc integer parameter between $$5$$ and $$\infty$$

Probability to render 1 at each step in the polarizer :
$$p_1 = \prod_{i=1}^{n}{ cos^2(a_i-\vartheta )} ;$$

Probability to render 0 at each step in the polarizer :
$$p_2 = \prod_{i=1}^{n}{ sin^2(a_i-\vartheta )} ;$$

Probability to fail and to try again :
$$p_0 = 1.0 – p_1 – p_2 ;$$

Final probability to render 1 after the whole polarization attempt :

#### $$P_1 = \frac{p_1 p_0^{\pi^{n-2}}}{ \left(p_1+p_2\right)} ;$$

Final probability to render -1 after the whole polarization attempt :

#### $$P_{-1} = \frac{p_2 p_0^{\pi^{n-2}}}{ \left(p_1+p_2\right)} ;$$

Final probability to render 0 for an undetected particle after the whole polarization attempt :
$$P_0 = 1.0 -P_1-P_{-1} ;$$

This hack describes correctly the experiments outcomes.