Say I have multiple uniform random variables. I want to know the CDF for selecting the highest result of all the variables.
As an example, say I have 3 uniform random variables from [0, 100). Using a simulation, I know that ~10% of the time, the best number is going to be 47 or lower, and that 90% of the time the best result is going to be 97 or lower. But I don't know the equation for going from 10% -> 47.
The CDF of the maximum $X_{max}$ of $N$ independent and identically distributed random variables can be computed as follows $$ P(X_{max}<t)=\int^t\cdots \int^t dx_1\cdots dx_N p(x_1)\cdots p(x_N)=\left[\int^t dx p(x)\right]^N\ , $$ where $p(x)$ is the pdf of each random variable. In the case of uniform random variables between $a$ to $b$, we have $p(x)=1/(b-a)$ and $$ P(X_{max}<t)=\left[\frac{1}{b-a}\int_a^t dx\right]^N=\left[\frac{t-a}{b-a}\right]^N\ . $$ In your case, with $N=3$, $a=0$ and $b=100$, we have $$ P(X_{max}<47)=\left(\frac{47}{100}\right)^3\approx 10.38\% $$ and $$ P(X_{max}<97)=\left(\frac{97}{100}\right)^3\approx 91.26\% $$