Laplace

Laplace's law of succession

Suppose that every time there is an opportunity for an event to happen, then it occurs with unknown probability $p$. Laplace's law of succession states that, if before we observed any events we thought all values of $p$ were equally likely, then after observing $r$ events out of $n$ opportunities a good estimate of $p$ is $\hat{p} = (r+1)/(n+2)$.

The classical approach

Due to our ignorance about the outcome of, say, a cast die, and because there is no indication for us to think one outcome more likely than any other, we must give them all an equal probability.