Halt with 50% non-Halting

Perl

fork || do {sleep(1) while(1)}

Each time you run this program, it halts and doesn't halt.

Python

import random
p=.3078458
while random.random()>=p:p/=2

Each time around the loop it breaks with exponentially decreasing probability. The chance of never breaking is the product \$(1-p)(1-\frac{p}{2})(1-\frac{p}{4})...\$ which is \$\frac{1}{2}\$. (Obligatory comment about floating point not being exact.)

JavaScript

Alternatives halting and not halting. (halts on first run, doesn't halt on second, ...)

var h = localStorage.halt;
while (h) localStorage.halt = false;
localStorage.halt = true;