Let’s say each round there’s a 50 percent probability of adding an extra bullet to the gun.
If I didn’t update based on the fact I’m still playing then I would quickly stop after a few rounds, since the probability I would see a bullet constantly increases.
But if I do update, then it’s worth it carrying on, since the fact I’m still playing is evidence there still are plenty of empty chambers.
To give a concrete counterexample.
Let’s say each round there’s a 50 percent probability of adding an extra bullet to the gun.
If I didn’t update based on the fact I’m still playing then I would quickly stop after a few rounds, since the probability I would see a bullet constantly increases.
But if I do update, then it’s worth it carrying on, since the fact I’m still playing is evidence there still are plenty of empty chambers.