And what is a monty haul?
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
It's called the Monty Hall problem. If you keep the same choice, you have a 1/3 chance of winning. If you switch your choice, you have 2/3 chance of winning, doubling your probability. It is important to note that the host always opens one of the doors with a goat behind them.
The intuitive answer is that both doors have a 50% chance of winning and a lot of people can't see any other interpretation. However, you have to think of the doors as sets instead of individual doors.
In the classic three door version, think of two sets A = {doors selected} and B = {doors not selected}. Set A contains one door, the one originally picked and set B has the remaining two doors, so the probability of set A of containing the winning door is 1/3 and the probability of set B of containing the winning door is 2/3.
Next, the host gives you free information, telling you that one of the doors in set B is not the winning door. But there as still two doors in set B, except that you know for certain that one of them does not contain the prize. Sets A and B retain their probabilities, so it is in the player's advantage to switch their initial choice to the remaining door in set B.
In the context of RPG's, Monty
Haul refers to giving players excessive loot (that they need to haul) for doing trivial tasks, like on a game show.
