4 ms·

When you look at it the right way, the solution to the Monty Hall problem is actually straight forward and doesn't require a simulation. If you choose the "no

When you look at it the right way, the solution to the Monty Hall problem is actually straight forward and doesn't require a simulation. If you choose the "no switching" strategy, you're probability of winning is 1/3. On the other hand, if you use the "switching" strategy, you win if you pick a goat at first and you loose if you pick the car at first. Thus, with the "switching" strategy, your probability of winning is 2/3. So once you recognize that with the "switching" strategy you win if and only if you start on a goat, the only thing you're really doing with a simulation is to contribute to the carbon footprint of the world. Without that realization, a simulation can be helpful, of course, since finding the right way to look at a problem is often so hard.

phailhaus 2y ago
The Monty Hall problem is confusing because the three-door case is the only time that the host opens just one door. It looks like a coin flip. If you ask the question with 100 doors, where the host goes and opens 98 other doors, the answer is obvious!
kqr 2y ago
Everything is straight forward when you look at it through the right abstractions. That's the point of abstraction. Simulation can be useful when you don't know what the right abstraction is, which is the problem most people have with Monty Hall -- this is the point I got from TFA. I disagree with the TFA that you need "a PhD in queueing theory" to know what the right abstractions are, but it's still beyond most people because we are still woefully statistically illiterate as a species. I could probably also solve that shard replica problem analytically -- or at least recursively (it sounds like a variant of coupon collection) -- but I'd still want to confirm my calculations by writing a simulation.
bsder 2y ago
The tricky part to explain about the Monty Hall problem is that there is extra information after the host opens the door. Because you picked a door, the choice the host had of which door to open is sometimes constrained and that gives you extra information as well. Everybody tries to do it solely with probabilities, which is fine, but it becomes far more intuitive when you point out the extra information.

phailhaus 2y ago

The Monty Hall problem is confusing because the three-door case is the only time that the host opens just one door. It looks like a coin flip. If you ask the question with 100 doors, where the host goes and opens 98 other doors, the answer is obvious!

kqr 2y ago

Everything is straight forward when you look at it through the right abstractions. That's the point of abstraction. Simulation can be useful when you don't know what the right abstraction is, which is the problem most people have with Monty Hall -- this is the point I got from TFA. I disagree with the TFA that you need "a PhD in queueing theory" to know what the right abstractions are, but it's still beyond most people because we are still woefully statistically illiterate as a species. I could probably also solve that shard replica problem analytically -- or at least recursively (it sounds like a variant of coupon collection) -- but I'd still want to confirm my calculations by writing a simulation.

bsder 2y ago

The tricky part to explain about the Monty Hall problem is that there is extra information after the host opens the door. Because you picked a door, the choice the host had of which door to open is sometimes constrained and that gives you extra information as well. Everybody tries to do it solely with probabilities, which is fine, but it becomes far more intuitive when you point out the extra information.