3 ms·
Bayes' theorem also helps clear up some of the subtleties behind the Monty Hall problem. Switching is advantageous because Monty knows which door has the prize.
by daveFNbuck 8y ago
Bayes' theorem also helps clear up some of the subtleties behind the Monty Hall problem. Switching is advantageous because Monty knows which door has the prize. If Monty doesn't know which door has the prize, seeing a non-prize door results in 50-50 odds that your door has the prize.
Depending on how you model Monty Hall's prior probability of revealing the prize, seeing a non-prize door can result in the probability anywhere between 0 and 2/3 of switching being advantageous.
- loup-vaillant 8y agoMy take on the subtleties, in painstaking details, with source code so you can reproduce my experimental results: http://loup-vaillant.fr/tutorials/monty-hall http://loup-vaillant.fr/tutorials/monty-hall I consider several kind of Monties there, including an "enemy" that will try to open the prize door if he can.
- daveFNbuck 8y agoI like your attention to detail on this! I'm a bit surprised you don't include the overall probability of winning against each Monty with an optimal strategy. I think it's very interesting that the helper doesn't increase your odds beyond 2/3.
- loup-vaillant 8y agoYeah, that and the spelling mistakes… I think I'll have another pass at this. I just re-read it, and I glossed over the numbers at times.