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<blockquote data-quote="Lonely Tylenol" data-source="post: 1728502" data-attributes="member: 18549">The thread of THE DARK SPEECHA lot of people run up against that difficulty, but it's actually pretty simple.[SPOILER]The thing is, that a randomly selecting player will in fact get the right answer 50% of the time.&nbsp; But that assumes a randomly selecting player, which is not what we're assuming here.Look at it this way.&nbsp; When you choose a door, there's a 1/3 chance you chose the right door, and a 2/3 chance it was one of the other doors.&nbsp; When Monty reveals one of the doors, that doesn't change any probabilities.&nbsp; It's still a 2/3 chance that it was one of the other doors, and a 1/3 chance it's your door.&nbsp; Only now you have an extra bit of information that you didn't have to begin with.&nbsp; You know that it wasn't a certain door.&nbsp; You're still picking from three doors, but you're &quot;cheating&quot; because you know one of the doors isn't the prize.&nbsp; No matter what, you know that the chance that Monty's doors contain the prize are 2/3.&nbsp; Let's say a second contestant came on, who hadn't seen which door had been revealed.&nbsp; He knows that you picked a door, and that Monty still had two doors.&nbsp; We ask him, &quot;what's the chance that the prize is still behind one of Monty's doors?&quot;&nbsp; He will say &quot;2/3.&quot;&nbsp; Because Monty has two doors and you have one and the prize was randomly placed, regardless of what you know about Monty's doors.Anyway, if you pick randomly, you'll win 50% of the time.&nbsp; But you will win 66% of the time if you switch every time you play.The other thread had a very good example (a bit messed up on first writing due to a missing line) involving eggs.&nbsp; But the fact of the matter is that my argument is supported by not only a solid mathematical proof, but also empirical evidence.&nbsp; The link I posted above has both.[/SPOILER]</blockquote>

[QUOTE="Lonely Tylenol, post: 1728502, member: 18549"] [b]The thread of THE DARK SPEECH[/b] A lot of people run up against that difficulty, but it's actually pretty simple. [SPOILER]The thing is, that a randomly selecting player will in fact get the right answer 50% of the time. But that assumes a [i]randomly selecting player[/i], which is not what we're assuming here. Look at it this way. When you choose a door, there's a 1/3 chance you chose the right door, and a 2/3 chance it was one of the other doors. When Monty reveals one of the doors, that doesn't change any probabilities. It's still a 2/3 chance that it was one of the other doors, and a 1/3 chance it's your door. Only now you have an extra bit of information that you didn't have to begin with. You know that it wasn't a certain door. You're still picking from three doors, but you're "cheating" because you know one of the doors isn't the prize. No matter what, you know that the chance that Monty's doors contain the prize are 2/3. Let's say a second contestant came on, who hadn't seen which door had been revealed. He knows that you picked a door, and that Monty still had two doors. We ask him, "what's the chance that the prize is still behind one of Monty's doors?" He will say "2/3." Because Monty has two doors and you have one and the prize was randomly placed, regardless of what you know about Monty's doors. Anyway, if you pick randomly, you'll win 50% of the time. But you will win 66% of the time if you switch every time you play. The other thread had a very good example (a bit messed up on first writing due to a missing line) involving eggs. But the fact of the matter is that my argument is supported by not only a solid mathematical proof, but also empirical evidence. The link I posted above has both.[/SPOILER] [/QUOTE]

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