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<blockquote data-quote="Pielorinho" data-source="post: 1694815" data-attributes="member: 259">&nbsp;THAT'S RIGHT!&nbsp;Stop right there.&nbsp;Now, we have one more step.&nbsp; I'm Monty, and you're the guesser.&nbsp; You know, since you just told me this, that I have a 2/3 chance of having the full egg in my hand.&nbsp; Now I give you a chance to change your mind, to choose any of the three eggs.&nbsp;You can choose the egg on the table.&nbsp; What's the chance that that's the right egg?&nbsp;You can choose BOTH eggs in my hand, and if EITHER of them is right, then we'll proceed to the endgame.&nbsp; You just told me what the chances were that I was still holding the correct egg--what was it you said?&nbsp; 2/3, right?&nbsp;Okay, so let's say you choose &quot;the eggs in your hands&quot; over &quot;the eggs on the table.&quot;&nbsp; 2/3 of the time, that'll be the right choice, right?&nbsp;If you're right, then I'll ask you the endgame question:&nbsp; of the two eggs in my hand, which one is the right one:&nbsp; the smashed one, or the whole one?&nbsp;I'm going to assume that you'll choose the whole one 100% of the time, since obviously the smashed on isn't right.&nbsp; That means 2/3 of the time, you'll win!&nbsp;As for your playing the game and being right 50% of the time, that baffles me.&nbsp; Do me a favor, wouldja?&nbsp; Play the game 30 times.&nbsp; Each time, choose 1 as your first guess, and then switch to the other one as your second guess.&nbsp; Tell me what you end up with.&nbsp; (I just went back to the game to verify my results and got an error).&nbsp;Daniel</blockquote>

[QUOTE="Pielorinho, post: 1694815, member: 259"] [i][/i] [i]THAT'S RIGHT![/i] Stop right there. Now, we have one more step. [i]I'm Monty[/i], and you're the guesser. You know, since you just told me this, that I have a 2/3 chance of having the full egg in my hand. Now I give you a chance to change your mind, to choose any of the three eggs. You can choose the egg on the table. What's the chance that that's the right egg? You can choose BOTH eggs in my hand, and if EITHER of them is right, then we'll proceed to the endgame. You just told me what the chances were that I was still holding the correct egg--what was it you said? 2/3, right? Okay, so let's say you choose "the eggs in your hands" over "the eggs on the table." 2/3 of the time, that'll be the right choice, right? If you're right, then I'll ask you the endgame question: of the two eggs in my hand, which one is the right one: the smashed one, or the whole one? I'm going to assume that you'll choose the whole one 100% of the time, since obviously the smashed on isn't right. That means 2/3 of the time, you'll win! As for your playing the game and being right 50% of the time, that baffles me. Do me a favor, wouldja? Play the game 30 times. Each time, choose 1 as your first guess, and then switch to the other one as your second guess. Tell me what you end up with. (I just went back to the game to verify my results and got an error). Daniel [/QUOTE]

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