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Message: <blockquote data-quote="jerichothebard" data-source="post: 1695812" data-attributes="member: 4705">See, right there is the flaw in your reasoning.  There aren't three eggs to choose from.  You didn't get what I'm trying to say a bit later - that there are only two real choices now. well, there are two viable eggs, one of which is a winner.  That's 1/2Wrong.  There aren't three choices, and you don't have 2 of them anymore.  You have one, out of two.Results attached.You're right that there is information gained when the egg is smashed.  That information is:"This egg is not a winner".You do NOT tell me that the odds of your egg being the winner are 2/3 - why?  Because there aren't 3 eggs in the game anymore, and you don't have 2 eggs anymore.  You have 1.  Out of 2.I don't know how to make it any more simple.2 eggs. 1 winner. 1 choice.  50% chance.When we started the game, each egg has an equal chance of being the winner.  That doesn't change because one egg is removed.  The 1 in 100 or 1000000 game as described is a fundamentally different game.Here's why.When you smash the egg, you are removing one egg from the game.  You are not reducing the choices to two, you are removing one egg.  The fact that this reduces the choices to 2 only happens to be a coincidence of the starting number.The only way these are the same game is if you reduce the number by one in each game.  In which case, the chances of being right = 1/2 or 1/99.In the game Monty Haul played on TV, each choice has an equal chance of being right.  No matter how many choices, as long as there is only a reduction of 1 choice at a time, the odds are equal to the number of choices.You are right that there is information gained if more than one choice is removed at once - because that is a fundamentally different game than the game we are talking about, where you remove one at a time.  basically, he says, "here are 99 more guesses, and all of them are right."  He packages all the losing guesses together with the win, which multiplies your odds of winning by switching by 99 times." It's now a game with 99 right choices and one wrong choice.You'd be stupid NOT to switch, because Monty gave away the game.Imagine you start with three choices, and Monty removes two!  That's a lot of information!  However, if you were to play the game with 100 doors, and Monty just keeps removing one door at a time and letting you guess all the way down to two doors, the answer still won't change! Your chance of winning = 1/2.Back to the original question:Imagine it with four choices, for a more clear example.Four Doors.  I choose #2.Monty removes #1.What's left?#2, #3, #4.What should I do?  switch?  stay?  It doesn't matter.  Each door has a 1/3 chance of winning!  Three doors.  One winner.  One choice.See how the game doesn't matter until the second round?  No matter what, the first bit of information isn't information at all - it's meaningless!  It's just for excitement and drama.Imagine if they only started with two doors.  No drama, just a simple coin toss.  BOOR-RING!  But by performing the sleight of hand with the two choices, they turn a simple coin toss into good *ahem* TV.jtb</blockquote>

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