civdiv Posted January 23, 2022 Share Posted January 23, 2022 Many have likely heard of it. You are on a game show. There are three curtains and behind one, there is a prize you win if you select the right curtain. You pick one of the curtains and before the host reveals what is behind it, he opens another curtain and it is empty. The host then gives you the chance to change your pick. Does changing your pick change your odds of winning? 0 Quote Link to comment Share on other sites More sharing options...
dbsapp Posted January 23, 2022 Share Posted January 23, 2022 Yes. Quantum mechanics. 0 Quote Link to comment Share on other sites More sharing options...
civdiv Posted January 23, 2022 Author Share Posted January 23, 2022 Oops, posted in the wrong forum, sorry! 0 Quote Link to comment Share on other sites More sharing options...
BornGinger Posted January 23, 2022 Share Posted January 23, 2022 44 minutes ago, civdiv said: Does changing your pick change your odds of winning? Oops, posted in the wrong forum, sorry! Not necessarily the wrong forum. If there was the possibility to buy a game from the Battlefront website and then, if one realised it was another game one wanted, there was the possibility to swap the game already payed for to get another one instead, your question would still be valid. Would the other game that one swapped actually be better or more fun that the one originally paid for? So would changing your choice of game by swapping change your odds of feeling that you picked the correct one or would you regret the swap? 0 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 (edited) 1 hour ago, civdiv said: Does changing your pick change your odds of winning? No. Edited January 23, 2022 by Sgt.Squarehead 0 Quote Link to comment Share on other sites More sharing options...
civdiv Posted January 23, 2022 Author Share Posted January 23, 2022 22 minutes ago, BornGinger said: Not necessarily the wrong forum. If there was the possibility to buy a game from the Battlefront website and then, if one realised it was another game one wanted, there was the possibility to swap the game already payed for to get another one instead, your question would still be valid. Would the other game that one swapped actually be better or more fun that the one originally paid for? So would changing your choice of game by swapping change your odds of feeling that you picked the correct one or would you regret the swap? Ok, let’s make it relevant. BF hosts a giveaway and the winner get a chance to win CM:WWI with Engine 5. There are three curtains, and you get to pick one, and if a copy of the game is behind the curtain, you win it. So you pick a curtain without opening it. Steve opens another curtain revealing nothing behind it. Steve then gives you the chance of changing your pick. Does changing your pick change your chances of winning a coveted copy of CM:WWI? 0 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 Still no. At that point it's fifty fifty. 0 Quote Link to comment Share on other sites More sharing options...
civdiv Posted January 23, 2022 Author Share Posted January 23, 2022 15 minutes ago, Sgt.Squarehead said: Still no. At that point it's fifty fifty. You are wrong as I was when first faced by this one. I had to write it out in a table and my mind still hasn’t quite wrapped itself around this. 0 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 (edited) There are two choices remaining, you can choose either.....That's fifty fifty. Unless you are asking if the new situation changes your probability of winniong re: the original state of play, in which case it does, it changes from 33.3r% to 50%. Edited January 23, 2022 by Sgt.Squarehead 0 Quote Link to comment Share on other sites More sharing options...
civdiv Posted January 23, 2022 Author Share Posted January 23, 2022 2 minutes ago, Sgt.Squarehead said: There are two choices remaining, you can choose either.....That's fifty fifty. Unless you are asking if the new situation changes you probability of winniong re:the original state of play, in which case it does, it changes from 33.3r% to 50%. 4 minutes ago, Sgt.Squarehead said: There are two choices remaining, you can choose either.....That's fifty fifty. Unless you are asking if the new situation changes you probability of winniong re:the original state of play, in which case it does, it changes from 33.3r% to 50%. If you switch your choice your chance of winning rises to 67%. 0 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 (edited) Just now, civdiv said: If you switch your choice your chance of winning rises to 67%. No it does not.....I explained it above. Edited January 23, 2022 by Sgt.Squarehead 0 Quote Link to comment Share on other sites More sharing options...
civdiv Posted January 23, 2022 Author Share Posted January 23, 2022 If you change your choice your chances of winning rises to 67%. 0 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 Nope. Constantly repeating idiocy doesn't make it correct, it makes you an idiot. 0 Quote Link to comment Share on other sites More sharing options...
civdiv Posted January 23, 2022 Author Share Posted January 23, 2022 Just now, Sgt.Squarehead said: Nope. Constantly repeating idiocy doesn't make it correct, it makes you an idiot. Ok, let me put it this way. If you switch your choice the only way you lose is if you originally picked the right curtain (33%). If you picked the wrong window at first (67%), when you switch your choice you win 67% of the time. If you do not switch your choice you win 33% of the time. 0 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 (edited) Nope, logical fallacy. Two boxes, pick either, that's fifty fifty. PS - Do you want to play some poker? Edited January 23, 2022 by Sgt.Squarehead 0 Quote Link to comment Share on other sites More sharing options...
civdiv Posted January 23, 2022 Author Share Posted January 23, 2022 (edited) 3 minutes ago, Sgt.Squarehead said: Nope, logical fallacy. Two boxes, pick either, that's fifty fifty. Sorry Sgt, this is called ‘The Monty Hall Problem’ and is fairly famous. Wiki has an article on it. Lots of PhDs wrote scathing letters saying the solution was wrong. One had to watch a computer do this problem thousands of times before he admitted he was wrong. The bottom line is that if you switch your choice the only way you lose is if you originally picked the right curtain, which you have a 33% chance of doing. Edited January 23, 2022 by civdiv 4 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 (edited) Mathematical Bollocks.....Pick a poker site! Edited January 23, 2022 by Sgt.Squarehead 0 Quote Link to comment Share on other sites More sharing options...
Suchy Posted January 23, 2022 Share Posted January 23, 2022 @Sgt.Squarehead This is a well-known mathematical problem. The solution is also perfectly known. civdiv is right although intuition suggests otherwise. But strict probability calculus is absolute. Don't forget that the knowledge of the person opening the curtains and knowing from the beginning what is behind each curtain also comes into play. This person opens one of them because he knows beforehand that it is empty. 2 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 (edited) Which essentially reduces the question to a fifty fifty choice....The initial three boxes become irrelevant. Surely at that point the probabilities are reset? Edited January 23, 2022 by Sgt.Squarehead 0 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 Just been reading through the Wiki article 5 minutes ago, Sgt.Squarehead said: Pigeons repeatedly exposed to the problem show that they rapidly learn to always switch, unlike humans. I'll play those b******s at poker any time too! (Excuse my dubious quoting once again) 0 Quote Link to comment Share on other sites More sharing options...
civdiv Posted January 23, 2022 Author Share Posted January 23, 2022 5 minutes ago, Sgt.Squarehead said: Which essentially reduces the question to a fifty fifty choice....The initial three boxes become irrelevant. Surely at that point the probabilities are reset? Sgt, when I was first faced with this problem I was as stubborn as you were on it being 50/50. 0 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 I'm still reading.....& as yet unconvinced. 0 Quote Link to comment Share on other sites More sharing options...
dbsapp Posted January 23, 2022 Share Posted January 23, 2022 Fact of observation changes the observed object. 1 Quote Link to comment Share on other sites More sharing options...
Sgt.Squarehead Posted January 23, 2022 Share Posted January 23, 2022 11 minutes ago, dbsapp said: Fact of observation changes the observed object. It appears that the quantum variant of this conundrum is even stranger: 15 minutes ago, Sgt.Squarehead said: Quantum version A quantum version of the paradox illustrates some points about the relation between classical or non-quantum information and quantum information, as encoded in the states of quantum mechanical systems. The formulation is loosely based on quantum game theory. The three doors are replaced by a quantum system allowing three alternatives; opening a door and looking behind it is translated as making a particular measurement. The rules can be stated in this language, and once again the choice for the player is to stick with the initial choice, or change to another "orthogonal" option. The latter strategy turns out to double the chances, just as in the classical case. However, if the show host has not randomized the position of the prize in a fully quantum mechanical way, the player can do even better, and can sometimes even win the prize with certainty.[65][66] 0 Quote Link to comment Share on other sites More sharing options...
civdiv Posted January 23, 2022 Author Share Posted January 23, 2022 The simplest way I can explain it is that with your first choice you have a 33% of picking the right curtain, so the chance is 67% you are wrong. Since your choice is now binary, changing your choice flips the odds. So you aren’t flipping 50/50, you are flipping 33/67. 1 Quote Link to comment Share on other sites More sharing options...
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