Monty Hall Door Switching Problem

[Frotz]

I think there should be a quest with the classic game of picking one of three doors, one of the other two doors being opened to reveal nothing, and then being given a choice to switch your pick to the one remaining non-picked, non-opened door.
I would love to have endless debates in chat over whether you should change your choice of door or not. Really, that would be fun. So much fun I can't think of anything I'd like to do more of. For all eternity.

P.S. Yes, this has been post frustrating argument rant. But actually, might be nice in a quest as long as I can get to the right door before someone else gets to the wrong door.

[Memnir]

.
.
.

.
.
.
Oh, how I miss DragonMirth...

[ssgcmwatson]

[InsanityIsYourFriend]

make it do a shroud end portal without the res if they get it wrong!

[Krelar]

make it do a shroud end portal without the res if they get it wrong!

So your saying that even if you use the correct strategy for choosing you want to lose 1/3 of the time?

[Psiandron]

Isn't this the Ascension Chamber?

[sebastianosmith]

I would love to have endless debates in chat over whether you should change your choice of door or not.

Always, always pick the other door. Doing so doubles your chances of winning.

[Krelar]

Always, always pick the other door. Doing so doubles your chances of winning.

Provided you are working under a certain set of conditions.

[sebastianosmith]

Provided you are working under a certain set of conditions.

Given the conditions set by the OP:

I think there should be a quest with the classic game of picking one of three doors, one of the other two doors being opened to reveal nothing, and then being given a choice to switch your pick to the one remaining non-picked, non-opened door.

I feel safe in my assertion.

[yawumpus]

Always, always pick the other door. Doing so doubles your chances of winning.

original chance of winning =1/3 (33%)
chance of winning after switching = 1/2 (50%)

Amount of increase = .5/.3 = 50%

Thus, it increases the odds of wining by 50%, not doubles. Still, you should always switch.

To OP, this sounds like an ideal time to begin wagering. Set up something that looks like a shell game (hide something under one of three cups) and wager away. You may have to do some type of back and forth deal where each of you plays, as people who can't handle this paradox are unlikely to wager reasonable odds.

[Krelar]

Given the conditions set by the OP:

I feel safe in my assertion.

He says one of the doors is opened to reveal nothing, we need information about how that door is chosen to make a decision.

[Krelar]

original chance of winning =1/3 (33%)
chance of winning after switching = 1/2 (50%)

Amount of increase = .5/.3 = 50%

Thus, it increases the odds of wining by 50%, not doubles. Still, you should always switch.

In the classic problem your chance of winning actually goes up to 2/3 if you switch

[twiliteslayer02]

Never, ever touch a gagglezoomers back!

[Frotz]

Provided you are working under a certain set of conditions.

Hmm, yes, in addition to having people argue that it's 50/50 after a door has been opened, we could have people arguing over whether the scripting/RNG is cheating. Whee.

And yes, I was assuming that the prize is placed before any decisions are made and remains where it is placed for the whole game; and that one of the doors is always opened after the initial choice, that opened door will never reveal the prize and is never the one the contestant has chosen.

[Vordax]

original chance of winning =1/3 (33%)
chance of winning after switching = 1/2 (50%)

Actually its:
original chance of winning =1/3 (33%)
chance of winning after switching = 2/3 (66%)

Amount of increase = .5/.3 = 50%
.5/.3 = 1.66

Read the wikipedia article, it explains it quite well your chances double to 66% if you switch.

Vordax

[Krelar]

Hmm, yes, in addition to having people argue that it's 50/50 after a door has been opened, we could have people arguing over whether the scripting/RNG is cheating. Whee.

And yes, I was assuming that the prize is placed before any decisions are made and remains where it is placed for the whole game; and that one of the doors is always opened after the initial choice, that opened door will never reveal the prize and is never the one the contestant has chosen.

You also have to assume that if the contestant chooses correctly (but of course doesn't know it yet) the first time then the opened door is randomly chosen between the two remaining. (If there is any bias in how the door is chosen in this case it will affect the probability, this also brings in the comment above about how people will start arguing over whether the random number generator is cheating or not)

[danotmano1998]

I think there should be a quest with the classic game of picking one of three doors, one of the other two doors being opened to reveal nothing, and then being given a choice to switch your pick to the one remaining non-picked, non-opened door.
I would love to have endless debates in chat over whether you should change your choice of door or not. Really, that would be fun. So much fun I can't think of anything I'd like to do more of. For all eternity.

P.S. Yes, this has been post frustrating argument rant. But actually, might be nice in a quest as long as I can get to the right door before someone else gets to the wrong door.

Meh,

It's been definitively proved by mythbusters already.

The recent episode of MythBusters featured four fan-submitted myths, one of which was perennial fave The Monty Hall problem.

I was impressed with the way they handled it. They divided it into two problems: first, that there is a strong psychological impulse to stick with your initial choice (assuming you aren't aware of the true probabilities) and second that switching is always a better bet (which it is.)

For the first, they had a horde of 20 volunteers play "pick a door" on a genuine three-door game show stage, with Jamie randomly resetting the prize door and Adam being Monty Hall and offering the switch. Every one of the 20 chose to stick!

For the second, they built a very clever door-picking-game simulator in which Adam and Jamie played 100 games, with Jamie always sticking and Adam always switching. Naturally, the results indicated that switching was a vastly superior strategy.

quoted from Here. Normally I wouldn't take a forum post as truth, but I actually watched the show.