Lets make a deal!

If you don't think that switching is better, try one of the many simulators out there ... try this one.

Monty Hall Simulation

I did 50 for each strategy

P(Winning if you stay) = 0.32 (16 out of 50 trials)
P(Winning if you switch) = 0.52 (26 out of 50 trials)

Do 10 or 20 or however many you want with each strategy and add to my totals here. As more people add in their totals, I think you'll become convinced that switching is better.

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Originally Posted by CloneAggie

If you don't think that switching is better, try one of the many simulators out there ... try this one.

Monty Hall Simulation

I did 50 for each strategy

P(Winning if you stay) = 0.32 (16 out of 50 trials)
P(Winning if you switch) = 0.52 (26 out of 50 trials)

Do 10 or 20 or however many you want with each strategy and add to my totals here. As more people add in their totals, I think you'll become convinced that switching is better.

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Odds don't change with results. That's stat 101.

I can flip a coin 1000 times and have it come up heads 1000.

Flip number 1001 still has a 1:2 chance of coming up tails.

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Originally Posted by DaddyMac

Look at it this way. You pick with a 1:3 chance. Box removed, you switch. The box you're holding has a 1:2 chance of winning, right?

What's the chance of the other box winning?

(hint: 1:2)

Here's another way of looking at it. You have a 1:2 chance of GIVING UP the winning box.

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No, actually you have a 1:3 chance of giving up the winning box. You're looking at the second choice while ignoring the first one. When you made the first choice you have a 1:3 chance of picking the winning box. If the host then asked if you'd like to make a switch, you'd have a 1:3 chance of giving up the winning box. Then the host does something that makes absolutely no difference to the box that's in your hand (because you already knew it) -- says there's a box on stage that doesn't win and then shows you which one it is. You still only have a 1:3 chance of having it right.

Imagine that, after picking your box, the host takes the other two boxes and combines their contents into one box. Now there are two boxes, but you still only have a 1:3 chance that the box in your hand is the winner. That's exactly what happened here.

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Originally Posted by markshir

I'm an English major so I assume I can try. Stats majors are just cheating... :)

The way I think of it is that there is a 33% chance you were right the first time, and a 66% chance you were wrong. By eliminating one of the two other choices, one assumes the probability of the other and so you should switch from your original choice.

Think of it with 100 choices. There is a 1% chance you were right. If the host took away 98 of the 99 that you didn't pick, and then asked you if you wanted to switch, of course you would. In fact, even if he took away 1 choice I think it would still be smart to switch because now you would be picking out of 99 instead of 100. I think...

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Not sure if it can be explained any better

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Originally Posted by DaddyMac

Odds don't change with results. That's stat 101.

I can flip a coin 1000 times and have it come up heads 1000.

Flip number 1001 still has a 1:2 chance of coming up tails.

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How many three sided coins do you have?:wink:

Everyone in the last half of this thread needs to take, retake or not ever acknowledge you took STAT.

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Originally Posted by DaddyMac

I haven't taken stat 331 in about 14 years now - so I don't have the textbook to show this. But it's pretty obvious.

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Umm, maybe you should retake stat...just sayin

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Originally Posted by chadm

How many three sided coins do you have?:wink:

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How many boxes are there when you are offered to switch.

You guys are WAY to hung up on the inital odds. There are only two chances at the time of the switch. One in two, 50/50.

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Originally Posted by MrGreg

Umm, maybe you should retake stat...just sayin

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I've asked the same question we are pondering to 3 other computer programmers, all have taken multiple stat courses, and not one has a problem with it.

But fine - you know so much. Explain to me WHY the box on stage has inherently better odds of winning?

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Originally Posted by cloneatlaw

No, actually you have a 1:3 chance of giving up the winning box. You're looking at the second choice while ignoring the first one.

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Why wouldn't you ignore the first choice? When there are two boxes left, Monty asks you if you want to switch boxes, but what he's really asking you is which of the two boxes you want. It's a new problem. One box has the prize, one doesn't, and he's asking you to pick which one has the prize. What you did previously is irrelevant.

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Originally Posted by DaddyMac

Everyone in the last half of this thread needs to take, retake or not ever acknowledge you took STAT.

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Can you give me back my time I spent in Stat class? I would gladly acknowledge I didn't take it if I can have some of my life back.

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Originally Posted by jbhtexas

Why wouldn't you ignore the first choice? When there are two boxes left, Monty asks you if you want to switch boxes, but what he's really asking you is which of the two boxes you want. It's a new problem. One box has the prize, one doesn't, and he's asking you to pick which one has the prize. What you did previously is irrelevant.

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I ask this again. If he didn't ask the question, do you have the same odds to have the winning prize in the box you originally picked? (1/2) Why does asking the question change the odds?

The difference is he takes away the losing box of the two left. It is not random.

Quote:

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Originally Posted by DaddyMac

Look at it this way. You pick with a 1:3 chance. Box removed, you switch. The box you're holding has a 1:2 chance of winning, right?

What's the chance of the other box winning?

(hint: 1:2)

Here's another way of looking at it. You have a 1:2 chance of GIVING UP the winning box.

Here's yet another way. You can re-pick your original box (again) and get the 1:2 chance.

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I agree. There is no benefit to switching boxes. Your odds are equal.

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Originally Posted by chadm

Can you give me back my time I spent in Stat class? I would gladly acknowledge I didn't take it if I can have some of my life back.

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Well that goes without saying.....

Quote:

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Originally Posted by chadm

I ask this again. If he didn't ask the question, do you have the same odds to have the winning prize in the box you originally picked? (1/2) Why does asking the question change the odds?

The difference is he takes away the losing box of the two left. It is not random.

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Didn't ask? Or didn't remove the box.

2 boxes. 1:2 chance. Doesn't matter if anything is asked.

3 boxes 1:3 chances. Again, doesn't matter what Monty does.

Unless of course you're planning on picking the revealed goat..???? :skeptical:

Then I'm just going to hit you on the head with a tack hammer...

:wink: