Would you "stick" or "switch"?

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Would you "stick" or "switch"?

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First you take the game host out of the equation. Then you imaging you have 10 doors.

You then have the choice of opening 1 door or 9 doors.

Set up like this it`s quite obvious that you have the best chances of winning if you open 9 doors instead of 1.

The thing that confuses people, I think, is that it`s someone else opening the doors for you.

Let`s name the possible outcomes "Win", "Fail 1" and "Fail 2"

If you had chosen door with "Fail 1", Host will open "Fail 2" door. You switch and you get "Win".

If you had chosen door with "Fail 2", Host will open "Fail 1" door. You switch and you get "Win".

If you had chosen door with "Win", Host will open "Fail 1" or "Fail 2" door. You switch and you get another "Fail".

You win 2 out of 3 times if you switch.

Monty then has 999 doors left to open for you, and he has to open doors that do not contain the prize. So he opens the 998 wrong doors for you, leaving the one that contains the prize, and your door. The fact that he opened those other doors doesn`t change the fact that you had a 0.1% chance of picking the right door in the beginning - the conditions haven`t changed.

So, if there are 1000 doors, sticking will win you the prize 0.1% of the time, while switching will win you the prize 99.9% of the time.

Boiling it down to 3 doors is the simplest form of the puzzle where it still works, but the odds are 33% vs 67% rather than 0.1% vs 99.9%. Either way, you should always switch.

Clear as mud?

To me, it SEEMS like if you are a switcher, meaning you will switch doors, you want your first pick to be an empty door. That will guarantee you a win. You have 2/3 chance of picking an empty door on your first pick. Therefore, a better chance than picking a prize the first time.

So where`s the paradox?

No, the beach ball explodes from the pressure releasing all the air. Do you really believe what you wrote?

I was pointing out that both the beach ball and this Monty issue are easily explained phenomenon and not paradoxes. So, thanks for playing.

If it is pointed out that to win by switching you have to pick incorrectly initially, whereas to win by sticking you have to pick correctly initially it becomes obvious that the switcher will win 2/3 but the sticker will only win 1/3.

A Pair of Docs

A Pair of Ducks

So, the paradox here, quite obviously (and even stated no less than three times in the video), is that even though it *seems* like sticking with your original choice is no more or less mathematically/statistically beneficial, in fact, switching gives you a 33% increased chance of being correct. That, right there, is a paradox.

So, even though looking at two unopened doors *seems* like a 50/50 proposition, it is, given the set-up, actually a 33.33/66.66 proposition, in favor of switching. It`s *seemingly* contradictory to think that switching helps you, but, in fact, it`s true that switching helps. Paradox.

I don`t think you know what a paradox is. The beach ball loses bouyancy because of the pressure/weight of the water pushing down on it.

Now explain why it is, not matter which check-out line you get in at WalMart, it is the slowest moving one.

THAT`s a mind-bender!

Numb3Rs Youtube link

Now that all goes to heck if the winning door is randomized a second time, but as long as it`s only done once, at the beginning of the game, you`re always better off switching.

"Picked a door, now do you switch?"

Before I hear their answer, I will say YES, switch.

When you originally picked Door #1 it had a 1 in 3 chance of winning. You iliminate Door #2 so Door #3 has a 2/3rds chance of winning. By switching you have increased your odds of winning. I think there is an actual mathmatical formula out there that proves this.

Now I`ll watch the rest to see if I`m right.

:-) I would have made a killing!

I am a wealth of useless knowledge.

But I guess the practical test can prove it better than the math can explain it.

Say you have 300 doors, same scenario. Pick 1, and then Monty eliminates 298 doors... would you stay or switch doors?

Mythbusters is running out of ideas. There are many proofs for this problem, some more mathematically rigorous than others, but there IS a 2/3 chance of winning if you switch.

Do they seriously get paid for this? I watch Mythbusters to watch them test myths I can`t test myself. I had a skeptical friend we performed this--about two out of the three times he switched, he won.

there is a scene in there about this thing...so i already knew the answer

- Would you `stick` or `switch`?