196 replies to this topic

[Martini]

So, in the game deal or no deal, the chance of getting a higher prize money at the end is 22 out of 23 if you switch to the last box remaining and only 1 in 23 if you stay with your own box???

No, I explained this in post #36. On Deal or No Deal all of the boxes chosen are done randomly. So switching doesn't matter; the probability of winning a higher amount doesn't change if you switch. But, if Howie Mandel were the one to eliminate boxes and he didn't do it randomly, he eliminated lower amount boxes first- definitely switch.

In this riddle, the host gives special protection to the car if it is among the two doors you didn't select (which it most likely is). Since he most likely has the car behind one of those doors, and he intentionally reveals which one has the goat behind it, then of course switching to the other door is the best bet.

[Maximus]

Ok this is still really confusing me and i cant seem to catch on but i am happy to accept that you are right

[Enlightened]

First off, let me say that I'm glad to find your site from among the Google add-ins.

With that said, this is not my first time to come across this problem. However, I just now saw the light for myself, and I thought I'd share how with those who still aren't convinced.

You initially have a 2/3 probability of picking a goat. This means that you also have a 2/3 possibility of the host revealing the only other goat on the stage. Therefore there is a 2/3 possibility that the other door on the stage holds the car. It's that simple.

[ALFRED]

You pick a door. If you pick a door with a goat (most likely), the host will show you which of the other door's also have the goat behind it. That makes switching to the other door the best bet.

For instance, if you pick the door with goat #1 behind it, the host will show you the door that has goat #2 behind it and by switching you will win a car.

If you pick the door with goat #2 behind it, the host will show you the door that has goat #1 behind it and by switching you will win a car.

If you pick the door with the car behind it, the host will show you a door that has one of the goats behind it and by switching you will win the other goat.

By switching doors when offered, you have a 2 out of 3 chance of winning the car.

Play with this a little and you'll see how it works.

Thank you martini for providing this link. Both for the simulation and for the link at the bottom of the simulation that provides articles about the puzzle's history which includes the discussion about Marilyn vos Savant. Back stories to the puzzles just makes them so much more interesting and debatable.

[gmarsha11]

No, he's not allowing you to trade your original door for the other two. That's why I said that it's essentially what he's doing.

No, that's not essentially what he is doing.

Essentially what he is doing is giving you a door, regardless of which of the other two doors you select. By your own logic, you still have 2/3 chance if you keep your original choice -- your original door AND the one that was opened to reveal one of the goats. This means that either of the remaining doors has a 2/3 chance, which makes them equally likely to contain the car.

[Noct]

No, that's not essentially what he is doing.

Essentially what he is doing is giving you a door, regardless of which of the other two doors you select. By your own logic, you still have 2/3 chance if you keep your original choice -- your original door AND the one that was opened to reveal one of the goats. This means that either of the remaining doors has a 2/3 chance, which makes them equally likely to contain the car.

No you don't keep your original door because you trade it. If you switch you double your chances from 1/3 to 2/3 of getting the car.

[gmarsha11]

No you don't keep your original door because you trade it. If you switch you double your chances from 1/3 to 2/3 of getting the car.

The argument was that switching gives you a 2/3 chance because you essentially get the 3rd door AND the revealed door. You get this same chance because you get your original door AND the revealed door. Same odds.

EDIT: BTW, I played the computer simulation 5 times without switching. I won the car 4 of the 5 times. Therefore, keeping my original choice gives me an 80% chance of winning the car. (kidding -- about the odds -- I really did win 4/5 times.)

Edited by gmarsha11, 24 March 2008 - 09:44 PM.

[Noct]

well it is like getting both. (aka doubling your chances).

Let's say there were 100 doors and you picked one. If i offered you the 99 other doors would you take them? What if i told you that at least 98 of the 99 other doors have goats behind them, would you still switch? Of course! because you increase your chances 99 times. When you do switch, even if i open 98 doors that have goats behind them, you still have a 99/100 chance of getting the car, instead of your original 1/100.

It's the same thing, except with 3 doors instead of two, and switching after he opens one.

[gmarsha11]

well it is like getting both. (aka doubling your chances).

Let's say there were 100 doors and you picked one. If i offered you the 99 other doors would you take them? What if i told you that at least 98 of the 99 other doors have goats behind them, would you still switch? Of course! because you increase your chances 99 times. When you do switch, even if i open 98 doors that have goats behind them, you still have a 99/100 chance of getting the car, instead of your original 1/100.

It's the same thing, except with 3 doors instead of two, and switching after he opens one.

If he opens 98 doors and I keep mine, don't I still have a 99/100 chance? 98 goats have been revealed. I now have a choice between my door and the other one for the 99th door.

[Noct]

If he opens 98 doors and I keep mine, don't I still have a 99/100 chance? 98 goats have been revealed. I now have a choice between my door and the other one for the 99th door.

Surprisingly no! The other door has a 99% chance of having the car, and yours only has a 1% chance