Two Donkeys and a Million Bucks

[AKHog]

Nope!    Your odds are not 1/2 because you made your guess with 3 possible choices.  What I show you has nothing to do with the probability of your guess being correct.

My odds are 1/2 because there are 2 doors, and I have picked one.

One door has the money, the other does not. After you eliminate the first choice, I now have a 1/2 shot of winning weather or not I switch. 

[hammer]

I picked the first door. Where's my donkey? 

[AKHog]

I just did the experiment, but I am by myself so I had to modify it.

I placed 3 pieces of cardboard face down, only one has a money sign drawn on it.

I shuffled the cards, then picked one at random.

Next I eliminate one card, and note if it was the money card or not.

Then I turned over the card I picked and noted if I won or not.

After all this I repeated the process, except I turned over the other remaining card that I did not pick.

My results are pretty much even. About 1/3 of the time I win, 1/3 of the time I loose, 1/3 of the time I accidentally eliminate the money card, ruining that specific test. If I eliminate all of the tests that were ruined, 1/2 the time I win.

[AKHog]

All I ask is for someone to explain mathematically why: I have one door picked out of 2 remaining doors. One has the prize, one does not. No matter if I picked the door before the others were eliminated, after, or was simply randomly assigned that door at any time, my chances are still now 1/2.

[Chalenge]

Glass half full versus half empty if you ask me.

[Anaxogoras]

You need to do the experiment with a friend, and try it from both sides.

Here's another way to think about it.  Instead of 3 doors, there are 100 doors.  You pick one, and I open 98 doors and show you 98 donkeys.  Do you want to switch or keep your original choice?  What are the odds that out of 100 doors, your choice is correct when I've eliminated 98 possibilities and left one extra remaining?  About 99:1.

[Lusche]

3 Doors, 2 donkeys.

I chose one.

Anax opens a door - donley.

2 doors left, one has a donkey.

The chance my door has the million bucks is NOW at 50% - not 33%. Even without having changed my choice. The fact alone that Anax had opened a door has increased my chances.

The original problem is more complex, as the hosts knowledge and behaviour plays an important role. See "Monty Hall problem"

[APDrone]

You need to do the experiment with a friend, and try it from both sides.

Here's another way to think about it.  Instead of 3 doors, there are 100 doors.  You pick one, and I open 98 doors and show you 98 donkeys.  Do you want to switch or keep your original choice?  What are the odds that out of 100 doors, your choice is correct when I've eliminated 98 possibilities and left one extra remaining?  About 99:1.

Yahhh... ummm.. errrr.. no.

Ultimately, you have 1 last choice between 2 doors.  You could have 100 billion doors/donkeys before hand, but the final choice is a fresh one between 2 doors.

You still have a 50/50 chance of choosing the right door.

[Masherbrum]

There are three doors.  Behind one of those doors is a million bucks.  Each of the other two doors hides a donkey.  Here's how the game works:  You pick a door at random, and then I open a different door and show you a donkey.  You now have the option of keeping your original pick, or switching.  What should you do?

A)  Keep my original choice
B)  Switch
C)  It doesn't matter, the two options are equivalent

B.   When you switch who have a 50/50 chance.   

[AKHog]

Yahhh... ummm.. errrr.. no.

Ultimately, you have 1 last choice between 2 doors.  You could have 100 billion doors/donkeys before hand, but the final choice is a fresh one between 2 doors.

You still have a 50/50 chance of choosing the right door.

Exactly. And even if you stay with your original door, after all the other doors are eliminated you still have a 1/2 chance during the final draw.

[AKHog]

Watch "Deal or No Deal".

As the suitcases get eliminated, and the million dollar winning case is still unaccounted for, the offers for the case you have already picked go up.

Thats because as there are less cases left, there becomes a higher chance that you may have the big money. If there are only two cases left, and its either $1 or $1 million, the 'bank' will likely offer you somewhere around $500,000, reflecting the current odds you have the million. They do NOT offer you $20,000, which would be reflecting the 1/50 chance you would have at the very start (before 48 cases are eliminated).

That means in the final draw of 2, even after a thousand cases or doors are eliminated, and assuming the winner is still unaccounted for, you have a 1/2 chance of winning WITH OUT re-picking.

[AKHog]

And just to put it one other way in case this is not confusing enough.


My uncle had 8 boys. He said he must have some luck to have 8. I explained that even though he had already had 7 boys in the past, when his 8th was conceived he still had exactly a 50/50 chance of it being a boy or girl.

That means despite preconditioning circumstances, when you are figuring the odds you can only consider the current possibilities. If there are two doors left, and one is the winner, despite overcoming any previous odds, your current odds are 1/2 no matter what door you pick, nor when or how you picked it.

[Tordon22]

I say there's a 25% chance.  

1.) You stay after a donkey is shown and you win the money.

2.) You stay after a donkey is shown and you lose.

3.) You switch after a donkey is shown and you win the money.

4.) You  switch after a donkey is shown and you lose. Making you look like a real...uh...donkey

4 options / 1 choice = 25% ! Am I right lol?


Seriously though. Cherry picker happens to be right.


It's all based off the likelihood that you chose wrong the first time because the 66% chance you missed your first guess is > the 33% chance you nailed it.

The probability of 1 of those 3 doors having the money is 100%. 1/3 + 1/3 + 1/3 . So when you make your first guess you have 1/3 that you're right and 2/3 you're wrong. When you are shown a donkey it doesn't magically become a 50/50 shot because that's not the probability you started with(you're working with thirds!). What you do have though is two doors, your original with a 1/3 chance of having the money and the other with a 2/3 chance of having the money.It really does work if you do the experiment. And if you're like hammer and would chose the door he showed you with the donkey, well there's no helping you.

-Zap

[AKHog]

When you are shown a donkey it doesn't magically become a 50/50 shot because that's not the probability you started with(you're working with thirds!).

No, it doesn't "magically" change, it changes because one possibility was completely eliminated, changing the odds of the current situation.

Again, like I say why does the deal or no deal "bank" make higher and higher offers for your case as other cases are eliminated and the million doesn't show? If its like you guys say, then the offer should be $20k from the start and never change as cases are eliminated (1 choice divided by 50 possibilities multiplied by 1 million dollar max possibility = $20k). After 47 cases are eliminated, and the million is still on the board, they offer roughly $333k for your original choice. Then if one more is eliminated, the offer goes up to $500k for your original choice. This is because every time they eliminated a case that was not a winner, your odds of winning actually go up.

[AKHog]

If you are watching a game of single elimination musical chairs with 50 people in Vegas, you have a slim chance of picking the winner, the odds would pay 50 for 1. If you pick a person, and he makes it to the final round, and you go back to bet more money on that person, the odds would pay 2 for 1. Thats because the odds of that person winning are now 50%.

This doesn't change the fact that you still won 50-1 on your first bet, but in that final match bet, your chances of winning were exactly 50%. Therefor; even if you did NOT bet in the final match, and only let your initial bet ride, your chances winning the final match (assuming you made it that far) would still be exactly 50%.