OK, I'll write that program, but Ill write if for ME.
I need to see the events happening.
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OK, I'll write that program, but Ill write if for ME.
I need to see the events happening.
OK, I conceede.
I finally 'get' it.
I demonstrated it to someone using a shoe and 3 potplants ... it worked until they got pissed off at the logic and threw the other shoe at me :D
Chuckle, thats funny!
I've long stopped trying to explain all things mathematical to my family. Just doesn't work...
the only person who ever agreed with this logic the first time around was my computer teacher, he was a math teacher and is quite good at logic so he didn't argue with it but i had to take at least 10 or 15 minutes argueing with everyone else
No, I dissagree with the logic completly.
given that you will never be shown the door you picked
and given that whether or not you picked a goat, one goat door
will be opened.
go like this, you pick door number 1.
host reaveals dorr number 3 (goats).
you get shot in the head and your twin gets out of his seat
and takes your place, but your twin was not watching, so he
has no idea what dorr you picked the first time.
so NOW there is 1:2 chance that he will get lucky and pick some goats.
good thing your twin owns some land.
nuf said.
This would hold true for a million doors to, except yo might need a pair of
binoculars to see the last one.
That is the crucial part of the game that you are changing. You do know what you picked the first time. I am tempted to get out my shoe and some potplants but I think others have explained it quite well on this thread. Try it out yourself on some unsuspecting member of your family.. do this....Quote:
Originally posted by JPicasso
you get shot in the head and your twin gets out of his seat
and takes your place, but your twin was not watching, so he
has no idea what dorr you picked the first time.
Put a shoe behind one potplant
Ask them to guess where it is.
Show them a potplant that they have not picked and where there is no shoe.
Ask them to pick again.
More often than not they will pick the shoe by switching.
ps Wear protective headwear :eek: :p
I'm not sure how many times this has been said (there's too many replies to read them all), but it IS BETTER TO SWAP.
think of it this way.
n>2
There are n doors.
You pick door X, with a 1/n chance of being right.
There are now two groups of doors. Chosen and Not Chosen
Chosen = door X, Not Chosen = the rest
P(Chosen) = 1/n as above.
P(Not Chosen) = (n-1)/n
By saying that what is behind all but one of the doors (let the door left be Door Y) in "Not Chosen", the host is saying:
Either stay with your "Chosen" Door, or move to the "Not Chosen" group. If you decide to change to the "Not Chosen" group, then the prize is behind door Y.
=> chosing door Y = (n-1)/n chance of winning.
Finally, try this:
Pick a door, 1 to 3
Now, either you are right (33%) or you are wrong (67%). If you are wrong, then you must change. The only way to change is to swap to the other door on offer. => if you are wrong (67% chance), and you change, then you will be right. => 67% right if you change.
And I say that working with one out of three doors
after the time where you know that the prize is behind
one of two doors is just bad math.
any time after you know that one of two doors (and an equal probability
that either door has a goat), you odds of switching to the correct door
or holding onto the correct door are exactly 50/50.....
wait a minute... let me think on this further.
the best solution is to write a program that would do it completely randomly
Deary me what a can of worms.
It's actually dead easy to work out as follows:
Suppose you pick door 1, then the possiblities are as follows:
So If you don't swap you have a 1 in 3 chance of winning. If you do swap you have a 2 in 3 chance of winning.Code:Contestants stratergy: Don't Swap Doors
Door 1 Door 2 Door 3
Car Goat Goat win
Goat Car Goat lose
Goat Goat Car lose
Contestants stratergy: Swap Doors
Door 1 Door 2 Door 3
Car Goat Goat lose
Goat Car Goat win
Goat Goat Car win
QED.
And Just for completeness the following is all possible results for any door picked.
Possible outcomes with no swapping 3 wins, 6 lose.Code:pick door 1
Contestants stratergy: Don't Swap Doors
Door 1 Door 2 Door 3
Car Goat Goat win
Goat Car Goat lose
Goat Goat Car lose
Contestants stratergy: Swap Doors
Door 1 Door 2 Door 3
Car Goat Goat lose
Goat Car Goat win
Goat Goat Car win
pick door 2
Contestants stratergy: Don't Swap Doors
Door 1 Door 2 Door 3
Car Goat Goat lose
Goat Car Goat win
Goat Goat Car lose
Contestants stratergy: Swap Doors
Door 1 Door 2 Door 3
Car Goat Goat win
Goat Car Goat lose
Goat Goat Car win
pick door 3
Contestants stratergy: Don't Swap Doors
Door 1 Door 2 Door 3
Car Goat Goat lose
Goat Car Goat lose
Goat Goat Car win
Contestants stratergy: Swap Doors
Door 1 Door 2 Door 3
Car Goat Goat win
Goat Car Goat win
Goat Goat Car lose
Possible outcomes with swapping 6 wins, 3 lose.
There for you have twice as much chance of winning if you swap.
Yes, i agree.
Just wanted to say:
Actually, the BEST way would be to write a program that checks all combinations, like what Slaine did.Quote:
the best solution is to write a program that would do it completely randomly
Randomly is still good, but mainly for real-life testing, where not all events can be checked.
Okay, I'm convinced.
The "trick" is knowing that your first choice is probably (67%) wrong.
and that switching your choice when you know what other door NOT to pick is a big help.
The other "trick" is not getting shot in the head so that your
twin can take all your fabulous prizes.
Fun.