Goat or Car, Rediculous or don't I get it?

Cherry7Up

Well-Known Member
#21
callipygian said:
I argue they did, and that people are confused about the answer (whether you believe you're right or I'm right, it's very clear one of us is puzzled) is evidence enough that it's a good problem.
This I certainly agree with, well said!
 

gibsonlp33stl

Well-Known Member
#22
callipygian said:
You'll need far more than 40 trials to differentiate between a 50% and 67% of being correct. As it stands, you'd expect 10 wins if the probability is 50% and 13 wins if the probability is 67%. That's a razor-thin margin.
Actually...the difference is between 33% and 67%. Obviously doing 20 rounds won't provide amazing data, but the expected win goes from 7 to 13...screw it! Just do 1000 rounds and you'll see!!! lol...i just said 20 b/c i couldn't see a reasonable person doing anymore than that.
 

callipygian

Well-Known Member
#23
gibsonlp33stl said:
Just do 1000 rounds and you'll see!!!
We can do even better than that. All gripes about the Excel RNG aside, here's 10,000 rounds of this game. (Edit: I'm not allowed to post more than 20,000 characters so I'm only pasting the first 1,000 rounds.)

Car = Door behind which the car actually resides (random # from 1-3)
Open = Door which Monty opens (if car = 1, then random # from 2-3)
Sw% = Win or Loss if you switch
Rnd = Randomly picking between the two unopened doors
Rnd% = Win or Loss if you pick randomly

Code:
Car	Opened	Switch%	Random	Random%
2	3	W	1	L
1	2	L	1	W
1	3	L	1	W
2	3	W	2	W
1	3	L	1	W
1	3	L	2	L
3	2	W	1	L
3	2	W	3	W
2	3	W	1	L
2	3	W	2	W
1	2	L	1	W
2	3	W	2	W
3	2	W	3	W
1	2	L	1	W
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
2	3	W	2	W
3	2	W	3	W
1	2	L	3	L
2	3	W	1	L
2	3	W	1	L
2	3	W	2	W
3	2	W	1	L
3	2	W	1	L
2	3	W	2	W
3	2	W	3	W
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
2	3	W	1	L
1	2	L	3	L
2	3	W	2	W
3	2	W	1	L
1	2	L	3	L
2	3	W	1	L
3	2	W	1	L
1	3	L	2	L
3	2	W	3	W
1	3	L	1	W
1	3	L	2	L
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
1	2	L	1	W
1	2	L	3	L
2	3	W	2	W
2	3	W	1	L
3	2	W	3	W
1	3	L	2	L
2	3	W	1	L
2	3	W	1	L
3	2	W	1	L
3	2	W	3	W
2	3	W	2	W
3	2	W	1	L
1	2	L	3	L
3	2	W	1	L
3	2	W	1	L
2	3	W	2	W
2	3	W	1	L
2	3	W	1	L
1	2	L	3	L
2	3	W	1	L
1	3	L	1	W
1	3	L	2	L
1	2	L	1	W
3	2	W	1	L
2	3	W	1	L
2	3	W	2	W
2	3	W	1	L
3	2	W	3	W
2	3	W	2	W
3	2	W	1	L
3	2	W	3	W
1	3	L	1	W
3	2	W	1	L
2	3	W	1	L
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
2	3	W	1	L
2	3	W	1	L
1	2	L	3	L
1	2	L	1	W
1	2	L	3	L
3	2	W	1	L
1	3	L	2	L
3	2	W	3	W
2	3	W	1	L
2	3	W	1	L
2	3	W	1	L
3	2	W	3	W
2	3	W	2	W
2	3	W	2	W
2	3	W	2	W
1	2	L	3	L
2	3	W	1	L
2	3	W	2	W
3	2	W	1	L
2	3	W	1	L
2	3	W	2	W
1	3	L	2	L
1	2	L	1	W
1	3	L	2	L
3	2	W	3	W
3	2	W	3	W
3	2	W	3	W
2	3	W	1	L
3	2	W	1	L
1	3	L	2	L
3	2	W	1	L
3	2	W	1	L
3	2	W	3	W
2	3	W	2	W
2	3	W	1	L
1	2	L	1	W
2	3	W	1	L
2	3	W	1	L
3	2	W	1	L
3	2	W	3	W
1	3	L	1	W
3	2	W	3	W
2	3	W	1	L
3	2	W	3	W
3	2	W	3	W
1	3	L	2	L
1	2	L	1	W
2	3	W	2	W
2	3	W	1	L
2	3	W	2	W
1	3	L	1	W
2	3	W	1	L
2	3	W	2	W
1	2	L	1	W
1	2	L	3	L
1	2	L	1	W
2	3	W	1	L
2	3	W	1	L
1	3	L	1	W
3	2	W	1	L
1	2	L	3	L
1	3	L	2	L
2	3	W	1	L
1	2	L	3	L
1	2	L	1	W
2	3	W	2	W
3	2	W	1	L
3	2	W	1	L
1	3	L	1	W
3	2	W	1	L
2	3	W	2	W
2	3	W	2	W
2	3	W	1	L
2	3	W	1	L
3	2	W	1	L
1	3	L	1	W
2	3	W	1	L
1	2	L	3	L
2	3	W	2	W
3	2	W	1	L
3	2	W	3	W
3	2	W	3	W
3	2	W	3	W
1	2	L	1	W
3	2	W	1	L
1	3	L	1	W
1	2	L	3	L
1	2	L	3	L
2	3	W	2	W
3	2	W	3	W
2	3	W	1	L
2	3	W	2	W
1	2	L	3	L
3	2	W	1	L
2	3	W	1	L
1	3	L	2	L
1	3	L	1	W
2	3	W	2	W
2	3	W	1	L
2	3	W	2	W
3	2	W	1	L
3	2	W	1	L
2	3	W	1	L
2	3	W	1	L
3	2	W	3	W
2	3	W	2	W
3	2	W	3	W
1	3	L	1	W
3	2	W	1	L
3	2	W	3	W
3	2	W	3	W
3	2	W	3	W
3	2	W	1	L
2	3	W	2	W
1	3	L	2	L
1	3	L	1	W
3	2	W	3	W
2	3	W	1	L
3	2	W	1	L
1	2	L	3	L
3	2	W	3	W
3	2	W	3	W
3	2	W	3	W
1	2	L	3	L
3	2	W	1	L
2	3	W	1	L
1	2	L	1	W
3	2	W	3	W
2	3	W	1	L
2	3	W	1	L
2	3	W	1	L
1	2	L	3	L
2	3	W	1	L
2	3	W	1	L
2	3	W	1	L
1	3	L	2	L
3	2	W	3	W
2	3	W	2	W
1	2	L	3	L
2	3	W	1	L
1	3	L	2	L
1	3	L	2	L
2	3	W	2	W
1	3	L	1	W
1	2	L	1	W
1	2	L	1	W
1	2	L	3	L
2	3	W	1	L
1	2	L	1	W
2	3	W	2	W
2	3	W	1	L
2	3	W	1	L
3	2	W	3	W
1	3	L	2	L
2	3	W	1	L
1	2	L	1	W
1	2	L	1	W
2	3	W	2	W
3	2	W	1	L
2	3	W	1	L
3	2	W	3	W
3	2	W	1	L
2	3	W	2	W
1	2	L	3	L
1	3	L	1	W
1	2	L	3	L
1	3	L	2	L
2	3	W	1	L
3	2	W	3	W
1	2	L	1	W
2	3	W	2	W
2	3	W	2	W
3	2	W	3	W
3	2	W	3	W
1	3	L	2	L
1	2	L	3	L
3	2	W	3	W
1	3	L	1	W
3	2	W	1	L
2	3	W	2	W
1	2	L	1	W
3	2	W	3	W
1	3	L	2	L
1	3	L	1	W
2	3	W	2	W
1	3	L	1	W
2	3	W	1	L
3	2	W	3	W
2	3	W	1	L
3	2	W	1	L
3	2	W	1	L
1	3	L	2	L
3	2	W	1	L
2	3	W	1	L
2	3	W	1	L
1	2	L	3	L
1	2	L	1	W
2	3	W	2	W
2	3	W	1	L
3	2	W	1	L
2	3	W	2	W
3	2	W	1	L
3	2	W	3	W
2	3	W	2	W
3	2	W	3	W
2	3	W	1	L
3	2	W	1	L
2	3	W	1	L
1	2	L	1	W
2	3	W	2	W
2	3	W	1	L
3	2	W	3	W
2	3	W	1	L
2	3	W	1	L
1	2	L	3	L
3	2	W	1	L
2	3	W	2	W
2	3	W	2	W
2	3	W	2	W
1	3	L	2	L
1	3	L	1	W
1	3	L	1	W
3	2	W	3	W
1	2	L	3	L
2	3	W	2	W
3	2	W	1	L
3	2	W	1	L
3	2	W	3	W
3	2	W	3	W
1	2	L	1	W
1	2	L	1	W
3	2	W	3	W
3	2	W	3	W
1	3	L	2	L
3	2	W	1	L
2	3	W	2	W
3	2	W	3	W
3	2	W	3	W
3	2	W	3	W
2	3	W	2	W
3	2	W	3	W
1	2	L	3	L
1	3	L	1	W
2	3	W	1	L
2	3	W	2	W
3	2	W	3	W
1	2	L	1	W
2	3	W	1	L
2	3	W	1	L
2	3	W	2	W
1	2	L	1	W
3	2	W	3	W
2	3	W	2	W
1	3	L	1	W
2	3	W	1	L
3	2	W	1	L
1	2	L	1	W
1	2	L	3	L
3	2	W	3	W
1	2	L	1	W
3	2	W	3	W
3	2	W	3	W
3	2	W	1	L
2	3	W	2	W
2	3	W	2	W
3	2	W	3	W
3	2	W	1	L
1	2	L	3	L
3	2	W	1	L
2	3	W	2	W
2	3	W	2	W
1	3	L	1	W
2	3	W	2	W
1	3	L	2	L
3	2	W	3	W
2	3	W	2	W
2	3	W	2	W
1	3	L	1	W
2	3	W	1	L
2	3	W	2	W
1	2	L	1	W
3	2	W	3	W
3	2	W	1	L
1	2	L	1	W
3	2	W	1	L
1	3	L	1	W
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
3	2	W	3	W
2	3	W	1	L
3	2	W	1	L
2	3	W	2	W
1	3	L	2	L
2	3	W	2	W
1	2	L	1	W
2	3	W	2	W
3	2	W	3	W
3	2	W	1	L
1	2	L	3	L
2	3	W	2	W
2	3	W	2	W
2	3	W	2	W
3	2	W	1	L
1	3	L	2	L
2	3	W	1	L
1	3	L	2	L
3	2	W	1	L
3	2	W	3	W
3	2	W	1	L
1	2	L	1	W
2	3	W	2	W
1	3	L	1	W
2	3	W	1	L
2	3	W	1	L
1	3	L	2	L
2	3	W	2	W
1	3	L	2	L
2	3	W	2	W
3	2	W	3	W
1	3	L	2	L
1	2	L	3	L
3	2	W	3	W
3	2	W	1	L
3	2	W	1	L
1	3	L	2	L
1	2	L	3	L
2	3	W	1	L
3	2	W	3	W
3	2	W	3	W
1	2	L	1	W
2	3	W	2	W
1	3	L	1	W
2	3	W	1	L
3	2	W	3	W
1	2	L	3	L
1	2	L	1	W
2	3	W	2	W
3	2	W	3	W
2	3	W	1	L
1	3	L	2	L
1	3	L	1	W
3	2	W	1	L
1	2	L	1	W
2	3	W	2	W
2	3	W	2	W
1	2	L	3	L
3	2	W	1	L
1	3	L	1	W
2	3	W	1	L
1	3	L	2	L
2	3	W	1	L
1	2	L	1	W
1	2	L	1	W
2	3	W	1	L
1	2	L	1	W
1	3	L	1	W
1	2	L	1	W
1	3	L	2	L
2	3	W	1	L
2	3	W	2	W
1	2	L	3	L
2	3	W	2	W
3	2	W	3	W
3	2	W	1	L
3	2	W	1	L
3	2	W	3	W
3	2	W	1	L
1	2	L	1	W
1	3	L	1	W
2	3	W	1	L
2	3	W	1	L
3	2	W	1	L
1	2	L	3	L
2	3	W	1	L
3	2	W	1	L
1	3	L	1	W
3	2	W	3	W
1	3	L	2	L
3	2	W	3	W
1	2	L	3	L
1	3	L	2	L
2	3	W	2	W
2	3	W	2	W
3	2	W	3	W
3	2	W	3	W
1	3	L	1	W
3	2	W	1	L
2	3	W	1	L
2	3	W	1	L
1	2	L	3	L
1	3	L	1	W
3	2	W	3	W
3	2	W	1	L
3	2	W	1	L
3	2	W	1	L
3	2	W	3	W
1	2	L	3	L
3	2	W	1	L
2	3	W	1	L
3	2	W	3	W
1	2	L	3	L
1	3	L	1	W
2	3	W	1	L
2	3	W	2	W
1	3	L	1	W
1	3	L	2	L
3	2	W	1	L
1	3	L	1	W
3	2	W	1	L
2	3	W	2	W
2	3	W	1	L
2	3	W	2	W
3	2	W	3	W
2	3	W	2	W
2	3	W	2	W
3	2	W	3	W
1	2	L	3	L
1	2	L	3	L
3	2	W	1	L
3	2	W	3	W
3	2	W	1	L
1	3	L	2	L
3	2	W	3	W
3	2	W	1	L
1	3	L	2	L
3	2	W	3	W
3	2	W	3	W
2	3	W	1	L
2	3	W	2	W
2	3	W	1	L
1	3	L	2	L
3	2	W	1	L
2	3	W	1	L
3	2	W	1	L
2	3	W	1	L
1	3	L	2	L
2	3	W	2	W
3	2	W	3	W
1	3	L	2	L
3	2	W	3	W
1	2	L	1	W
3	2	W	3	W
2	3	W	1	L
1	3	L	1	W
3	2	W	1	L
1	2	L	1	W
2	3	W	1	L
3	2	W	3	W
2	3	W	1	L
1	3	L	1	W
1	2	L	3	L
1	2	L	1	W
2	3	W	2	W
2	3	W	2	W
2	3	W	1	L
3	2	W	1	L
3	2	W	3	W
1	2	L	3	L
1	2	L	1	W
1	3	L	1	W
3	2	W	1	L
3	2	W	1	L
3	2	W	3	W
3	2	W	3	W
3	2	W	3	W
2	3	W	2	W
1	2	L	1	W
3	2	W	3	W
3	2	W	1	L
3	2	W	1	L
3	2	W	3	W
1	2	L	1	W
1	2	L	1	W
3	2	W	3	W
1	3	L	1	W
1	2	L	1	W
2	3	W	1	L
1	3	L	2	L
1	2	L	3	L
1	3	L	2	L
3	2	W	3	W
2	3	W	1	L
2	3	W	1	L
3	2	W	1	L
2	3	W	1	L
3	2	W	3	W
3	2	W	3	W
3	2	W	1	L
3	2	W	1	L
1	3	L	2	L
2	3	W	2	W
2	3	W	1	L
1	3	L	1	W
2	3	W	1	L
1	3	L	2	L
2	3	W	1	L
3	2	W	1	L
2	3	W	2	W
1	2	L	1	W
1	3	L	1	W
2	3	W	2	W
1	2	L	3	L
3	2	W	1	L
2	3	W	1	L
3	2	W	1	L
2	3	W	1	L
2	3	W	1	L
2	3	W	2	W
1	2	L	1	W
2	3	W	2	W
3	2	W	1	L
2	3	W	2	W
3	2	W	1	L
2	3	W	1	L
1	2	L	3	L
3	2	W	1	L
1	2	L	3	L
2	3	W	1	L
3	2	W	1	L
1	3	L	1	W
2	3	W	2	W
1	2	L	1	W
2	3	W	1	L
3	2	W	3	W
3	2	W	3	W
2	3	W	2	W
1	3	L	2	L
1	2	L	1	W
1	2	L	3	L
2	3	W	1	L
1	3	L	1	W
1	2	L	1	W
2	3	W	2	W
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
3	2	W	1	L
2	3	W	2	W
1	3	L	2	L
2	3	W	1	L
3	2	W	3	W
2	3	W	2	W
2	3	W	2	W
1	2	L	3	L
2	3	W	2	W
1	2	L	1	W
3	2	W	1	L
3	2	W	3	W
3	2	W	3	W
3	2	W	1	L
3	2	W	1	L
1	2	L	3	L
3	2	W	1	L
3	2	W	3	W
3	2	W	3	W
1	2	L	3	L
3	2	W	1	L
1	2	L	3	L
1	3	L	2	L
2	3	W	1	L
1	3	L	2	L
1	3	L	1	W
3	2	W	1	L
3	2	W	1	L
3	2	W	3	W
1	2	L	1	W
1	3	L	2	L
2	3	W	1	L
2	3	W	2	W
2	3	W	2	W
2	3	W	1	L
1	3	L	1	W
3	2	W	1	L
3	2	W	1	L
2	3	W	2	W
2	3	W	1	L
1	2	L	3	L
2	3	W	1	L
3	2	W	3	W
2	3	W	2	W
1	3	L	2	L
1	3	L	1	W
1	2	L	1	W
1	2	L	3	L
1	3	L	1	W
3	2	W	3	W
3	2	W	1	L
1	2	L	1	W
2	3	W	1	L
2	3	W	1	L
2	3	W	1	L
1	2	L	3	L
1	2	L	1	W
2	3	W	1	L
1	3	L	1	W
1	3	L	2	L
3	2	W	3	W
3	2	W	1	L
1	2	L	3	L
1	2	L	1	W
3	2	W	1	L
3	2	W	1	L
2	3	W	1	L
3	2	W	3	W
3	2	W	1	L
3	2	W	1	L
2	3	W	2	W
3	2	W	1	L
1	3	L	2	L
1	2	L	1	W
3	2	W	3	W
1	3	L	2	L
1	3	L	2	L
2	3	W	2	W
2	3	W	1	L
3	2	W	1	L
2	3	W	2	W
3	2	W	3	W
1	3	L	1	W
1	2	L	3	L
3	2	W	3	W
1	2	L	3	L
1	3	L	1	W
1	2	L	1	W
2	3	W	1	L
2	3	W	1	L
1	2	L	3	L
2	3	W	2	W
2	3	W	2	W
2	3	W	1	L
3	2	W	1	L
3	2	W	3	W
3	2	W	1	L
2	3	W	2	W
1	2	L	3	L
1	2	L	3	L
3	2	W	3	W
2	3	W	1	L
2	3	W	1	L
2	3	W	2	W
2	3	W	2	W
2	3	W	2	W
3	2	W	3	W
1	3	L	1	W
2	3	W	2	W
3	2	W	3	W
3	2	W	1	L
2	3	W	2	W
2	3	W	2	W
1	2	L	1	W
1	3	L	2	L
2	3	W	2	W
1	3	L	2	L
2	3	W	1	L
2	3	W	2	W
2	3	W	1	L
1	3	L	2	L
1	3	L	1	W
3	2	W	3	W
1	3	L	1	W
2	3	W	2	W
1	3	L	1	W
1	2	L	3	L
1	2	L	1	W
2	3	W	2	W
3	2	W	3	W
2	3	W	2	W
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
3	2	W	3	W
2	3	W	1	L
2	3	W	2	W
2	3	W	2	W
2	3	W	2	W
3	2	W	1	L
3	2	W	3	W
1	2	L	1	W
3	2	W	3	W
1	3	L	2	L
1	3	L	2	L
1	3	L	1	W
3	2	W	3	W
3	2	W	1	L
1	2	L	1	W
3	2	W	3	W
1	2	L	3	L
2	3	W	2	W
3	2	W	3	W
2	3	W	2	W
1	3	L	1	W
3	2	W	1	L
2	3	W	2	W
1	2	L	3	L
3	2	W	3	W
1	3	L	1	W
1	2	L	3	L
2	3	W	2	W
1	3	L	1	W
2	3	W	1	L
2	3	W	2	W
2	3	W	2	W
1	3	L	2	L
2	3	W	2	W
3	2	W	1	L
1	2	L	1	W
2	3	W	2	W
3	2	W	3	W
2	3	W	1	L
2	3	W	2	W
3	2	W	1	L
2	3	W	1	L
1	2	L	3	L
1	2	L	3	L
1	3	L	2	L
1	3	L	2	L
1	2	L	3	L
1	3	L	2	L
2	3	W	1	L
3	2	W	1	L
3	2	W	1	L
2	3	W	2	W
2	3	W	1	L
1	2	L	3	L
3	2	W	1	L
3	2	W	3	W
3	2	W	3	W
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
2	3	W	2	W
2	3	W	1	L
3	2	W	1	L
1	3	L	2	L
1	2	L	1	W
2	3	W	1	L
2	3	W	2	W
2	3	W	2	W
1	3	L	1	W
2	3	W	1	L
2	3	W	1	L
3	2	W	1	L
2	3	W	1	L
1	3	L	1	W
2	3	W	1	L
1	3	L	2	L
3	2	W	1	L
2	3	W	1	L
3	2	W	3	W
2	3	W	2	W
3	2	W	3	W
3	2	W	1	L
3	2	W	3	W
1	2	L	3	L
1	3	L	1	W
1	2	L	3	L
2	3	W	2	W
1	3	L	1	W
3	2	W	1	L
3	2	W	1	L
1	3	L	1	W
2	3	W	2	W
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
1	2	L	3	L
2	3	W	2	W
1	3	L	2	L
1	3	L	2	L
1	3	L	2	L
1	2	L	3	L
2	3	W	2	W
2	3	W	2	W
1	2	L	1	W
2	3	W	2	W
2	3	W	1	L
2	3	W	2	W
1	3	L	2	L
3	2	W	3	W
1	3	L	2	L
2	3	W	2	W
2	3	W	1	L
3	2	W	3	W
2	3	W	2	W
1	3	L	2	L
3	2	W	1	L
3	2	W	3	W
3	2	W	1	L
2	3	W	2	W
2	3	W	2	W
3	2	W	3	W
3	2	W	3	W
1	2	L	3	L
1	2	L	3	L
3	2	W	3	W
1	3	L	1	W
2	3	W	1	L
2	3	W	1	L
1	3	L	2	L
1	3	L	2	L
3	2	W	1	L
2	3	W	1	L
3	2	W	1	L
3	2	W	1	L
2	3	W	1	L
3	2	W	1	L
2	3	W	1	L
1	3	L	1	W
3	2	W	1	L
1	3	L	2	L
1	2	L	1	W
2	3	W	2	W
2	3	W	2	W
3	2	W	3	W
3	2	W	1	L
1	2	L	1	W
3	2	W	1	L
1	3	L	1	W
3	2	W	1	L
3	2	W	1	L
1	3	L	2	L
1	2	L	3	L
2	3	W	1	L
1	3	L	2	L
1	3	L	1	W
2	3	W	1	L
2	3	W	1	L
3	2	W	1	L
1	3	L	2	L
1	2	L	1	W
1	2	L	1	W
3	2	W	1	L
3	2	W	3	W
3	2	W	3	W
1	2	L	1	W
3	2	W	3	W
1	2	L	1	W
2	3	W	2	W
2	3	W	1	L
1	2	L	1	W
3	2	W	1	L
1	3	L	2	L
1	2	L	1	W
3	2	W	3	W
1	2	L	3	L
1	2	L	1	W
3	2	W	1	L
3	2	W	3	W
1	2	L	1	W
3	2	W	1	L
3	2	W	3	W
1	3	L	1	W
2	3	W	2	W
3	2	W	3	W
3	2	W	3	W
3	2	W	1	L
3	2	W	1	L
1	2	L	1	W
2	3	W	1	L
3	2	W	1	L
3	2	W	3	W
1	2	L	1	W
1	3	L	1	W
2	3	W	2	W
3	2	W	3	W
3	2	W	3	W
3	2	W	1	L
2	3	W	1	L
2	3	W	2	W
2	3	W	1	L
1	3	L	2	L
3	2	W	1	L
3	2	W	1	L
1	2	L	3	L
2	3	W	2	W
1	2	L	3	L
2	3	W	2	W
3	2	W	1	L
2	3	W	2	W
2	3	W	1	L
3	2	W	3	W
2	3	W	2	W
1	2	L	3	L
3	2	W	3	W
1	3	L	1	W
3	2	W	1	L
2	3	W	2	W
3	2	W	1	L
3	2	W	1	L
3	2	W	3	W
3	2	W	3	W
3	2	W	1	L
2	3	W	2	W
2	3	W	1	L
2	3	W	1	L
3	2	W	1	L
2	3	W	2	W
1	3	L	2	L
2	3	W	2	W
3	2	W	1	L
2	3	W	1	L
1	2	L	3	L
1	3	L	1	W
1	3	L	2	L
2	3	W	1	L
3	2	W	1	L
2	3	W	2	W
3	2	W	3	W
1	3	L	2	L
1	2	L	1	W
1	2	L	3	L
1	3	L	2	L
2	3	W	1	L
1	2	L	1	W
3	2	W	1	L
2	3	W	2	W
1	2	L	1	W
3	2	W	3	W
Checking to make sure the RNG is okay:

Car = 1, Open = 1 : 0 instances
Car = 1, Open = 2 (scenario 1a): 1673 instances
Car = 1, Open = 3 (scenario 1b): 1640 instances
Car = 2, Open = 1 : 0 instances
Car = 2, Open = 2 : 0 instances
Car = 2, Open = 3 : 3379 instances
Car = 3, Open = 1 : 0 instances
Car = 3, Open = 2 : 3308 instances
Car = 3, Open = 3 : 0 instances

Total wins by switching: 6687
Total wins by picking randomly: 5054

As a matter of fact, let me do this a bunch of times (just refreshing).

Code:
Sw%	Rnd%
6646	4903
6627	5044
6722	4943
6717	5001
6600	5045
6647	4973
6567	4992
6721	4970
6614	4922
6724	4943
6741	4934
6635	5054
6755	4980
6608	5068
6650	4908
6607	5079
6641	5000
6688	5089
6661	5020
6637	4930
6651	4993
6649	4989
6701	4956
6705	4928
6617	4970
6761	5154
6587	4976
6690	5008
6660	4920
6682	5037
6663	4996
6818	5014
6634	5035
6755	5046
6705	4896
6711	4932
6641	4938
6687	4992
6672	5048
6686	4985
6736	4984
6607	5127
6715	5012
6579	5078
6643	5130
6641	5120
6644	4987
6739	4951
6601	5023
6665	5051
6644	5017
6736	5026
6654	5038
6578	5029
6697	4994
6730	4939
6621	5038
6657	4911
6683	4981
6608	5052
6681	4995
6600	5060
6652	5028
6637	5065
6622	5040
6604	5024
6713	5016
6575	4891
6756	5000
6643	4999
6622	4925
6687	5026
6734	4990
6683	4995
6665	4946
6680	4960
6554	4998
6571	5065
6677	5062
6793	4974
6598	4975
6701	4997
6754	4996
6673	5076
6696	5073
6673	4959
6682	4999
6670	4931
6718	4949
6665	4970
6617	5077
6682	4922
6721	4942
6752	5037
6740	5031
6604	4996
6580	4985
6695	4991
6619	5083
6637	4994
6586	4927
6693	4979
6690	4935
6663	4963
6706	4981
6669	4886
6708	4973
6652	5012
6714	4998
6639	4932
That's 1.09 million hands of Monty Hall that say switching will win 0.667 +/- 0.011 of the time and picking randomly will win 0.500 +/- 0.011 of the time.
 
#24
this example is a typical one for probability in maths..you have got three doors probability for each is 33,33% you choose d1 there is 33,33% probability that you chose the right doors and 66,66% that you didnt choose the rght doors..so than the moderator opens the d3..2 doors are left-d1-theres 33,33% that car is inside and d2-theres 66,66% that car is there..so of course 66 is better than 33 so you will change your choose
 

Cherry7Up

Well-Known Member
#25
callipygian said:
That's 1.09 million hands of Monty Hall that say switching will win 0.667 +/- 0.011 of the time and picking randomly will win 0.500 +/- 0.011 of the time.
The reasoning still doesn't make sense to me, but thanks for running the sim--pretty convincing results.
 
#26
Website Game

Sorry to beat a dead horse here, but I was just thinking about this.

Door 1 represents 33%.

Doors 2 & 3 represent 66%.

You choose door 1, and door 2 is unveiled.

Doors 1 & 3 are the only doors left.

You only had a 33% chance of guessing right the first time so your guess was probably wrong.

You want to move from the 33% side to the 66% side. The 66% side includes doors 2 & 3, and now you know it is not door 2.

That is why switching increases your odds. The odds were against that you guessed right the first time since it was only 33%.

Here is an online game to play:

http://www.mste.uiuc.edu/reese/monty/MontyGame5.html
 

ace157

Well-Known Member
#27
Blackjacker2 said:
Sorry to beat a dead horse here, but I was just thinking about this.

Door 1 represents 33%.

Doors 2 & 3 represent 66%.

You choose door 1, and door 2 is unveiled.

Doors 1 & 3 are the only doors left.

You only had a 33% chance of guessing right the first time so your guess was probably wrong.

You want to move from the 33% side to the 66% side. The 66% side includes doors 2 & 3, and now you know it is not door 2.

That is why switching increases your odds. The odds were against that you guessed right the first time since it was only 33%.

Here is an online game to play:

http://www.mste.uiuc.edu/reese/monty/MontyGame5.html
good explanation; that always made sense to me, but i never understood it... thankz
 
#28
Its sooooo simple

Here ya go....you all obviously need "visual" confirmation! This is what you do....
Get another person..take a standard 52 deck of card...pull out 3...for example 8dia 9dia A spa.....
Mix them up....set them out on a table 3 across....you look for the A...have someone pick 1 spot of the three....afterwards turn over one of the NON A cards and allow that person to change there pick...
Keep track of how often they win (get the Ace AFTER they are allowed to switch)
You will see that by CHANGING to the non selected card after the card is exposed...they would win at LEAST 66.6% of the time....

ITS SOOOOOO SIMPLE
 
#29
This is how I began to understand this

Let's come a little closer to the modern day, we will play "Let's Make a Deal." If there were 1,000,000 cases to choose from and you chose 177 (with a 1:1,000,000 chance) and then started eliminating the cases one by one, and at the end all that was left was your choice #177 and #234,876 would you change then?
Of course you would! On the blind shot you took you had a 1 in a million chance! You are more than likely wrong! But since 999,998 have been eliminated your probability still stays the same when you initially chose #177, the variable being that #234,876 COULDN'T be eliminated because that is where the money is!
So utilizing this example I feel it is much more clear that you should change, especially if dealing with more than just 3 choices.
 
Top