Posted Tue Sep 13, 2005 4:16 am GMT by Muck
Sorry if you’ve heard it already and I know it’s not poker related but I just though it was cool.
You’re in a room with 3 doors.
1 is the exit
2 lead to certain death
You randomly pick a door.
Before you open it, are you sure? Do you want to change and pick one of the other 2?
Answer:
Change doors.
Reason:
1 door = life. 2 doors = death.
So the chance that the current door is going to result in your death is 2/3.
Which means the likelihood is that one of the two remaining doors is the exit.
By changing you give yourself a 1/2 (50:50) chance.
Result:
You happen to pick the wrong door and die anyway.
Moral:
Don’t play death door puzzle games.
Sorry got of side tracked there.
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Posted Tue Sep 13, 2005 7:31 am GMT by wEbMaStEr
lol
complete bullshit but pretty funny 
Posted Tue Sep 13, 2005 3:33 pm GMT by Loonbat
Yup - pretty poor math being displayed.
Two scenarios:
Door you're at = death; switch and 50% chance of life; chance of your being at the death door is 2 in 3, so EV for life (by switching) is 50% x 2/3 = 0.33 (approx)
Door you're at = life; switch and 0% chance of life; chance of your being at the life door is 1 in 3, so EV for life (by switching) is 0% x 1/3 = 0.00 (exact)
Overall EV for life is 0.33 (approx) ... why the hell do I play these death games?
Posted Tue Sep 13, 2005 4:03 pm GMT by Geno
I once saw some program where they tried to justify changing in a 1 in 3 game, they were also idiots 
Posted Tue Sep 13, 2005 4:05 pm GMT by Sean_in_NJ
| wEbMaStEr wrote: | | complete bullshit but pretty funny |
| loonbat wrote: | | Yup - pretty poor math being displayed. |
Wrong on both counts. It's just a variation of the Monte Hall problem.
It's implied that you're shown one of the other doors after you make your first selection, right?
Posted Tue Sep 13, 2005 4:24 pm GMT by Loonbat
No ...
The difference is that they are shown one of the poor choices in the Monte Hall problem and therefore would not choose the door which has the goat (death). In this particular case, they are not shown a door behind which a negative consequence lies, thus the problem is in fact different. The odds are as I have stated them.
Posted Tue Sep 13, 2005 4:39 pm GMT by Iron Butt
... or from a more philosophical or logical standpoint, in the problem as posted changing your pick doesn't actually do anything, it's just as if you had never chosen at all. In the real version, you receive new information after your first pick, changing the situation and giving meaning to the second pick.
Extra credit: True or false: You should always choose the center box, because it's 2 to 1 that the prize will be in one of the end boxes. Since you will be shown one of the end boxes after you pick, this increases your odds by 1/3.
Posted Tue Sep 13, 2005 4:52 pm GMT by Geno
I swear this Monty Java Game is rigged:
http://www.shodor.org/interactivate/activities/monty3/
After 50 tries (ok, that is not a big sample), I got:
Games stayed: 30
Games won: 10
Percentage: 33%
Games switched: 20
Games won: 15
Percentage: 75%
Posted Tue Sep 13, 2005 5:33 pm GMT by Loonbat
| Iron Butt wrote: |
Extra credit: True or false: You should always choose the center box, because it's 2 to 1 that the prize will be in one of the end boxes. Since you will be shown one of the end boxes after you pick, this increases your odds by 1/3. |
False - being shown a box after you pick (which in no way influences your decision) still gives you a 1 in 3 chance of winning, assuming that the prize is evenly distributed over all 3 boxes.
Posted Tue Sep 13, 2005 5:57 pm GMT by Iron Butt
Ooook, fine... yes, the center box has no significance, it's 2 to 1 against on the first pick no matter which you choose. Fooled myself with that one for about 5 seconds when I was thinking about this LOL, thought I'd see if I could get anyone else to bite.
Your switch win percentage is a little high there Geno, maybe you're just lucky, or doesn't that make you unlucky since you're missing your first pick more than you should LOL.
Posted Tue Sep 13, 2005 6:05 pm GMT by Sean_in_NJ
| Loonbat wrote: | | False - being shown a box after you pick (which in no way influences your decision) still gives you a 1 in 3 chance of winning, assuming that the prize is evenly distributed over all 3 boxes. |
That is the Monty Hall problem exactly. In this case, you are certainly incorrect.
If you switch your selection after being shown one of the non-winners, you will win 2/3 of the time. If you do not switch, you win 1/3 of the time. Geno's numbers bear it out, even if he refuses to acknowledge it.
Posted Tue Sep 13, 2005 7:57 pm GMT by xDiamond_CutteRx
WTF have I been smoking to be stupid enough to get into such a room?
Posted Wed Sep 14, 2005 4:29 am GMT by Muck
| Iron Butt wrote: | | In the real version, you receive new information after your first pick, |
Okay, okay I wrote it from memory after someone told me it at lunch so I might have left some stuff (read: critical) out. People are so anal retentive it’s like they want every number to be right so the math to works 
Plan B
I’ll show you why it’s better to change doors through a 5 minute performance of modern interpretive dance. Death will be represented with black scarves and life with this candle.
Posted Wed Sep 14, 2005 11:14 am GMT by Loonbat
| Sean_in_NJ wrote: | | Loonbat wrote: | | False - being shown a box after you pick (which in no way influences your decision) still gives you a 1 in 3 chance of winning, assuming that the prize is evenly distributed over all 3 boxes. |
That is the Monty Hall problem exactly. In this case, you are certainly incorrect.
|
Pffttzz - go reread what the extra credit problem stated and then come back and type (100 times) "I will reread until I understand ... " You don't get shown a box and then a chance to switch. You constantly pick the center and remain with that pick.
Posted Wed Sep 14, 2005 12:00 pm GMT by Iron Butt
Sorry, I should have specified that I meant the real Monty Hall problem (where you have a first pick, a remaining negative option is shown, you are then given the option to switch), I thought it was given that we were talking about that now. Picking the center box/door/whatever has no real significance in either version.
Posted Wed Sep 14, 2005 12:30 pm GMT by Sean_in_NJ
| Loonbat wrote: | | Pffttzz - go reread what the extra credit problem stated and then come back and type (100 times) "I will reread until I understand ... " |
Well, according to subsequent posts by Muck and Iron Butt, it appears that I was the only one who was able to discern the actual topic under discussion. To rely on the exact wording of a post, given the grammatical "liberties" we're exposed to on a daily basis here, is a bit optimistic. I suggest you come back and type (100 times) "I need to work on my inductive reasoning skills."
| Loonbat wrote: |
False - being shown a box after you pick (which in no way influences your decision) still gives you a 1 in 3 chance of winning, assuming that the prize is evenly distributed over all 3 boxes. |
This statement is still grossly incorrect, regardless of context.
Posted Wed Sep 14, 2005 12:50 pm GMT by Loonbat
| Sean_in_NJ wrote: |
| Loonbat wrote: |
False - being shown a box after you pick (which in no way influences your decision) still gives you a 1 in 3 chance of winning, assuming that the prize is evenly distributed over all 3 boxes. |
This statement is still grossly incorrect, regardless of context. |
You yourself stated I was correct with the following:
"If you switch your selection after being shown one of the non-winners, you will win 2/3 of the time. If you do not switch, you win 1/3 of the time. ...
The rest is obvious and is left to the reader (ie it takes little induction to realize you argued my point for me).
Posted Wed Sep 14, 2005 1:06 pm GMT by Loonbat
| Sean_in_NJ wrote: | | Loonbat wrote: | | Pffttzz - go reread what the extra credit problem stated and then come back and type (100 times) "I will reread until I understand ... " |
Well, according to subsequent posts by Muck and Iron Butt, it appears that I was the only one who was able to discern the actual topic under discussion. To rely on the exact wording of a post, given the grammatical "liberties" we're exposed to on a daily basis here, is a bit optimistic. I suggest you come back and type (100 times) "I need to work on my inductive reasoning skills."
|
Furthermore, I respond to the actual conditions stated and perimeters set, not those that I purport or project, based on my own biases. I prefer sticking to the facts and deduction based on what is presented.
Inductive reasoning is a wonderful skill to have, however ... it showed us the earth was flat, the atom is the smallest divisible unit of matter, and that the sun travels around the Earth.
Posted Wed Sep 14, 2005 1:10 pm GMT by Sean_in_NJ
| Loonbat wrote: | | Furthermore, I respond to the actual conditions stated and perimeters set, not those that I purport or project, based on my own biases. I prefer sticking to the facts and deduction based on what is presented. |
Whatever you have to tell yourself, but congratulations nonetheless. You won an argument based on precepts that no one else was using.
Posted Thu Sep 15, 2005 12:45 pm GMT by BeerWench13
To hell with all of that math. Make someone else pick first. Then you have a 50/50 chance unless they choose correctly.
Posted Thu Sep 15, 2005 1:28 pm GMT by Geno
Odds are 1 in 3 no matter what you are shown. The end.
Posted Fri Sep 16, 2005 9:04 am GMT by zeroswarm
| Geno wrote: | | Odds are 1 in 3 no matter what you are shown. The end. |
Thank God for that. 
Posted Fri Sep 16, 2005 9:31 am GMT by Sean_in_NJ
| Geno wrote: | | Odds are 1 in 3 no matter what you are shown. The end. |
No, they're not.
| zeroswarm wrote: | | Thank God for that. |
Thanks for the stellar contribution, now go put your tin hat back on.
Posted Fri Sep 16, 2005 12:38 pm GMT by Loonbat
I have to agree with Geno - I've seen the picture of him wearing a "Harvard" shirt.
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