# brain teaser - what's your best move to win the ganja?

Discussion in 'Seasoned Tokers' started by highline, Oct 26, 2003.

1. Okay, let's say you're on a game show and there are three curtains in front of you, #1, #2, & #3. You get to choose one of the curtains and receive the prize behind it. Behind one of the curtains is a pound of superb hydro, behind the other two are empty baggies.

You decide to go for curtain #1. And to help you, the show now reveals where one of the empty baggies is - and it's behind #2. Now, you have the opportunity to either stay with curtain #1, or you can switch over to curtain #3. What's your best bet?

Answer: If you switch over to curtain #3, you double your chances of getting the ganja. While it may seem like the odds should be 50/50 whether you pick #1 or #3, it's not. When you pick one curtain out of three to have the ganja (ie. choosing #1), you have a one-third, or 33% chance, of picking the right curtain. If you take away one of the other two curtains (ie. #2), and then choose the remaining one (#3) to have the ganja, you have now chosen a curtain that has a 2/3 chance (66%) of containing it, and so you have doubled your odds. In other words, #3's chances of having the ganja doubled when we revealed a baggy behind #2.

I hope that makes sense. I'm not great at math.

- D.

2. but couldn't there also be an empty bag behind curtain three? If you eliminate curtain #2, your left with 1 bag between 2 doors still. What if you pick #3, and the show still reveals a bag in #2, does that mean your odds double if you choose curtain #1? I'm runnin on no sleep in past 24 hours, so my mind may be playing tricks with me, not letting me think straight ..lol.

3. yes, there is still a one-third (33%) chance that #3 has the other baggy. But it's twice as likely that it has the weed, which is why you want to switch over.

And you're right, you would also double your odds if you originally picked #3, they revealed #2 to have a baggy, and you then switched over to #1. Works the same way.

- D.

4. No it doesnt...if you have 3 doors, and u have to pick 1 ( 33.3% chance of getting it).....if 1 of the options is eliminated, then there are 2 choices left, and its a 50/50 shot, pickyour poison boss, thats all it is

5. nope, i think that reasoning is false.

because once you are shown where one o the empty bag is, you choose out of the two remaing curtains (unless of course you still have eyes on surtain #2) so you still have 1 out of two chances..

6. No, you actually double your odds from 33% to 66% by switching your choice. Here's why: if you pick #1, you have a 33% chance of choosing the prize. That means that the other two choices, #2 and #3, together represent a 66% chance (33% + 33%) of having the prize. Even if you take away one of those choices, the remaining one still retains that original 66% probability, it didn't drop to 50% just because you now know what was behind the other one. In other words, the odds didn't suddenly become 50/50 now that you're down to two choices, you're still working with the original odds involving all three choices.

Here's a good explanation by someone else:

http://www.mitan.co.uk/gameshow/gshw.htm

I also posted this puzzle on Overgrow (smoker's lounge) with the same subject line, you can read some good explanations over there too.

- D.

7. Exactly right ROSS

8. If you pick curtain #1, and then you take away curtain #2, the odds of the ganja being behind #3 are still 66%. If you then bring in a new contestant, and he only is given the choice of choosing from one of the remaining two curtiains, then yes, HE is making a 50/50 choice. But your odds are different since you started with three curtains. Just because you now know what's behind one of them doesn't change YOUR original odds, they're still 66% that it's behind #3.

9. keep popping those blood vessles as you get your mind around this! It took me awhile to understand it too. When you get to the point of choosing between #1 and #3, it's not a brand new 50/50 contest between two choices. You can't simply dismiss the effects of #2 as if it never existed. It represented a 33% chance (just like each of the others) of holding the prize, and so by taking it away you're obviously increasing the chances that the prize is behind the remaining curtains. But not equally. If you hold on to #1 then you retain just that original 33% chance. But if you switch over to #3, then you now have a 66% chance of finding the prize because you know that together, #2 and #3 represented a 66% chance of holding the prize, a fact that doesn't change even if you now know that it's not behind #2. In a scenario where you pick #1 and they take away curtain #3, you'd still want to switch over to #2 because again, it's part of a group that has a 66% chance of holding the prize.

I need a huge bong hit now.

10. u got a 33% chance at first and after they reveal u have a 50% chance. all there is too it.

11. I think it becomes a 50/50 chance once you eliminate one of the empties. It's either #1(50% of all remaining possibilities) or #3(50% of all remaining possibilities.) You don't know whether you picked the right one at first so that dosn't help you at all. I'm not understanding what exactly would make #3 more likely then #1??? It's either one or the other. 50/50.

edit: try this one out

There is a man looking at someone's picture and says:

Brothers and Sisters I have none,
but this man's father is my father's son.

Whose picture is the man looking at?

12. hmmm i just read this thread...and ummm im confused!!...my brain hurts!

13. its 50/50... lets do it with 3 being eliminated... ok, so you picked 1, and 3 was eliminated, so now one has weed, the other had a baggie, its a 50/50 chance.. the third curtain can be considered of as never existing... its a 50/50 chance... its starts with 33 + 33 + 33, so whatever you pick has a 33% chance... then one is eliminated... so now you have a 50 + 50 percent chance, curtain 2 doesnt somehow pick up the chances of #3

14. Ok, here's another source paper on the problem (also known as the "Monty Hall problem"). It has diagrams and shows you exactly why you are increasing your odds to 2/3 (66%) if you make that final switch. It also cites additional reference papers to prove these odds.

http://www.io.com/~kmellis/monty.html

Here's an excerpt - I changed the word "door" to "curtain" to match our example:

"The probabilities of your initial choice being correct (1/3, or 33%), and the remaining choices have to equal one. Therefore, the probability of the remaining choices have to equal one minus the probability of your initial choice. In this case (with three curtains), they have to equal 2/3 (because your first choice represents 1/3). Say a curtain isn't opened. Then, you would have two choices to switch to, and your chance of picking the correct one would be 1/2 * 2/3. Well, that's 1/3, just like your initial choice. But with only having one curtain to switch to, in this case you'll pick the remaining curtain - so that'd be 1 * 2/3. And that's a probability of 2/3."

15. Forget that, I bum-rush both remaining curtains tripling my chances to 100% and run out the back with the weedbag in my hands scot-free. Werd.

-viperware-

16. OK Matheteers,
When door number 2 was eliminated, the 33.333 chance
was divided between 1 & 3, giving each a ~50% chance.
Why would #3 get the whole 33 from 2? It is not is a separate universe (or SET as the math geeksters say)
and any redistribution would go to the remaining equally.

I want to be a contestant or at least a member of
the studio audience.

OT

17. Well i won so send me my Superb Hydro or im gonna sue... lol

18. How is it that you get to win? I don't see any guesses from you. Your evidence will never stand up in court. Let all of those who gave right answers sue if they don't get their weed.