[d20] What don't you know? (free pdf books)

[Kae'Yoss]

I win? Woohoo. I guess that's what they said when they told me that I will need all that maths stuff even after I'm done with school

 

[reveal]

I win? Woohoo. I guess that's what they said when they told me that I will need all that maths stuff even after I'm done with school

Actually, they said math was very important but you weren't paying attention... as usual.

 

[fafhrd]

It's all statistics. No matter how you want to think about it, it's still 33% on one and 66% on the other. This has been argued to death (I first saw the Monte Hall/Let's Make a Deal conundrum in 1998). There's no point in arguing because it's all been done before and no one has changed their mind.

The point I was trying to make is that The Le's scenario is distinct from the Monte Hall version because the dragon restates the problem as quoted above. The elaboration leads to a second problem with a separate set of odds.

 

[IcyCool]

The point I was trying to make is that The Le's scenario is distinct from the Monte Hall version because the dragon restates the problem as quoted above. The elaboration leads to a second problem with a separate set of odds.

Not at all, it's exactly Monty's version. You pick a door, he reveals a bad door and then says, "You can keep your door, or go for what's behind door number [whatever number the remaining door is]."

You would be correct if the Dragon initially presented the problem as, "Pick one of these two doors."

You are trying to discount the initial setup, which you can't do, because it is part of the problem.

You can try it at home as well, do the Monty Haul setup 100 times, and the 50/50 setup 100 times. Observe the results .

 

[reveal]

The point I was trying to make is that The Le's scenario is distinct from the Monte Hall version because the dragon restates the problem as quoted above. The elaboration leads to a second problem with a separate set of odds.

Not at all. In Let's Make a Deal, he would do exactly the same thing. He would give you a choice of the other two doors (let's say 2 and 3). Whether or not you know specifically what's behind door number 1 is irrelevant statistically. The odds are the same regardless. That's where people get confused because, logically, one would think that once you are presented with two choices, from the original 3 and after being told what the 1st choice is, it would be 50/50. But, statistically speaking, the odds don't change.

And this is why I don't like higher level math.

 

[fafhrd]

I have a suspicion that phrasing plays a larger part in this than is being admitted, but in the interest of not dragging this out I'll concede to the weight of opinion.

 

[Macbeth]

Huh. I hadn't seent his thread, but this looks like fun. I'll have to watch out for postings.

 

[Land Outcast]

Couldn't help but notice the dragon said "the death you avoided", taking it as true, then I'll keep the chosen door.

 

[TheLe]

...

Look, all of you doubters, just do me a favor okey?

Expand it to 5 doors, and play it with a friend. Select one door number as the treasure and write it down, but do not show it to him.

Let the friend choose a door. Then eliminate 3 unchosen doors, each of which MUST have death behind it.

Then give your friend the option to keep the initially chosen door or switch to the last door.

Is it really 50/50?

Play this game 10 times.

If it is truly 50/50, then you will know. But I guarantee you that nearly every single time, the initially chosen door will be death, while the last door will be the treasure.

Go ahead. Is it really 50/50?

Play it 10 times and prove me wrong.

~Le

 

[jerichothebard]

Thanks for the prize. I sent you an email - the address starts with "ianc"

The answer to the dragon question seemed odd to me so I looked up some references and reviewed the proofs and I'm pretty sure the ones I saw were wrong. My calcs show that you have a 50% chance of winning. I wasn't elegible to enter, but if anyone reading this knows Bayesian analysis I'd be interedted in a critique of my calculations.

Nope. I ran an analysis of it, with 20000 iterations of it as an automated script, and it came within 1% of being 2/3 winning for switching. I don't know Bayesian Analysis, but emperical results don't lie (in this case, at least).

If you're interested, you can try it yourself at http://www.maestrakara.com/srjosh/autogame.php. Note that the iterations are capped at 1000 per trial, please don't abuse my bandwidth.

There's also a detailed examination of it in this thread: http://www.enworld.org/showthread.php?t=96512