addams wrote: There is no such thing as an Unbiased Jury.
Scuttlemutt wrote:[spoiler]I think I see the similarities to a Monty Hall problem. Imagine the reverse of the usual scenario; There's 6 doors with 5 cars behind it, and one door is empty. You pick one door, and then he reveals the other doors until it's down to just your picked door and the empty door. Should you switch doors? The problem with 5 empty doors and 1 car suggests that to get a car, your chances are greatest if you do (original pick is 1/6 of being right); But doesn't this imply that the reverse scenario has the reverse solution too (don't switch, original pick is 1/6 of being wrong)?
Now just substitute doors with wands, cars with dragons, and empty doors with toads, and remove the option of switching to just figure out if your original pick was a correct choice after all. Doesn't the situation imply that it is still more likely that you picked a Dragon? (3/5 odds)
Yakk wrote:The usual problem with this kind of logic puzzle is that it doesn't include information required to solve it.
Describing the sequence of events that happen is not sufficient to determine the distribution of probability.
As an example, suppose you know (are 100 certain) that the last wand is a frog wand. And when you picked a wand, you picked the last wand. This fits the described events, yet in this case the probability that you summoned a frog is 100%. Similarly, if you knew the first wand was a dragon wand, and you picked it, then the probability you summoned a dragon is 100% -- and this also fits the described events.
So to solve this problem, we need a description of the algorithm that each of the wizards used to select their wand. Now, we could invent an algorithm -- but that makes this a mind-reading puzzle rather than a logic puzzle. The Monte Hall puzzle has a similar problem.
It is true that entire classes of algorithms that pick wands (or doors) lead to the same result. But there are classes of algorithms that are not restricted by the description that lead to results that don't agree. So short of assigning a probability to each algorithm (either explicitly, or implicitly by picking one and saying that is the one that is used), the question lacks sufficient information to answer.
This is also the reason why you don't place bets with magicians.
Making a bet with real cash would not be foolish at all. It would be foolish if you made the bet with the wizards who were picking up the wands, or anyone who could control the outcome.Yakk wrote:The point is that you cannot, from the observations described, exactly determine the probability you summoned a dragon. Ie, if you where in an equivalent situation, making a bet with real cash at 1:3 or 1:5 odds would be foolish, as the described events aren't sufficient to generate enough knowledge about the odds of the situation. If you disagree with this and think you can build a strong probability model from a description like the above, would you like to pick a pea from under a shell?
mfb wrote:An interpretation which cannot give you a probability that you picked a dragon wand, given the information you have, has bad limits to its applicability.
We cannot say that the 345,876,912th digit has a ten percent probability of being a 3.
Halleck wrote:4 wands will produce a dragon. 2 will produce a frog.
What is the probability you conjured a toad.