Riddles Round 2

[Eric James Stone]

Your solution works.

It's not the solution I was looking for, but I think that's because I'm not setting the limitations correctly.  I guess I'll have to try to locate the exact wording of the original puzzle the i read.

[Firemeboy]

Ok, new puzzle.

You are on death row, but it is customary for the governor, on the night of execution, to let you play a game of chance to try to get out of your sentence.

The governor and the prison guard brings two buckets to you.  One bucket is filled with 50 white golf balls, the other bucket is filled with 50 orange golf balls.  The golf balls are identical in every way except for the color.

The idea is that the guard will blindfold the governor, then the governor will pick one of the balls out of one of the buckets.  If it's white, you are saved.  If it's orange, you're toast.  In other words, you have a roughly 50/50 chance.

The caveat is that you are allowed to mix up the balls, if you wish.  However, when you are done mixing them up, there must still be 50 white balls, and 50 orange balls.  You can't eat or paint some of the orange balls.

Is there a way to increase your chance of living through the night?

[Archon]

Take 49 of the white balls and put them in the barrel with the orange balls. That way, if he picks one barrel, you have a 100% chance, and if he picks the other, you have about a 49% chance. In all, I believe that gives you about a 75% chance.

[Eric James Stone]

Take 49 white balls and put them in the bucket with the 50 orange balls.  (If the bucket will not hold 99 balls, then put as many white balls as possible in with the orange balls.)

Your chances are almost 75% (assuming the buckets can hold 99 balls).

The Governor then has a 50% chance of picking the bucket with only one white ball.

The other 50% is split between white balls (49/99) and orange balls (50/99).  That works out to about 24.7% for white and 25.3 for orange.

Thus the total probability the governor will pick a white is about 74.7%.

Of course, if the fewer balls the bucket will hold, the less you can increase your chances.

Also, this doesn't take into account whether the governor has a tendency to take a ball off the top or to reach down and take a ball from deep inside the bucket.  Knowing of such a tendency would allow you to increase the odds even further in your favor.

Good puzzle, firemeboy.  I hadn't seen that one before.

[Eric James Stone]

And I see Archon beat me to it.

[Archon]

Only a little.   Someone else can take my turn, as I can not currently remember any riddles that would require any amount of thought.

[Firemeboy]

That is the correct answer.  Nicely done.

[Peter Ahlstrom]

I don't think it's a very good solution... If the governor puts his hand into the bucket with only one ball, he will probably feel that there's only one ball, and thus NOT pick that ball, but instead take a ball out of the other bucket--so you in fact only have a 49/99 chance of being successful--unless you fake the governor out by putting an orange ball in a bucket by itself; then you have a 50/99 chance of survival.

Well, that scenario isn't necessarily true, but the point is that you definitely don't have close to a 75% chance of survival. It may be slightly higher than 50%, since the governor may have played this game before and thus might be assuming you'll try to fake him out, but it's not near 75%.

[Fellfrosch]

You're assuming that the governor wants you to die. Though you are correct in saying that the human factor destroys any sense of exact probability here--we can't know or control the behavior of the governor. Who's to say he won't just dump them all out on the floor and pick one that's rolling around?

[Legion]

statistly it is close to 75%, but one thing that you can not add into satistics is the pure randomness of a persons thoughts.

[The Holy Saint, Grand High Poobah, Master of Monkeys, Ehlers]

The only thing you have to do to control for that is say there's a rule that he has to choose a bucket then stick with it. It could be part of the game. *shrug*

[Firemeboy]

True, you can never account for human will.  But in this case the governor really doesn't care.  He will pick one pucket, and then pick a ball at random from that (deep in, on top, only one, etc.).  So taking the human variation out of that, this is statistically the best move to make.

[Peter Ahlstrom]

Some governor...he should be impeached for playing with people's lives like that. Not to mention disrespecting the families of the murder victims.

[Skar]

I agree with Ookla.  Firemeboy should be ashamed for behaving that way as a governor.  In fact, I think he should be banned from the forums.

Arrrrr.

[Eric James Stone]

he should be impeached for playing with people's lives like that.

Actually, under state law, the governor can only be removed from office if the chief justice of the state supreme court reaches into a bucket and pulls out an orange golf ball...