4 ms·

It didn't seem like much of a paradox to me, since game B is really two different games, and interleaving plays of game A changes the likelihood of playing B1 v

by adamc 14y ago

It didn't seem like much of a paradox to me, since game B is really two different games, and interleaving plays of game A changes the likelihood of playing B1 vs. B2. Interesting, perhaps, but not terribly unintuitive.

SonicSoul 14y ago
the un-intuitive part is that the odds supposedly flip in your favor just by alternating 2 games with negative odds.
- ErrantX 14y ago
  I'm not so sure; when you read the description for Game B it should be clear that it's odds rely on your balance, an external factor. As that is something that can be manipulated then it isn't a major leap, I think, to the idea that combinations of the two games would produce different outcomes - and that some outcomes would be positive. Whilst fun; I rather preferred the latter part of the post - it reminded me of a brilliant book I had as a kid with many such puzzles in it :)
Almaviva 14y ago
I agree. Imagine that time is used (instead of current balance), and A pays out if the current second is divisible by three, and B pays out if it is one more than a multiple of three. A and B are both losing games if played every second, but it's not hard to combine them to win. And few people would call this a paradox.
dclowd9901 14y ago
Right. When I got to the part about Game B, my first thought was, "Wait, this isn't what you described in the story above..." What a crock. I think the Monty Hall Problem (http://en.wikipedia.org/wiki/Monty_Hall_problem http://en.wikipedia.org/wiki/Monty_Hall_problem) is far more vexxing and interesting.
- pulplobster 14y ago
  I think the Monty Hall Problem is also extremely misleading in its formulation. Take Wikipedia's formulation for example: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? What's not being explicitly said here is that the host knows what's behind the doors (this part is said) but that he also always chooses the goat. With that information, it's pretty clear that when the contestant first made the choice of a door, the probability of getting the right one was 1/3. The probability that the right door is among the other two is 2/3. NOW however, the host removes the one of (or the only) wrong option among those two doors. The thing to realize is that the host opening one of those doors does not give us ANY new information that would change the distribution. Therefore, the other door that the contestant didn't pick must have the probability 2/3.
  - dclowd9901 14y ago
    It's true that that's the crux of the Monty Hall problem, but it's also the understood nature of it. You just don't realize how much impact that would have on the outcome unless you actually start delving into the outcomes.

by adamc 14y ago

SonicSoul 14y ago

the un-intuitive part is that the odds supposedly flip in your favor just by alternating 2 games with negative odds.

ErrantX 14y ago
I'm not so sure; when you read the description for Game B it should be clear that it's odds rely on your balance, an external factor. As that is something that can be manipulated then it isn't a major leap, I think, to the idea that combinations of the two games would produce different outcomes - and that some outcomes would be positive. Whilst fun; I rather preferred the latter part of the post - it reminded me of a brilliant book I had as a kid with many such puzzles in it :)

Almaviva 14y ago

I agree. Imagine that time is used (instead of current balance), and A pays out if the current second is divisible by three, and B pays out if it is one more than a multiple of three. A and B are both losing games if played every second, but it's not hard to combine them to win. And few people would call this a paradox.

dclowd9901 14y ago

Right. When I got to the part about Game B, my first thought was, "Wait, this isn't what you described in the story above..." What a crock. I think the Monty Hall Problem (http://en.wikipedia.org/wiki/Monty_Hall_problem http://en.wikipedia.org/wiki/Monty_Hall_problem) is far more vexxing and interesting.

pulplobster 14y ago
I think the Monty Hall Problem is also extremely misleading in its formulation. Take Wikipedia's formulation for example: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? What's not being explicitly said here is that the host knows what's behind the doors (this part is said) but that he also always chooses the goat. With that information, it's pretty clear that when the contestant first made the choice of a door, the probability of getting the right one was 1/3. The probability that the right door is among the other two is 2/3. NOW however, the host removes the one of (or the only) wrong option among those two doors. The thing to realize is that the host opening one of those doors does not give us ANY new information that would change the distribution. Therefore, the other door that the contestant didn't pick must have the probability 2/3.
- dclowd9901 14y ago
  It's true that that's the crux of the Monty Hall problem, but it's also the understood nature of it. You just don't realize how much impact that would have on the outcome unless you actually start delving into the outcomes.