New Sailing puzzle

[Rich Smith]

You know...at first blush I would have agreed with Chip...but I would have been wrong...try it for yourself...go to http://www.stat.sc.edu/~west/javahtml/L ... aDeal.html at play the "Let's make a deal game...

I played 2 hundred times (yes, I need to get a life)

100 times I switched and won 76 times
100 times I didn't switch and won 35 times

I admit that it isn't quite 2/3 vs 1/3 but the trend is moving in that direction...I'm convinced that if I played each game 1000 times I would end up winning 2/3 of the times that I switched and 1/3 of the times that I didn't.

[DLT]

Again, there is a fundemental difference between the "let's make a deal" simulations and the stated problem.

In the simulations, you are getting information about the two doors you didn't choose. The door you get information about is chosen specifically, because you didn't choose it, if that makes sense.

In the stated problem the ship you are going to get information about is chosen before Chirs' initial choice. There is nothing conditional about it.

Furthermore, as Chip points out, at the time Chris makes his second choice, it is a 50/50 question. Namely, stay with first choice or go with the other ship that might have food. At that point in time, you know only one of the two remaining ships has food. Because there is nothing conditional here, you know absolutely nothing more about those two ships.

Father Guido's help reduces it from a "1 in 3" to a "1 in 2". It was a 1/3 before Father Guido pops up, but it is a straight 1/2 after...

[kmclemore]

Thats only true 99 44/100% of the time Kevin

The last time I saw someone associated with 99 44/100% she ended up in a porn movie.

[Catigale]

Its 1/3 if you dont switch, 2/3 (not 1/2) if you do.

In the stated problem the ship you are going to get information about is chosen before Christophers' initial choice. There is nothing conditional about it

The information is conditional, the condition is not obvious. Father Guido is not on the ship you chose, and thats important, and by design of the puzzle - that information occurs AFTER you choose your first choice...ie, it is conditional on your first choice.

If you were told your first choice did not have the food, you would then have a 50-50 chance on a second guess (and therefore wouldnt matter if you switched or not.

Kevin - did the Lets Make a Deal show give the people a chance to switch after showing them a door, or just show them one of the choices they didnt pick? I was raised without television (explains a lot of my anger) so I dont recall this show directly...

[DLT]

Its 1/3 if you dont switch, 2/3 (not 1/2) if you do.

Maybe I'm just dense. But, at the point you decide to switch or not, you know the food is supposed to be on one of two ships. The food is either on the ship you chose or on the other ship, since Guido says it is not on his ship. So, you are, in effect, choosing one of two possible ships... How is that not 1 in 2?

If you were told your first choice did not have the food, you would then have a 50-50 chance on a second guess (and therefore wouldnt matter if you switched or not.

Huh? If I'm trying to make an ocean voyage, you bet it matters to me that the ship I've chosen doesn't have any food. Yes, I have a 50-50 choice, or a 1 in 2, but I am forced to switch. I know the ship I've chosen doesn't have food, so I MUST chose one of the other two.

Ultimately, your second decision is the same in both cases. You are presented with three ships, one of which does not have food. Since you know that a specific ship doesn't have food, only a fool would even consider that ship. Thus, anyone who likes to eat, is not faced with three options. Rather, they are faced with 2 options.

You are asked to assume that only one ship has food. Thus, only 1 ship will prove successful.

Hence, the probability with respect to the second choice, after one possibility is eliminated, must be 1 in 2.


If it were 2/3, then two of the ships would have to have food and you'd still have to be considering making your voyage on that one ship that you know doesn't have food...

Bottom line, in this problem as stated, the first choice 1 in 3. The second choice is 1 in 2.

[Frank C]

Kevin - did the Lets Make a Deal show give the people a chance to switch after showing them a door, or just show them one of the choices they didnt pick? I was raised without television

Monty Hall always added the new information AFTER the contestant had already made the initial 1-in-3 choice. Both puzzles clearly offer two "wrong doors." Regardless of the contestant's first guess, Monty edits the circumstances by demonstrating either:

• * the single remaining wrong door (assuming initial failure)
  * or one of two remaining "wrong doors" (assuming initial success)

The fact that Guido's knowledge is less conprehensive than Monty's does not alter the essence of the puzzles. In both cases, Chris and the contestant are still presented with identical circumstances, identically imperfect knowledge, and identical probabilities ... which probabilities favor abandonment of the initial choice.

[Catigale]

DLT - I was confusing in that last post...

So, you are, in effect, choosing one of two possible ships... How is that not 1 in 2?

The point of the puzzle is that being faced with choosing one of three ships, getting some more information, then being faced with choosing between two ships is not the same as walking up and just choosing between two ships ..so the probability of success can also vary, and it does.

In the other scenario, where you are told the ship you have chosen does NOT have the food (which is NOT the original puzzle), my statement that it doesnt matter if you switch was wrong. I meant to say, it doesnt matter which of the other ships you choose, the odds then are 50-50. I did smuggle in the assumption that the player isnt a moron and once told his first choice didnt have food, he would choose one of the other ships.

The key to the original puzzle is that you get information about one of the ships that you did not choose, and that this information is that the food is not on that ship.