Colour of your HAT ???

Originally posted by Palynka
But then you don't know what the colour of your hat is, if you're not sure.

Let's try to write up the strategy (symmetric across opponents):

1) As long as you don't value the death of your opponents, then you'd say the colour of your hat immediately when you deduce it.
2) If you're not sure, then you shouldn't say anything.

Since this is val ...[text shortened]... ing to be pedantic here, I'm interested to see this through since I like game theory.

This was solved ages ago there just seem to be a few people here who cannot admit when they are wrong: I was wrong I admitted it and got over it.

Originally posted by demonseed
This was solved ages ago there just seem to be a few people here who cannot admit when they are wrong: I was wrong I admitted it and got over it.

Although I usually agree with that, I would like to see how far his line of reasoning can go as I find it interesting...

Originally posted by Palynka
Although I usually agree with that, I would like to see how far his line of reasoning can go as I find it interesting...

It could have been avoided had the setter added that the princes were fair as well as intelligent.

Originally posted by Palynka
But then you don't know what the colour of your hat is, if you're not sure.

Let's try to write up the strategy (symmetric across opponents):

1) As long as you don't value the death of your opponents, then you'd say the colour of your hat immediately when you deduce it.
2) If you're not sure, then you shouldn't say anything.

Since this is val ...[text shortened]... ing to be pedantic here, I'm interested to see this through since I like game theory.

And how do you determine the colour of your hat? If you are unable to decide what colour of hat you have, then by your steps you have lost. Instead act in such a way as to have your opponents lose first, and therefore grant you a win. I couldn't say anything, but maybe I would make eye contact with an opponent and gesture with my eyse that his hat is the same colour as his opponents. If this wasn't true, they might both guess that they have the same colour hat and be killed. If they had the same colour hat I might stare and shake my head to indicate that they don't have the same colour hat.

My scheme requires you to have no value for your opponents life, but you don't necessarily need to value the death of your opponents.

Of course this is a silly way of going about it, but is the only way you could win if you could not logically determine your hat colour. And also the only way to win if you know that your opponents DO value your death.

Originally posted by Gastel
And how do you determine the colour of your hat? If you are unable to decide what colour of hat you have, then by your steps you have lost. Instead act in such a way as to have your opponents lose first, and therefore grant you a win. I couldn't say anything, but maybe I would make eye contact with an opponent and gesture with my eyse that his hat is the s ...[text shortened]... t colour. And also the only way to win if you know that your opponents DO value your death.

I disagree by the reasons I've mentioned before.

If you don't say the colour of your hat, then you don't know with certainty what colour it is. That is information is enough for the necessary extrapolation. All one needs to know is that the opponents aren't sure of what their hat is.

Originally posted by Palynka
I disagree by the reasons I've mentioned before.

If you don't say the colour of your hat, then you don't know with certainty what colour it is. That is information is enough for the necessary extrapolation. All one needs to know is that the opponents aren't sure of what their hat is.

First, you can know the colour of your hat without opening your mouth (unless you count by mumbling...) And what tells you that your opponents don't know the colour of their hats?

Originally posted by Gastel
First, you can know the colour of your hat without opening your mouth (unless you count by mumbling...) And what tells you that your opponents don't know the colour of their hats?

If you "know", the best strategy is to say it immediately. Waiting only increases the chance someone else is able to "know" or guess correctly.

I think we're running in circles.

Originally posted by Palynka
If you "know", the best strategy is to say it immediately. Waiting only increases the chance someone else is able to "know" or guess correctly.

I think we're running in circles.

Except that in order to "know" the answer the others have to not "know" their answer. And there is also the assumption that they are reacting appropriately. I would not trust another to give me information which could potentially kill me if it is incorrect; especially when we are competing. So if we ever play a game of chess and you state "for victory, move your king to e4" at some point in the game, I would not consider your suggestion at all (as either a positive or a negative comment).