“I am a time traveller!” said the time traveller. “Bullshit!” said I. “I will prove it to you. Get a fair dice. Color the side 1,2 and 3 as red. Color the sides 4 and 5 as green. And finally colour the side 6 as blue.” I did as the traveller asked.
“Now I will write down the color which you will roll” said the traveller and wrote down something on a piece of card which was placed face down so I could not see what was written.
“Roll the die!” the time traveller demanded. I did. “now watch this!” the traveller said and turn over the card.
The card showed a word correctly described the color of the side of the dice which I rolled.
Question: Assuming the time traveller is a Fraud, what is the probability of writing down the correct result on the card before I rolled the dice?
depends on what’s their strategy (i.e distribution of words written down)? Clearly the most probable color would be red and that just means
1/2, in any case, it would be the
P_red * 1/2 + P_green * 1/3 + P_blue * 1/6 each
P depends on how this fraud is designed? (
Ps adds to
1 of course, so clearly it means
P_red == 1?)
Conceptually, I would look for the mixed strategy Nash equilibrium of the zero-sum game. It’s a nice intro game theory exercise.
I don’t think there’s game theory here, roller can’t control the die
Good point, I somehow thought that the roller writes something down too (for no good reason).
In that case, I think the best strategy is to write down the most probable color, and get it right 1/2 of the time.
But with puzzles like this, there is always some underspecified ingredient, which I usually miss.
The time traveler didn’t write a color, but a description. If there is an alternate, ambiguous description, used, maybe the time traveler added the final piece of information after showing the card, to desambiguate the result to whatever color is rolled