# Last puzzle of 2019

“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? (`P`s 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.

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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

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