Red Card - Green Card Game

The Game Room
41

In the red card green card puzzle,
as presented, some people try to conclude that the chances of the red/red
card is 2/3. That is incorrect.

There is a different reason that the con man will make the offer.

there’s 1/3 chance the card is red/red
there’s 1/3 chance the card is grn/grn
there’s 1/3 chance the card is red/grn

or, stated differently, there’s 2/3 chance the card you pick has the same
color on both sides.

Over the long run, the con man wins because he keeps switching the offer.
If red is shown first, the offer is that the other side is red.
If grn is shown first, the offer is that the other side is grn.
That will win 2/3 of the time.

What’s a little confusing is considering the probability in one trial.
one way to think about it:
the chance of picking the red/red card is 1/3.
so if you see red, there’s 2/3 chance to win taking the bet.

or
once you know one side is red, the combinations for other sides
are: 1 is red, 1 is green.
So the chances are 50/50 on the first trial.

If you could convince the con man to keep betting that the other side is red,
each time, then you’d win 2/3 of the time.

42

This all happens in California, 1849. I’d draw and fire, then take his money.

Sheriff will side with me when he rolls the corpse over and sees his flashy clothes, silk purse, and hinky cards.

43

> In the red card green card puzzle,
> as presented, some people try to conclude that the chances of the red/red
> card is 2/3. That is incorrect.

heh.
I’m going to correct myself.
It is true, counterintuitive as this is.
see Bertrand's box paradox - Wikipedia

the chances of red/red + grn/grn before the first pick is 2/3.
After a color is revealed, the chances of the other side being the same is also 2/3.