Pick a colour - continued.

Well - would you take my bet (see last Thursday's post)?  Seems a good thing - odds of 6/4 against on what appears to be an even money shot.  But then, if it seems to be too good to be true, it usually is!  So let's go through it carefully. There are three cards, each with two sides, so six sides in all - three red and three black. Let's label them.  For the red/red card we'll call one side Red1 and the other Red2. Same with the black/black card - Black1 and Black2.  The third card is red on one side - call that Red3 - and black on the other - Black3.  OK, we are looking at a card, the top side of which is red.  So we could be looking at Red1, in which case the other side is Red2 - so it's red.  Equally we could be looking at Red2, in which case the other side is Red1 - so it's red.  Or we could be looking at Red3 in which case the other side is Black3 - so it's black.  Three possibilities - two of which lead to the other side being red, and one to the other side being black.  So it is not, as I suggested in my original spiel, a 50-50 chance - it is actually twice as likely that the other side is red, and the true odds I should be offering you is 2/1 against.  Don't take the bet!