15 Apr 2012

Red or Black?

So here's a nice little puzzle that I stole from the Internet and tweaked a bit:

You and a friend have been asked to play a slightly interesting game that is all about luck.

There are 2 rooms next to each other, separated by a soundproof opaque wall. There's a nice little slot that both of you can access, and in there is a standard deck of 52 poker cards, randomly shuffled.

Both of you are supposed to go into your respective rooms, and upon a signal draw a card. Then you have two options for your guesses: red or black. What you and your friend must do is guess the wrong colour of the other person's card, i.e. if your friend's card is a red one, you should guess black. Problem is, you can't see each other's card, and there's strictly no communication allowed between the two of you.

If somehow both of you guess correctly the colour of each other's cards, the game ends and both of you lose. If however at least one of you guesses wrongly, both of you must draw another card from the deck and guess again. Only when you've both gone through the ENTIRE deck without once both having correct guesses, then you win the game!

Sounds absurd? Of course you are allowed a few minutes to discuss some sort of strategy with your friend before going in and starting the game. Strategy? Of course there's a strategy! It's not merely luck. In fact there is a way to guarantee that for each round of drawing, one of you will guess wrongly!

...so what's the winning strategy here?

Figure out for yourself, then look below for the answer to check!

Or if you're simply too lazy to think...

It's a really simple method: make sure that when both of you draw your cards, you simply guess the colour of your own card, while your friend guesses the opposite colour of his own card. So there are 4 cases:

1. You = Red, Friend = Red; you guess red (correct), friend guesses black (wrong)
2. You = Red, Friend = Black; you guess red (wrong), friend guesses red (correct)
3. You = Black, Friend = Red; you guess black (wrong), friend guesses black (correct)
4. You = Black, Friend = Black; you guess black (correct), friend guesses red (wrong)

...so you see, no matter which case it is, as long as you and your friend follow this strategy, you're guaranteed that one of you makes a wrong guess! :D