Imagine you're at a casino. The game you're playing consists of the following:
There are 52 cards, half of them are red, and the other half are black. Croupier mixes the cards and he draws two. If both of them are red, you get a point, if they are of different color, they get discarded and nobody gets a point, and if both of them are black, then the croupier gets the point. After this, croupier mixes the cards again and he does the same. Points are given as said before. This process is then repeated until all 52 cards have been drawn. You win the game if you get more points strictly than the house. Question is: How much money would you be willing to bet on this game?
The answer a friend of mine came up with is that you should never bet anything because you are never going to win, as the game will always result in a draw, having drawn the same number of pair of reds as blacks.
Thing is, I haven't been able to come up with a rigourous mathematical explanation, so I was hoping someone would know how to do it.
Thank you :)