I was playing a card game called Mille Bornes with my daughter. She dealt a hand while I was getting a cup of coffee in the other room. I came back and we started playing. She immediately played the four safety cards. These cards not only prevent the other player/team from playing bad cards on you, you also get an extra turn after playing them. I told her that it wasn't fun for me to play when the other person is cheating and that we could either play fair or not play at all. My math's a bit rusty, so while I'm confident enough that the odds for her drawing that hand are slim-to-none, to put it mildly. I was wondering what the exact odds were.
To sum up:
- 106 cards in the deck
- Each player is dealt 6 cards
- What are the odds of getting the 4 best cards in your initial hand?