Wednesday, April 7, 2010

Vegas at Home

I just finished three initiation reports -- I follow stocks for a living -- and needed a diversion. So, I decided to teach Paulina how to play cards. It occurred to me earlier today that card games are a great vehicle to teach basic probability concepts. Conditional probability, in particular, arises naturally. We tried it, and Paulina had a lot of fun.

Here is what we did. I first taught her the various suits and the cards in each suit. That took very little time. I then asked her the following questions:
  1. Before dealing any cards, what is the chance of dealing a heart?
  2. Assuming that a heart is the only card that has been dealt, what is the probability of dealing another heart?
  3. Assuming that a heart is the only card that has been dealt, what is the probability of dealing a spade?
  4. Assuming that a heart has been dealt, what is a better bet for the next card? A heart or a diamond?
Shuffle the deck. Deal two cards for you and two for your child. Forget about the dealer's cards. This just complicates the setup. Now is when things get educational. Let the child be the first player. Ask the kid "hit" or "stay." He or she is going to look at you funny. Explain that you say "hit" if you want more cards and '"stay" if you are done. Remind the child that an "A" works as a 1 or an 11. Remind the child going over 21 gets you busted. Tell the kid to look at all the cards that have been dealt and ask for the probability of going bust. Chances are the kid won't have a clue. In fact, Paulina had no idea where to start. However, she got it quickly once I showed her the thought process. If your child has been paying attention, he or she will get it too. Here is an example. Let's say that you dealt:
  • a 10 of hearts and a 5 of clubs for your child
  • a 2 of diamonds and 5 of diamonds for you
  • a 10 of hearts and a card facing down
You can compute the probability of your child going bust as follows:
  • To bust, you must deal a card with a value of 7 or higher.
  • Given what has already being dealt, the following cards will get you busted: 4 sevens, 4 eights, 4 nines, 4 tens, 4 jacks, 4 queens, and 4 kings
This is a total of 28 cards out of 48 cards that have yet to be dealt. This means that the probability of going bust is 28 out of 48 or 7/12. Your child should know that this is more than 1 out of every two cards. This is not a lot over 1/2, but one is more likely than not to go bust at this point by taking one more card.

You could continue playing the game. As you work through the deck, you can ask your child to remember what has been dealt and to decide on every play whether or not it is a good idea to take another card.

Remember that this is not Vegas. You can count cards here. Lay out in front of you the cards that have been used so your kid can tell what is left in the deck. Don't be too serious. That's not the point. Have fun. Raise the stakes by using chocolate chips to bet. Let me repeat this. HAVE FUN. EAT CHOCOLATE. COMPUTE. THINK. If you make this too serious, you will fail.

There are a million questions you could ask. For example, you could ask the probability of getting a 21 when dealt the first two cards from a deck. However, you should just play and ask the kid to make educated guesses about whether or not to bet. Once again. Raise the stakes by using chocolate. Trust me. Chocolate works when teaching math.

Have fun,


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