Understanding Data - Data Points: Visualization That Means Something - page 373

One day I thought to myself, “Hey, I have some statistics and probability know-
how and a deck of cards. I'm going to become an expert blackjack player
like those kids from MIT. Forget this stupid job. I'm gonna be rich!” And my
1-month obsession with blackjack began. (To save you the suspense, I didn't
get rich, and it's not nearly as exciting as they make it look in the movies.)

In case you're unfamiliar with the game, here's a quick rundown. There's a
dealer and a player. The dealer deals two cards to each (one of his is face
down), and the goal is to get a card total as close to 21 as possible, without
going over. You can choose to take additional cards (called a hit ) or not ( stay ).
In some cases, you can also split your hand of two cards, as if you're playing
two separate hands; you can also double down , which means to double your
bet. The more you bet, the more you can win. If you go over 21, to bust, you
automatically lose, and if not, the dealer hits or stays, and whoever is closer
to 21 wins.

By design, the dealer has the advantage, but if you hit and stay when you're
supposed to, you can decrease that advantage. These rules are based on aver-
ages, but as anyone who has played blackjack can tell you, there is uncertainty
in each hand of cards. You can still lose even when you make the right move.
For example, imagine you are dealt a 5 and a 6 for a total of 11, and the dealer
shows a 6. The right move is to double your bet because it's impossible for
you to bust with an additional card, and there's a decent chance of getting
21. There's also a good chance the dealer will bust with a 6 showing.

So you double down, and you get a 3, for a total of 14. Ouch. That's not good.
Your only hope is for a dealer bust. So he flips his hidden card, and it's a 10
for a total of 16. By rule, he has to hit, and it's a 5. Dealer total: 21. You lose.

Had you not double downed, you would have lost only half the money that you
did playing the right way. But if it were that easy to win, the casino wouldn't
bother putting the game on the floor.

There's uncertainty in each hand because you are playing against distributions,
or rather, you know only the approximate probabilities of drawing cards. You
might have an idea of what cards are in the deck, but you can make only an
educated guess about what card comes next.

Note: If you count cards, or keep track of
what's left in the deck, the probabilities change
as you modify your bet based on your advan-
tage, but uncertainty remains.

Of course, uncertainty applies to things outside of cards, and
it comes in a variety of forms. Take the weather for example.
How many times have you looked up the forecast for the