Is poker a game of pure luck, or is there skill involved, too?
One way to test, as Stephen Dubner suggested, is to check if it's possible to lose on purpose. If it is, then there must be skill involved, because the player has some control of the outcome. And, of course, it is possible to lose at poker at will, if you want to ... so it's reasonable to argue that poker is a game of skill.
On the other hand, you can't lose the lottery on purpose, no matter how hard you try. So, the lottery is just a game of luck.
But ... there are exceptions to the "lose on purpose" rule.
An easy one is tic-tac-toe. It's easy to lose on purpose—just go second, and take a side square when it's your turn. The first player, assuming he plays his best, is certain to beat you. On the other hand, you can't win on purpose. If both competitors play optimally, the result will always be a draw.
If you don't like that one, try casino blackjack. You can lose on purpose just by hitting every hand—eventually, you'll go over 21 and bust. But, can you win on purpose? Only to a certain limit. If you aren't a card counter, the best you can do is to faithfully follow "basic strategy." In that case, you'll reduce the house advantage to its minimum possible value—0.5 percent—which means that you'll lose, on average, $1 for every $200 you bet. Any deviation from that will be random luck.
That is: You can lose as much as you want, on purpose. But you can't win any more than the best of the other players, on purpose.
Even though blackjack passes the "lose on purpose" rule, I think most people would argue that it's a game of luck. Even though you can lose on purpose, there's no way to win on purpose ... that is, there's no way to beat the best players by improving your skill.
Why is this, that you can lose on purpose, but you can't win on purpose? In this case, it's deliberate, human-caused. When we invent games of skill, we keep the ones that have an interesting struggle to win. We don't care whether there's a struggle to lose, because, who cares? The object is to win.
Or, you can look at it this way. When there's competition for a goal, it's hard to win, because you have to beat your opponent, who's trying just as hard as you. When there's no competition for a goal—like losing—it's easy, because nobody is trying to prevent you.
If everyone is trying for X, it's hard to be the most X. But it's easy to be the most "not X.”
This seems like it doesn't matter much, but ... there are interesting consequences. Let's suppose that you're a baseball team, and you're trying to decide who to draft. There are 29 other teams competing with you to make the best choice, but nobody competing with you to make the worst choice.
That means it's hard to beat the other teams on purpose. But it's easy to lose to the other teams on purpose—just pick your mother, for instance.
Now, the interesting part. The same thing applies about winning and losing by accident. It's hard to beat the other teams by accident, but it's easy to lose to the other teams by accident.
Suppose you scout a player, and you think he's the next Mike Trout. The other teams are scouting him too. If you're right about him, and the other teams are too, the only way you're going to get him is if you have the first draft choice. Otherwise, some other team will snap him up before you.
But ... suppose he's not the next Mike Trout. You just happened to see him on a day he went 5-for-5 with three home runs. He's really just a fourth-round pick, and you've badly overrated him. What happens? You inevitably draft him too high, and you suffer. You've lost by "accident." By mistake. By lack of skill.
It's hard to win by intention, fluke, or skill—but it's easy to lose by intention, fluke, or (lack of) skill.
Let's suppose your scouting department concentrates on a few players. It spends substantial time analyzing those players, and it usually does OK valuating them.
There's a player named Andrew. The MLB consensus is that he's going to be the 20th pick. Your scouts spent a lot of time on him, and they think he's better than that. Their opinion is that he's actually the ninth best player in the draft.
There's another player named Bob. MLB consensus says he's the 16th best player. Your scouts think he's only the 30th best.
The draft comes along, and you have pick number 16. How much benefit do you gain from all that intelligence gathering? Suppose, if you like, that your scouts are absolutely correct, that they have the players ranked perfectly.
Well, if Andrew is available when your turn comes along, you snap him up for a gain of seven spots. But that's not guaranteed, because, after all, you're not the only team doing scouting! If any one of the teams drafting from ninth to 15th came to the same conclusion, they've already grabbed him. In that case, your benefit from all that scouting winds up being ... zero.
What if Bob is available when your turn comes along? Well, you're going to pass on him, because you know he's not that good. But, if you hadn't done the scouting, you would have taken him with your No. 16 pick. You would have had a loss of 14 spots.
In the case of Bob, your intelligence did help you. It helped you a lot. And, it doesn't matter if other teams scouted him. Even if every other team reached the same conclusion you did, you've still saved yourself a big mistake by scouting him too. If you hadn't scouted him, you would have made a big mistake.
The moral: You gain more by not being stupid than you do by being smart. Smart gets neutralized by other smart people. Stupid does not.
If you're still not convinced, try this. I gather 10 people, and show them a jar that contains $1, $5, $20, and $100 bills in equal proportions. I pull one out, at random, so nobody can see, and I auction it off. The bidding will probably top out at around $31.50, which is the value of the average bill.
I do it again, but, this time, I'm not that careful, and you get a glimpse of the bill. So does Susan, the stranger sitting next to you.
Well, if it's a $100 bill, you and Susan bid up the price to $99.99. Neither of you really benefit.
But, if it's a $1 bill ... neither you nor Susan bids. Each of you would have had a 1-in-10 chance of paying $31.50 for the bill and suffering a loss of $30.50. On an expected value basis, each of you gained $3.05 from your secret knowledge.
As I said at the Sloan Conference—well, I don't remember saying it, but someone else said I did—"one of the things that analytics can do really well is filter out the really stupid decisions."
What I was probably thinking, was something like this: If the 1980 Expos had had a sabermetrics department, they could have spent hours trying to squeeze out a couple of extra runs by lineup management ... but they would have been much, much better off figuring out that Rodney Scott's offense was so bad, he shouldn't have been a starter.
It works that way in your personal life, too. You can spend a lot of time and money picking out the perfect floral bouquet for your date, but you're probably better off checking if you have bad breath and taking the porn out of the glove compartment.
If it's true that sabermetrics helps teams win, I'd bet that most of the benefit comes from the "negative" side: having a framework that flags bad decisions before they get made.
"what if there were no hypothetical situations?"