When to Rob a Bank: ...And 131 More Warped Suggestions and Well-Intended Rants (18 page)

It’s an interesting question. Let’s define optimal first.

Let’s say a program has an evaluation function (EV). Given a position, the EV returns a number from one to ten based on how good the position is for the person whose move it is. If it’s a ten, the person with the move wants to get to that position. The EV is a function of various heuristics added up (how many people are on the center, how many pips I’m ahead in the race, how many slots I control, how many loose pieces I have, etc.). When it’s my turn, the computer looks at all my initial moves and finds the ones resulting in the best EV. It then looks at all my opponent’s responses to each move and finds the ones resulting in the lowest EV for me (this now propagates up to become the EV of my initial move). It then looks at all my responses to my opponent’s responses and finds the ones with the best EV (and does the propagation again). This is called
min-max
. Looking at all the best moves only is called alpha-beta search and is how most game programs work.

So the question is, what is “optimal”? On a scale of one to ten, if a move is three better than the next move, is that optimal? Let’s say it is.

In chess, it’s easy to see optimal moves. If someone
does rook takes queen, then hopefully I can take his queen and it’s a fair trade. By far that will be the only optimal move. Other optimal moves lead to checkmate or great increases in material. Otherwise, it’s probably not optimal. In a typical chess game, maybe 5 percent of the moves have a value greater than “one pawn’s worth.”

In backgammon, I’d say it’s 10 percent. I’m saying this based on experience with Backgammon NJ [
an excellent program
, BTW], discussions with backgammon game programmers in the past, and I’m using 10 percent rather than 5 percent because backgammon is slightly less complex than chess. It’s not simple, though. To be a backgammon master probably requires almost as much study but not quite.

Hope this was helpful.

Yes, James, helpful indeed—because I now know a bit better how you think about the game, which I desperately need to finally beat you in our 101-point matches. Thanks!

Despite the fact that I am not very good at golf, my secret fantasy is to someday play on the Champions Tour, the professional
golf tour for fifty-somethings. As I approach my forty-fourth birthday, I realize it is time to get serious in this endeavor.

The right way to spend my time if I really wanted to make the tour, I suppose, would be to practice more. My friend
Anders Ericsson
popularized the magic number of ten thousand hours of practice to become an expert. Depending on exactly what you count as practice, by my rough calculations I have logged about five thousand hours of golf practice over the course of my life. Given how mediocre I am after the first five thousand hours, however, I’m not so optimistic that the next five thousand hours will lead me anywhere good.

So instead, I spent some time today figuring out how just how much I will need to improve. The best PGA Tour pros tend not to have regular handicaps, but are said to be the equivalent of Plus 8 on the handicap scale—i.e., eight strokes better than a scratch golfer. I claim to be a six handicap. That means that, to a first approximation, if I played eighteen holes today against the best players in the world, I should lose by fourteen strokes.

The probability that I will improve by fourteen strokes in the next six years is easy to estimate: zero.

Fortunately, my goal isn’t to be the best golfer in the world, just to be the worst golfer on the Champions Tour. Surely, that can’t be so hard, can it?

So I set out to measure just how much worse that guy is than the world’s very best golfers. A direct comparison is hard to make because the bottom feeders on the Champions
Tour rarely play against the Tiger Woodses of the world. The stars of the Champions Tour do, however, play an occasional PGA Tour event. I was able to find nineteen players who competed on both tours in 2010. On average, these players had a stroke average of 70.54 when playing on the Champions Tour, compared to an average of 71.77 when they played PGA Tour events. This suggests that the typical Champions Tour course plays a little more than one stroke easier than the typical PGA Tour course.

The top players on the PGA Tour post average scores of a little below seventy strokes per round, meaning that the upper echelon of senior golfers is about two strokes worse per round than the best players in the world. The low performers on the Champions Tour score around seventy-three on Champions Tour courses, or about two and a half strokes worse than the top senior golfers. If the world’s best golfers are Plus 8 handicappers, then that means the “bad” golfers on the senior tour are roughly Plus 3 or Plus 4.

That’s “only” nine or ten strokes a round better than me. Surely I can close that gap! If I can squeeze merely one stroke of improvement out of each incremental five hundred hours of practice, then by the time I hit ten thousand hours, I will be a Plus 4.

With that goal in mind, I recently started taking golf lessons for the first time since I was thirteen years old. One reason I chose my new golf coach, Pat Goss, is that he was an undergraduate economics major at Northwestern. I thought maybe he would understand the way I think.

On our first meeting, Pat first told me I swing like
a character out of
Caddyshack
, and then asked me about my golf goals.

I responded with 100 percent honesty: “I want to play on the Champions Tour. But if you decide I’ll never be that good, then I have a very different objective. I don’t care the slightest bit about what my handicap ends up being in that case. All that matters to me then is being able to hit the ball as far as possible, even if I can’t break a hundred.”

I guess he’s not used to getting an honest answer to this question, because he was so overcome with laughter he practically fell to the ground.

The good news is that six lessons later we are still devoting time to perfecting my short game, suggesting he thinks I can achieve my dream of making the tour.

Or maybe he’s just maximizing revenue. After all, he is an economist by training.

Last spring, I jokingly (okay, maybe half jokingly) wrote about
my quest to make the Champions Tour
, the professional golf tour for people over the age of fifty. In that post, I made reference to the ideas of Anders Ericsson, who argues that with ten thousand hours of the right kind of deliberate practice, more or less anyone can become more or less world
class at anything. I’ve spent five thousand hours practicing golf, so if I could just find the time for five thousand more, I should be able to compete with the pros. Or at least that is what the theory says. My scorecards seem to be telling a different story!

It turns out I’ve got a kindred spirit in this pursuit, only this guy is dead serious. A few years back, twenty-something Dan McLaughlin decided he wanted to play on the PGA Tour. Never mind that he had only played golf once or twice in his life and had done quite poorly those times. He knew the 10,000-hour argument, and he thought it would be fun to give it a test. So he quit his job, found a golf coach, and has devoted his life to golf ever since. So far he is 2,500 hours into his 10,000-hour quest, which he chronicles at
thedanplan.com
.
*

A while back I happened to find myself at Bandon Dunes, the golfers’ haven on the Oregon coast. I met Dan there, and we had the chance to play thirty-six holes together. We had a great time, and it was fascinating to get to know him and hear about his approach.

The golf pro who has been guiding him had a very unusual plan, to say the least. For the first six months of Dan’s golfing life, he was only allowed to putt. We are literally talking about Dan standing on a putting green for six to eight hours a day, six or seven days a week, hitting one putt after another. That is nearly one thousand hours of putting before he ever touched another club. Then he was given a wedge. He used just the wedge and the putter for another
few months, before he got an eight iron. It wasn’t until a year and a half into his golfing life—two thousand hours of practice—that he hit a driver for the first time.

I understand the basic logic of starting close to the hole (most shots in golf, after all, do occur close to the hole), but to my economist’s mind, this sounds like a very bad strategy for at least two reasons.

First, one of the most basic tenets of economics is what we call diminishing marginal returns. The first little bit of something yields big returns; the more you do of something, the less valuable it is. For example, the first ice cream cone is delicious. The fourth is nauseating. The same must be true of putting. The first half hour is fun and engaging. By the eighth straight hour, it must be mind-numbing. I just can’t imagine a person could focus that single-mindedly on putting, not just one day, but for months and months on end.

Second, my own experience suggests that there are spillovers across different aspects of golf. Things you feel when chipping help inform the full swing. Sometimes I can feel what I should be doing with a driver, and that helps me with my irons. Sometimes it is the opposite. To be putting and chipping for months without any idea what a full swing is—that just seems wrong to me.

So is the strategy working? After 2,500 hours, Dan is still really excited about golf, so that is a victory in and of itself. He is an eleven handicap, which means he is about fifteen to sixteen strokes per round away from being good enough for the PGA Tour. That means he has to shave off about one
stroke for every five hundred hours of practice from here on out. I suspect he can keep that rate of improvement for the next few thousand hours, but it will be a tough haul after that.

Whatever the outcome, I’ll be rooting for him. Partly because he is a nice guy, and partly because he promised me free tickets to the 2016 U.S. Open, but only if he qualifies.

*
As of this writing (January 2015), Dan has just over 4,200 hours to go, and his handicap is down to 3.1.

Levitt has made no secret of his desire to become a good enough golfer to
someday play the Champions Tour
, for players fifty and older.

After watching his amazing performance last week, I now believe Levitt does stand a chance of landing on the senior professional tour. But not in golf.

I was out in Chicago for a couple of days to work with Levitt. After a long day, we went out for dinner at a place near the University of Chicago called Seven Ten. It has food, beer, and bowling alleys—just a couple of them and nothing fancy. Old-school bowling.

After the meal, I tried to get Levitt to bowl a game or two. He wasn’t interested. Said he was worried about hurting his golf swing. (Puh-leeze.) He said he’d watch me bowl. I can’t
think of anything less fun than bowling alone except having someone sit and watch you bowl alone. So I lied and told him that bowling would probably be good for his golf swing—the heavy ball could loosen up his joints, yada yada, etc.

He finally agreed when I suggested the loser pay for dinner.

He somehow found a ten-pound ball that fit his fingers, and in his first practice frame he rolled it as if it were a duckpin ball. It missed everything. I was feeling pretty good about the bet. Out of friendship, I suggested he try a heavier ball. He moved up to a twelve-pounder. And then he proceeded to bowl a 158, which he told me was about thirty pins above his average. He won.

There was nothing impressive about his form: even though he’s a righty, he delivered from left to right and he put no movement on the ball. But he knocked the pins down.

So of course I suggested we bowl a second game. He said he wasn’t interested but, again, he came around.

He opened with a spare and then a turkey—three strikes in a row. Amazing! Then two open frames. His luck had seemingly run out. But it hadn’t: he now rolled four more consecutive strikes. It is hard to describe how unlikely this seemed, and was. He wound up with a 222. A 222! I took bowling as a PE requirement in college, and my career high is only 184.

When we got back to his house, Levitt looked up the
current top PBA bowlers
: a 222 average would put you firmly in the top twenty. And he bowled his 222 cross-lane, with
a twelve-pound ball, after a big dinner, a beer, and a day of work.

My best explanation is that Levitt’s maniacal devotion to golf, especially his thousands of hours of short-game practice, may have unwittingly turned him into a bowling dynamo. Either that, or he was lying about his existing average and he simply sandbagged me into buying dinner.

In either case, it was a pretty impressive feat. Unfortunately, his appearance on the
PBA’s senior tour
is unlikely: wanting to go out on top, he has vowed never to bowl again.

True to his word, Levitt hasn’t touched a bowling ball since.

Football coaches are known for being extraordinarily conservative when it comes to calling risky plays, since a single bad decision (or even a good decision that doesn’t work out) can get you fired. In the jargon of behavioral economics, coaches are “loss-averse”; this concept, pioneered by Amos Tversky and Daniel Kahneman, holds that we experience more pain with a loss of x than we experience pleasure with a gain of x. Who experiences loss aversion? Well, just about everyone: day traders,
capuchin monkeys
, and especially football coaches.

Which is why the last play of yesterday’s Chiefs-Raiders game was so interesting. With five seconds left, Chiefs coach Dick Vermeil had a tough decision to make. His team was trailing by three points with the ball inside the Raiders’ one-yard line. If the Chiefs ran a play and didn’t score, they would likely not have time for another play and would lose. If they kicked the easy field goal, the game would go to overtime—and even though the Chiefs were playing at home, the Raiders had moved the ball easily late in the game, and Vermeil, as he would later admit, was scared that the Raiders would win the coin toss in overtime and promptly score, winning the game without the Chiefs ever having a chance.