## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## May 19, 2007

### Gambling Dogs

How do you train a dog to sit?

One way is to give your dog a treat—a cookie, toy, or meat-flavored byproduct—the instant it does the right thing. This seems obvious enough. But what should you do once the dog has learned the trick? Do you dole out a treat every time your dog sits? Surprisingly, the answer is no. The dog will be much more persistent if the reward is unpredictable than if it gets a treat every time it performs.

In the beginning, you should reward the behavior you want each and every time it occurs. Later, as the dog gets the idea, you offer treats most of the time, then about half the time, then less and less often. Otherwise, as soon as the dog stops getting rewards, it stops sitting. In the end, you'll be offering treats only occasionally, but the dog will still perform on command. The dog doesn't know if you'll come across with the cookie, so it sits just to be on the safe side.

As Treat Distribution Officer, you're more like a slot machine at a gambling casino than a soda machine. Every time you put money in a soda machine, you expect a reward—a can of soda. If the can doesn't tumble down the chute, you get very annoyed. On the other hand, when you put money in a slot machine, reels spin, then stop at some combination of symbols that may or may not reward you with a jackpot. You know you won't get a prize every time, so you keep on putting in coins in the hope of eventually winning something. Companies that manufacture slot machines use mathematics to work out, on average, how often they need to pay out to keep you putting in.

Random rewards have a similar effect on dogs, people—and even pigeons. The power of random rewards was first discovered in experiments in which pigeons got a bit of grain if they pecked a key. If a pigeon got grain every time it pecked a key, and the grain was then cut off, it would peck the key only 50 to 100 times before giving up. But if it had been rewarded only occasionally for pecking, it would peck 4,000 to 10,000 times without any reward.

It seems all creatures are gamblers at heart. So it's probably a bad idea to take your dog to Las Vegas. (Or your pigeon, either.)

Muse, November/December 2002, p. 45.