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MatheMUSEments
Gambling Dogs
By Ivars Peterson
Muse, November/December 2002, p. 45.
How do you train a dog to sit?
One way is to give your dog a treata cookie, toy, or meat-flavored
byproductthe 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 rewarda 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, peopleand 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.)
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