
Title:
0530 Impressing Pig Scouts

Description:

Now let's see how we did.

So I'm going to define a set of strategies

the clueless strategy we expect to do the worst;

strategies that try to

solve the problem in 4 chunks, in 3 chunks in 2 chunks,

and to solve it all in one win;

and then the max win strategy.

Now, we play a tournament with these strategies,

and here's the results we get back.

So you can see that the clueless strategy does very poorly

only wins 23 games out of 500.

The max win strategy does the best of all

wins 325, but there's some competitors that are pretty close.

So hold at 20 wins 314

not that much worse off than the optimal strategy.

And that holds up if we play a tournament with more games

just to get a little bit more accuracy.

You wouldn't be able to hit the run button and do this

because it would time out,

but if you bring it in to your own development environment, you can do that.

And here we see max wins gets

13,100 wins, and hold at 20 is 12,900.

So only a couple percent better for max wins

over hold at 20, but still it's nice to know

that no strategy can do better.

And it turns out that if we increase the goal

and made a longer game than just playing to 40 points

that the advantage for max wins over any of these other strategies

would only increase.

In the betting game, we had different utility functions.

We tried out the linear utility,

and we tried out the logarithmic utility.

What about here?

Well, we defined our utility as a probability of winning,

and the way the game is defined, that's really the only sensible one.

If you're trying to win the game,

you should maximize the probability of winning.

But maybe your only goal isn't just to maximize

the probability of winning.

Maybe you're in a big Pig tournament,

and your seated at the Pig table, rolling the dice,

and in the stands are lots of spectators,

watching the game with excitement.

And you know that somewhere in the stands,

there's a scout from the NPAthe National Pig Association.

And what you want to do is not just win the game

because lots of people are going to win the games

but you really want to get the attention of that NPA scout

so that you can move on and have a professional career.

So maybe what your utility function would be

would not just be to win the game,

maybe your utility would be

to maximize the differential, to say, "If I just won the game by a couple points,

nobody is going to notice, but if I won by a lot

if I really clobbered my opponent

then maybe this guy would take notice, and that would be worth more to me."

So you'd give up on the goal of just winning,

and try to go for the maximizing your differential.