Showing Revision 1 created 05/13/2012 by Amara Bot.

1. Title:
   05-30 Impressing Pig Scouts
2. Description:

   dummy description

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   Now let's see how we did.
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   So I'm going to define a set of strategies--
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   the clueless strategy we expect to do the worst;
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   strategies that try to
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   solve the problem in 4 chunks, in 3 chunks in 2 chunks,
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   and to solve it all in one win;
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   and then the max win strategy.
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    Now, we play a tournament with these strategies,
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    and here's the results we get back.
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    So you can see that the clueless strategy does very poorly--
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    only wins 23 games out of 500.
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    The max win strategy does the best of all--
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    wins 325, but there's some competitors that are pretty close.
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    So hold at 20 wins 314--
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    not that much worse off than the optimal strategy.
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    And that holds up if we play a tournament with more games
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    just to get a little bit more accuracy.
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    You wouldn't be able to hit the run button and do this
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    because it would time out,
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    but if you bring it in to your own development environment, you can do that.
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    And here we see max wins gets
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    13,100 wins, and hold at 20 is 12,900.
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    So only a couple percent better for max wins
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    over hold at 20, but still it's nice to know
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    that no strategy can do better.
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    And it turns out that if we increase the goal
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    and made a longer game than just playing to 40 points--
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    that the advantage for max wins over any of these other strategies
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    would only increase.
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    In the betting game, we had different utility functions.
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    We tried out the linear utility,
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    and we tried out the logarithmic utility.
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    What about here?
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    Well, we defined our utility as a probability of winning,
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    and the way the game is defined, that's really the only sensible one.
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    If you're trying to win the game,
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    you should maximize the probability of winning.
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    But maybe your only goal isn't just to maximize
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    the probability of winning.
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    Maybe you're in a big Pig tournament,
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    and your seated at the Pig table, rolling the dice,
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    and in the stands are lots of spectators,
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    watching the game with excitement.
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    And you know that somewhere in the stands,
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    there's a scout from the NPA--the National Pig Association.
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    And what you want to do is not just win the game--
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    because lots of people are going to win the games--
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    but you really want to get the attention of that NPA scout
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    so that you can move on and have a professional career.
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    So maybe what your utility function would be
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    would not just be to win the game,
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    maybe your utility would be
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    to maximize the differential, to say, "If I just won the game by a couple points,
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    nobody is going to notice, but if I won by a lot--
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    if I really clobbered my opponent--
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    then maybe this guy would take notice, and that would be worth more to me."
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    So you'd give up on the goal of just winning,
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    and try to go for the maximizing your differential.