English subtitles

← 05-30 Impressing Pig Scouts

dummy description

Get Embed Code
1 Language

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

  1. Now let's see how we did.
  2. So I'm going to define a set of strategies--
  3. the clueless strategy we expect to do the worst;
  4. strategies that try to
  5. solve the problem in 4 chunks, in 3 chunks in 2 chunks,
  6. and to solve it all in one win;
  7. and then the max win strategy.
  8. Now, we play a tournament with these strategies,
  9. and here's the results we get back.
  10. So you can see that the clueless strategy does very poorly--
  11. only wins 23 games out of 500.
  12. The max win strategy does the best of all--
  13. wins 325, but there's some competitors that are pretty close.
  14. So hold at 20 wins 314--
  15. not that much worse off than the optimal strategy.
  16. And that holds up if we play a tournament with more games
  17. just to get a little bit more accuracy.
  18. You wouldn't be able to hit the run button and do this
  19. because it would time out,
  20. but if you bring it in to your own development environment, you can do that.
  21. And here we see max wins gets
  22. 13,100 wins, and hold at 20 is 12,900.
  23. So only a couple percent better for max wins
  24. over hold at 20, but still it's nice to know
  25. that no strategy can do better.
  26. And it turns out that if we increase the goal
  27. and made a longer game than just playing to 40 points--
  28. that the advantage for max wins over any of these other strategies
  29. would only increase.
  30. In the betting game, we had different utility functions.
  31. We tried out the linear utility,
  32. and we tried out the logarithmic utility.
  33. What about here?
  34. Well, we defined our utility as a probability of winning,
  35. and the way the game is defined, that's really the only sensible one.
  36. If you're trying to win the game,
  37. you should maximize the probability of winning.
  38. But maybe your only goal isn't just to maximize
  39. the probability of winning.
  40. Maybe you're in a big Pig tournament,
  41. and your seated at the Pig table, rolling the dice,
  42. and in the stands are lots of spectators,
  43. watching the game with excitement.
  44. And you know that somewhere in the stands,
  45. there's a scout from the NPA--the National Pig Association.
  46. And what you want to do is not just win the game--
  47. because lots of people are going to win the games--
  48. but you really want to get the attention of that NPA scout
  49. so that you can move on and have a professional career.
  50. So maybe what your utility function would be
  51. would not just be to win the game,
  52. maybe your utility would be
  53. to maximize the differential, to say, "If I just won the game by a couple points,
  54. nobody is going to notice, but if I won by a lot--
  55. if I really clobbered my opponent--
  56. then maybe this guy would take notice, and that would be worth more to me."
  57. So you'd give up on the goal of just winning,
  58. and try to go for the maximizing your differential.