1. Cambridge April 12, 2008 My Best Attempt to Explain the Logic Behind the Results April Madness How Did Michael get to the Final 8?

2. Players are characterized according to their strategies—(how often they raise with a bad card; how often they call) Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards

3. Because of your strategy, you have great chances to win against someone who often bluffs and calls Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% Michael Looser 1

4. Nonetheless, that player would be in advantage with someone who folds and bluffs less often Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% Looser 2 Looser 1

5. And this last player would be in advantage with someone who also folds and bluffs less often Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% Looser 2 Looser 3

6. That type of player is the only one who has a good chance to win against you Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% Michael Looser 3

7. As I mentioned, there is an equilibrium player who neutralizes his opponents—when you play against him, your chances of winning are 50% Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% Equilibrium You will have to trust me for now with the numbers, but there is

8. In short, there are four types of players and each type is a natural winner against another kind Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% 1 2 3 4

9. Luck has a greater role when players choose and strategy “less pure” and get closer to the equilibrium—the results of the matches become more random Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% Looser 2 Looser 4

10. Here is the distribution of the players’ strategies for this tournamnet… Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% 8 11 22 4 0 5 0 2 0 64 in total—only 7 choose a strategy similar to yours (and they’ve been studying Game Theory for a while)

11. You got so far because you had few enemies and they were beaten in the first rounds Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% 8 11 22 4 0 5 0 2 0 Your friends: the enemies of your enemies Your enemies

12. You lost against someone of your own kind, who chose a stronger strategy than you Filename/RPS Number Call Fold Raise w/ Bad Card Don’t Raise w/ Bad Card GotCards NoCards 17% 67% Michael Rick LaPoint