1. More Game Enumeration and the Folly of Math
By Joe Brown

2. Outline Discuss enumeration in five card draw and Texas holdem
Talk about unsuitability of math to give perfect advice for these games
Talk about Fermi problems and the problems with precision in math (and problems with math in general)

3. Basic format of each game
Five card draw: Dealing->Returning Cards->Getting Cards Back
Texas holdem: Dealing->Burn and Flop->Burn and Turn->Burn and River

4. Outline of number of possible game states
Opening Hands
End of game, and what we mean by that

5. How much should we be betting?
When do we bet high?
When do we bluff?

6. Math can help, but not perfectly
Guides conflict with emotion
Intuition vs statistics
Stagnation of strategies

7. Where else is math not perfect?
Prisoner’s Dilemma (How do we model loyalty?)
Games of (near)-infinite variety
Cheating
Others?

8. Fermi Problems A different type of difficulty in math
“When is an estimate good enough?”

9. Piano Tuner Equation How many piano tuners are there in Chicago?
~9,000,000 people in Chicago
~2 people per household in Chicago
~1 in 20 households have a piano
~1 tuning a year is needed for pianos
~2 hours for a tuner to tune a piano
Each tuner works 8 hours a day, 5 days a week, 50 weeks a year

10. Why this questions matters
Dimensional Analysis
Scope of problems
What information do we value in this problem?

11. Drake Equation N=R**fp*ne*fl*fi*fc*L
N=Number of communication feasible civilizations in Milky Way
R*=Average rate of star formation
fp=Fraction of those with planets
ne=Average number of planets that could support life
fl=Fraction of those that develop life
fi=Fraction of those that develop intelligent life
fc=Fraction of those that could develop a signal that reaches us
L=Length of time they release such a signal

12. Uncertainty of variables and use
We don’t know the last four variables
Equation still gives us generally useful information

13. So what are the real “problems” in math
Emotion doesn’t mix with logic
Exact values often aren’t the most necessary information
This doesn’t mean math is bad

14. Questions?

15. References
Burchell, M.J. (2006). "W(h)ither the Drake equation?". International Journal of Astrobiology. 5 (3): 243–250. Bibcode:2006IJAsB B. doi: /S
Glade, N.; Ballet, P.; Bastien, O. (2012). "A stochastic process approach of the drake equation parameters". International Journal of Astrobiology. 11 (2): 103–108 .