More Game Enumeration and the Folly of Math By Joe Brown

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)

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

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

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

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

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

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

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

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

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

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

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

Questions?

References Burchell, M.J. (2006). "W(h)ither the Drake equation?". International Journal of Astrobiology. 5 (3): 243–250. Bibcode:2006IJAsB...5..243B. doi:10.1017/S1473550406003107. Glade, N.; Ballet, P.; Bastien, O. (2012). "A stochastic process approach of the drake equation parameters". International Journal of Astrobiology. 11 (2): 103–108 https://www.pokerstrategy.com/poker-hand-charts-evaluations/ https://gowers.wordpress.com/2012/06/08/how-should-mathematics-be-taught-to-non-mathematicians/ . https://en.wikipedia.org/wiki/Fermi_problem