Speaker: Prof. Ian Morrison, Fordham University, USA
Time: 9.30, Friday, 14 February 2014
Venue: Room 301, Building A5, Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Cau Giay, Ha Noi.
Abstract: Craps, the most popular dice game in American casinos, involves rolling 2 dice: winning or losing the game depends only on the totals that are rolled. The question in the title asks whether it is possible to find 2 loaded dice (dice for which some sides are more likely than others), for which the probabilities of all totals match those of a fair pair (having all side probabilities equal). My talk will discuss generalizations and refinements of this problem and explain how fairly elementary ideas from algebraic geometry—both computational and theoretical, number theory, orthogonal polynomials and other areas can be combined to answer them. I will conclude by discussing conjectures and open questions about the asymptotics of such loaded pairs that reveal some surprisingly subtle behavior.
I plan to start my talk by reviewing how the rules of the game but I invite anyone who is interested in getting a feel for real-life play to watch the following videos before the talk:
- First, a scene from "A Bronx Tale" (set in the 1960s in the neighborhood in the Bronx where Fordham University is located) in which the hero, a young child, learns to play the game. Warning: contains profanity.
http://www.youtube.com/watch?v=wK2dAoIxWBQ
- Next, a scene in a casino from the classic James Bond film "Diamonds are Forever":
- Last, clips that show how to test whether dice are fair,
http://www.youtube.com/watch?v=iqBNF2BnWSo
and how they can be loaded by baking them:
http://www.youtube.com/watch?v=dURhrY9Z-xg
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