Monday, June 16, 2014
4:00 PM -
5:00 PM
Annenberg 314
Special Seminar in Computing + Mathematical Sciences
How to Gamble Against All Odds
Ron Peretz,
Assistant Professor,
Mathematics,
London School of Economics and Political Science,
This is joint work with Gilad Bavly (Tel Aviv University).
Motivated by questions in algorithmic randomness (Bienvenu et al. 2012, Chalcraft et al. 2013, Teutcsh 2014) we study the following situation.
Player 0, the cousin of the casino owner, is allowed to bet sums of money only within a set A (a subset of the real numbers). The regular casino players 1,2,3,... (countably many players) are allowed to make bets only within another set B. Player 0 announces her bets first; then the regular players announce theirs. Now the casino owner wants to fix an infinite sequence of heads and tails, such that player 0 makes infinite gains, while every regular player gains only a finite amount. Can this be done when, e.g., A is the set of all even integers, and B the set of all odds? We will present some sufficient and necessary conditions on the pair of sets A and B.
Motivated by questions in algorithmic randomness (Bienvenu et al. 2012, Chalcraft et al. 2013, Teutcsh 2014) we study the following situation.
Player 0, the cousin of the casino owner, is allowed to bet sums of money only within a set A (a subset of the real numbers). The regular casino players 1,2,3,... (countably many players) are allowed to make bets only within another set B. Player 0 announces her bets first; then the regular players announce theirs. Now the casino owner wants to fix an infinite sequence of heads and tails, such that player 0 makes infinite gains, while every regular player gains only a finite amount. Can this be done when, e.g., A is the set of all even integers, and B the set of all odds? We will present some sufficient and necessary conditions on the pair of sets A and B.
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