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SUMMARY:Tobias Fritz (University of Innsbruck\, Austria)
DTSTART:20260211T123000Z
DTEND:20260211T133000Z
DTSTAMP:20260415T022311Z
UID:PHK-cohomology-seminar/146
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PHK-cohomolo
 gy-seminar/146/">Optimizing over iid distributions and the Beat the Averag
 e game</a>\nby Tobias Fritz (University of Innsbruck\, Austria) as part of
  Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics 
 and statistics\n\nLecture held in ZOOM meeting.\n\nAbstract\nA casino offe
 rs the following game. There are three cups each containing a die. You are
  being told that the dice in the cups are all the same\, but possibly nons
 tandard. For a bet of \\$1\, the game master shakes all three cups and let
 s you choose one of them. You win \\$2 if the die in your cup displays at 
 least the average of the other two\, and you lose otherwise. Is this game 
 fair? If not\, how should the casino design the dice to maximize their pro
 fit?\n\nIn this talk\, I will answer this question\, explain what it is an
  example of\, and outline our partial results on a more difficult question
  of the same type: how likely can we make the event $X_1 + X_2 + X_3 < 2 X
 _4$\, given the constraint that the random variables $X_1\, ...\, X_4$ mus
 t be iid? Surprisingly\, obtaining good bounds involves solving challengin
 g combinatorial optimization problems.\n\nBased on joint work with Pierre 
 C Bellec (arXiv:2412.15179)\, which has recently been featured as a test c
 ase for the AI tool AlphaEvolve (arXiv:2511.02864).\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/146/
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