Optimizing stakes in simultaneous bets
Robbert Fokkink (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Ludolf Meester (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Christos Pelekis (The American College of Greece)
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Abstract
We want to find the convex combination S of iid Bernoulli random variables that maximizes P(S ≥ t) for a given threshold t. Endre Csóka conjectured that such an S is an average if t ≥ p, where p is the success probability of the Bernoulli random variables. We prove this conjecture for a range of p and t