Abstract
Suppose that the scores of $n$ players are independent integer-valued random variables with probabilities $p_j$. We study the probability $P(T_n)$ that there is a tie for the highest score. The asymptotic behavior of this probability is surprising. Depending on the limit of $p_{j+1}/p_j$, we find different limits of different subsequences $P(T_{n(m)})$. These limits are evaluated for several families of discrete distributions.
Citation
Bennett Eisenberg. Gilbert Stengle. Gilbert Strang. "The Asymptotic Probability of a Tie for First Place." Ann. Appl. Probab. 3 (3) 731 - 745, August, 1993. https://doi.org/10.1214/aoap/1177005360
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