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Beat the average game (AlphaEvolve problem 39)

Beat the average game (AlphaEvolve problem 39). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

MSC 60E15 · Inequalities; stochastic orderings

Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.

Licensed source statementAs of Repository at commit 8f44745 (2026-07-11); the repository records AlphaEvolve results, not current research statusSource & evidence ↓
Read original source ↗ 0Submit progressLean 4 ↓Discussion (0)

Problem statement

Let CC denote the quantity

C≔sup⁡μP[X1+X2+X3<2X4]C \coloneqq \sup_{\mu} \mathbb{P}[X_1 + X_2 + X_3 < 2X_4]

where μ\mu ranges over probability measures on [0,∞)[0, \infty) and let X1,…,X4∼μX_1, \ldots, X_4 \sim \mu are independent random variables with law μ\mu. Establish upper and lower bounds on CC that are as strong as possible.

Lean 4

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Background

Repository result category: worse than record — AlphaEvolve did not reach the best known result. See Section 6.22 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.

Progress & source assessment

The repository page records no bounds for this problem.

References
  1. [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — Beat the average game (AlphaEvolve problem 39) linkApache-2.0 (repository license); problem pages reproduced with attribution.

Recorded progress

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Discussion

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