| viXra.org > Mathematical Physics > viXra:2602.0017 |
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| viXra.org > Mathematical Physics > viXra:2602.0017 |
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Mathematical Physics |
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Authors: Goutham Netha Anagandula
The "Gambler’s Fallacy" is often treated as a cognitive bias, but it can be rigorously understood as a violation of translational invariance in probability space. In this paper, we define a "Global Correlation Functional" G(u20d7S) representing the expected overlap between a fixed control sequence (strategy)u20d7 S and a random Bernoulli target vector (nature)u20d7 X. By treating the strategyu20d7 S as a gauge degree of freedom, we demonstrate—both analytically and via Monte Carlo simulation—that the expectation value of the overlap is invariant under all local permutations ofu20d7 S. We conclude that in memoryless systems, the derivative of success with respect to strategy is identically zero(∇u20d7 S G = 0), implying that all strategies are microcanonically equivalent. This framework offers a pedagogical bridge between classical probability and the concept of gauge invariance in theoretical physics.
Comments: 2 Pages. Pedagogical derivation connecting the Gambler's Fallacy to Gauge Invariance
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[v1] 2026-02-03 18:14:55
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