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State-Dependent Asymmetry in Soft-Pity Gacha Waiting-Time Models: Exact Recurrences, Tail Risk, and Featured-Target Extensions

2026-05-27

Abstract excerpt

Randomized reward mechanisms are often described as repeated trials with a fixed success probability. Pity and guarantee rules depart from this symmetric baseline by making the hazard depend on the current state. This paper studies that state-dependent asymmetry for a finite soft-pity waiting-time model. The waiting time for one rare item is represented as an absorption time of a Markov chain whose transient state...

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Literature Corpus work
034218bb-1ae4-5b0e-9108-3f31fe30084b
DOI
10.20944/preprints202605.1832.v1
Open publication

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State-Dependent Asymmetry in Soft-Pity Gacha Waiting-Time Models: Exact Recurrences, Tail Risk, and Featured-Target ExtensionsDOI 10.20944/preprints202605.1832.v1
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