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E(h+s pity) < E(h pity) < E(no pity) (round up) ≈ 63 < 70 < 167
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P(no pity) < P(h pity) < P(h+s pity) (based on above approximations) ≈ 0.59% < 1.43% < 1.59%
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Based on the h+s pity system, with 160 primogems per roll: E(# primogems per 5-star) = 63*160 = 10 080 Compared to the naive estimate of 90 rolls per 5-star, which is 90*160 = 14 400
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