{ "version": "fusion-v3-20261017", "kind": "inclusive_rate_cycle_means_and_separate_stock_plus_pity_budgets", "budgetRevision": "balanced-attack-defense-v1", "probabilities": { "version": "fusion-v3-20261017", "source": { "kind": "user_supplied_probability_disclosure_image_and_explicit_clarification", "receivedDate": "2026-10-17", "image": "assets/fusion/probability-rules-20261017.jpg", "scope": "Only the three sealed-material fusion tables; equipment reforging is excluded.", "note": "All fusion rates include pity and are rounded to two decimal percentage points; they are not independent per-attempt base rates." }, "countUpgrade": [ { "input": [ 1, 1 ], "output": 2, "effectiveRate": 0.2572, "pity": 10 }, { "input": [ 2, 2 ], "output": 3, "effectiveRate": 0.2472, "pity": 10 }, { "input": [ 3, 3 ], "output": 4, "effectiveRate": 0.2391, "pity": 8 }, { "input": [ 4, 4 ], "output": 5, "effectiveRate": 0.2288, "pity": 8 }, { "input": [ 5, 5 ], "output": 6, "effectiveRate": 0.2192, "pity": 8 } ], "mutation": { "rare": { "total": 6, "routes": [ "4+2", "3+3", "5+1" ], "effectiveRate": 0.0195, "pity": 73 }, "fool": { "total": 8, "routes": [ "4+4", "5+3", "6+2" ], "effectiveRate": 0.0112, "pity": 105 } }, "counterRules": { "materialTypes": [ "attack", "defense" ], "attackDefenseShared": false, "mutationKey": [ "materialType", "inputTotal" ], "countUpgradeKey": [ "materialType", "equalInputTier" ], "sameMutationGroupSharesRateAndPity": true, "unequalInputsAdvanceCountUpgradePity": false, "higherTierSatisfiesLowerInventoryGate": true }, "rareAffixConditionalDistribution": { "attack": [ { "name": "战争主教", "probability": 0.05 }, { "name": "恐惧主教", "probability": 0.05 }, { "name": "神明之手", "probability": 0.05 }, { "name": "天灾化身", "probability": 0.05 }, { "name": "收割者", "probability": 0.2 }, { "name": "风眷者", "probability": 0.2 }, { "name": "催眠师", "probability": 0.2 }, { "name": "通灵者", "probability": 0.2 } ], "defense": [ { "name": "荒芜主母", "probability": 0.05 }, { "name": "隐秘之仆", "probability": 0.05 }, { "name": "混乱行者", "probability": 0.05 }, { "name": "沉默门徒", "probability": 0.05 }, { "name": "守护者", "probability": 0.2 }, { "name": "无暗者", "probability": 0.2 }, { "name": "教唆者", "probability": 0.2 }, { "name": "格斗家", "probability": 0.2 } ] } }, "tiers": { "1": { "raw": 1.0, "factors": 0.0, "proficiency": 0.0, "rawMax": 1, "factorsMax": 0 }, "2": { "raw": 4.888024883359254, "factors": 23.328149300155523, "proficiency": 31.10419906687403, "rawMax": 11, "factorsMax": 60, "attempts": 3.888024883359254, "effectiveRate": 0.2572, "countPity": 10 }, "3": { "raw": 24.66158832736918, "factors": 166.24137462440925, "proficiency": 221.655166165879, "rawMax": 121, "factorsMax": 780, "attempts": 4.0453074433656955, "effectiveRate": 0.2472, "countPity": 10 }, "4": { "raw": 127.80499412983333, "factors": 986.9915821710811, "proficiency": 1315.988776228108, "rawMax": 1089, "factorsMax": 7260, "attempts": 4.182350480970305, "effectiveRate": 0.2391, "countPity": 8 }, "5": { "raw": 686.3932551867972, "factors": 5825.241504247484, "proficiency": 7766.988672329979, "rawMax": 9801, "factorsMax": 66300, "attempts": 4.370629370629371, "effectiveRate": 0.2288, "countPity": 8 }, "6": { "raw": 3817.7493463674414, "factors": 33495.13887763929, "proficiency": 44660.18517018572, "rawMax": 88209, "factorsMax": 598620, "attempts": 4.562043795620438, "effectiveRate": 0.2192, "countPity": 8 } }, "meanRare": [ { "route": "4+2", "base": 4, "feed": 2, "total": 6, "attempts": 51.282051282051285, "attemptsPerType": 51.282051282051285, "materialTypes": 1, "stockPieces": 0, "raw": 250.667942736372, "factors": 2734.7768871874628, "proficiency": 3646.369182916617, "directFactors": 1538.4615384615386, "directSule": 1538461.5384615385, "rawMax": 564.1025641025641, "factorsMax": 4615.384615384615 }, { "route": "3+3", "base": 3, "feed": 3, "total": 6, "attempts": 51.282051282051285, "attemptsPerType": 51.282051282051285, "materialTypes": 1, "stockPieces": 0, "raw": 1264.6968373009836, "factors": 10063.660237149192, "proficiency": 13418.213649532256, "directFactors": 1538.4615384615386, "directSule": 1538461.5384615385, "rawMax": 6205.128205128205, "factorsMax": 41538.46153846154 }, { "route": "5+1", "base": 5, "feed": 1, "total": 6, "attempts": 51.282051282051285, "attemptsPerType": 51.282051282051285, "materialTypes": 1, "stockPieces": 0, "raw": 51.282051282051285, "factors": 1538.4615384615386, "proficiency": 2051.2820512820513, "directFactors": 1538.4615384615386, "directSule": 1538461.5384615385, "rawMax": 51.282051282051285, "factorsMax": 1538.4615384615386 } ], "meanFool": [ { "route": "4+4", "base": 4, "feed": 4, "total": 8, "attempts": 89.28571428571429, "attemptsPerType": 89.28571428571429, "materialTypes": 1, "stockPieces": 0, "raw": 11411.160190163691, "factors": 98838.53412241796, "proficiency": 131784.71216322394, "directFactors": 10714.285714285716, "directSule": 10714285.714285716, "rawMax": 97232.14285714287, "factorsMax": 658928.5714285715 }, { "route": "5+3", "base": 5, "feed": 3, "total": 8, "attempts": 89.28571428571429, "attemptsPerType": 89.28571428571429, "materialTypes": 1, "stockPieces": 0, "raw": 2201.9275292293914, "factors": 25557.26559146511, "proficiency": 34076.35412195348, "directFactors": 10714.285714285716, "directSule": 10714285.714285716, "rawMax": 10803.57142857143, "factorsMax": 80357.14285714287 }, { "route": "6+2", "base": 6, "feed": 2, "total": 8, "attempts": 89.28571428571429, "attemptsPerType": 89.28571428571429, "materialTypes": 1, "stockPieces": 0, "raw": 436.43079315707627, "factors": 12797.156187513887, "proficiency": 17062.87491668518, "directFactors": 10714.285714285716, "directSule": 10714285.714285716, "rawMax": 982.1428571428572, "factorsMax": 16071.428571428572 } ], "freshRare": [ { "route": "4+2", "base": 4, "feed": 2, "total": 6, "attempts": 73, "attemptsPerType": 73, "materialTypes": 1, "stockPieces": 4, "raw": 868.0457930045588, "factors": 7840.921227595678, "proficiency": 10454.561636794237, "directFactors": 2190, "directSule": 2190000, "rawMax": 5159, "factorsMax": 35610 }, { "route": "3+3", "base": 3, "feed": 3, "total": 6, "attempts": 73, "attemptsPerType": 73, "materialTypes": 1, "stockPieces": 1, "raw": 1824.9575362253192, "factors": 14491.861722206284, "proficiency": 19322.482296275044, "directFactors": 2190, "directSule": 2190000, "rawMax": 8954, "factorsMax": 59910 }, { "route": "5+1", "base": 5, "feed": 1, "total": 6, "attempts": 73, "attemptsPerType": 73, "materialTypes": 1, "stockPieces": 4, "raw": 2818.573020747189, "factors": 25490.966016989936, "proficiency": 33987.954689319915, "directFactors": 2190, "directSule": 2190000, "rawMax": 39277, "factorsMax": 267390 } ], "freshFool": [ { "route": "4+4", "base": 4, "feed": 4, "total": 8, "attempts": 105, "attemptsPerType": 105, "materialTypes": 1, "stockPieces": 4, "raw": 13930.744360151833, "factors": 120182.08245664784, "proficiency": 160242.7766088638, "directFactors": 12600, "directSule": 12600000, "rawMax": 118701, "factorsMax": 803940 }, { "route": "5+3", "base": 5, "feed": 3, "total": 8, "attempts": 105, "attemptsPerType": 105, "materialTypes": 1, "stockPieces": 4, "raw": 5335.0397951209525, "factors": 53356.3103525529, "proficiency": 71141.7471367372, "directFactors": 12600, "directSule": 12600000, "rawMax": 51909, "factorsMax": 359700 }, { "route": "6+2", "base": 6, "feed": 2, "total": 8, "attempts": 105, "attemptsPerType": 105, "materialTypes": 1, "stockPieces": 4, "raw": 15784.239998222487, "factors": 149030.0111870735, "proficiency": 198706.6815827647, "directFactors": 12600, "directSule": 12600000, "rawMax": 353991, "factorsMax": 2413380 } ], "balancedRare": [ { "route": "4+2", "base": 4, "feed": 2, "total": 6, "attempts": 146, "attemptsPerType": 73, "materialTypes": 2, "stockPieces": 4, "raw": 1224.8716094897843, "factors": 11733.876126507032, "proficiency": 15645.168168676042, "directFactors": 4380, "directSule": 4380000, "rawMax": 5962, "factorsMax": 42180, "rawAttack": 612.4358047448922, "rawDefense": 612.4358047448922, "rawPreparedAttack": 613, "rawPreparedDefense": 613, "rawPreparedTotal": 1226 }, { "route": "3+3", "base": 3, "feed": 3, "total": 6, "attempts": 146, "attemptsPerType": 73, "materialTypes": 2, "stockPieces": 2, "raw": 3649.9150724506385, "factors": 28983.723444412568, "proficiency": 38644.96459255009, "directFactors": 4380, "directSule": 4380000, "rawMax": 17908, "factorsMax": 119820, "rawAttack": 1824.9575362253192, "rawDefense": 1824.9575362253192, "rawPreparedAttack": 1825, "rawPreparedDefense": 1825, "rawPreparedTotal": 3650 }, { "route": "5+1", "base": 5, "feed": 1, "total": 6, "attempts": 146, "attemptsPerType": 73, "materialTypes": 2, "stockPieces": 4, "raw": 2891.573020747189, "factors": 27680.966016989936, "proficiency": 36907.954689319915, "directFactors": 4380, "directSule": 4380000, "rawMax": 39350, "factorsMax": 269580, "rawAttack": 1445.7865103735944, "rawDefense": 1445.7865103735944, "rawPreparedAttack": 1446, "rawPreparedDefense": 1446, "rawPreparedTotal": 2892 } ], "balancedFool": [ { "route": "4+4", "base": 4, "feed": 4, "total": 8, "attempts": 210, "attemptsPerType": 105, "materialTypes": 2, "stockPieces": 4, "raw": 27350.268743784334, "factors": 236416.19858461135, "proficiency": 315221.5981128151, "directFactors": 25200, "directSule": 25200000, "rawMax": 233046, "factorsMax": 1578840, "rawAttack": 13675.134371892167, "rawDefense": 13675.134371892167, "rawPreparedAttack": 13676, "rawPreparedDefense": 13676, "rawPreparedTotal": 27352 }, { "route": "5+3", "base": 5, "feed": 3, "total": 8, "attempts": 210, "attemptsPerType": 105, "materialTypes": 2, "stockPieces": 4, "raw": 7924.506569494717, "factors": 83411.65468811587, "proficiency": 111215.5395841545, "directFactors": 25200, "directSule": 25200000, "rawMax": 64614, "factorsMax": 454200, "rawAttack": 3962.2532847473585, "rawDefense": 3962.2532847473585, "rawPreparedAttack": 3963, "rawPreparedDefense": 3963, "rawPreparedTotal": 7926 }, { "route": "6+2", "base": 6, "feed": 2, "total": 8, "attempts": 210, "attemptsPerType": 105, "materialTypes": 2, "stockPieces": 4, "raw": 16297.482610975208, "factors": 164079.46686358983, "proficiency": 218772.62248478644, "directFactors": 25200, "directSule": 25200000, "rawMax": 355146, "factorsMax": 2432280, "rawAttack": 8148.741305487604, "rawDefense": 8148.741305487604, "rawPreparedAttack": 8149, "rawPreparedDefense": 8149, "rawPreparedTotal": 16298 } ], "startupStock": [ { "route": "4+2", "pieces": 4, "raw": 511.21997651933333, "factors": 3947.9663286843243 }, { "route": "3+3", "pieces": 1, "raw": 24.66158832736918, "factors": 166.24137462440925 }, { "route": "5+1", "pieces": 4, "raw": 2745.573020747189, "factors": 23300.966016989936 }, { "route": "4+4", "pieces": 4, "raw": 511.21997651933333, "factors": 3947.9663286843243 }, { "route": "5+3", "pieces": 4, "raw": 2745.573020747189, "factors": 23300.966016989936 }, { "route": "6+2", "pieces": 4, "raw": 15270.997385469766, "factors": 133980.55551055717 } ], "confirmed": { "rarePityRoutes": [ "4+2", "3+3", "5+1" ], "rarePity": 73, "foolPityRoutes": [ "4+4", "5+3", "6+2" ], "foolPity": 105, "countPityByInputTier": { "1": 10, "2": 10, "3": 8, "4": 8, "5": 8 }, "attackDefenseCountersShared": false, "countPitySameTierOnly": true, "keepOrSwapBasePreservesCountPity": true, "sharedMutationCounterRouteGroups": [ [ "4+2", "3+3", "5+1" ], [ "4+4", "5+3", "6+2" ] ] }, "assumptions": [ "Rates are rounded inclusive long-run rates. Expected cycle attempts use 1/r, never a second capped geometric calculation.", "Each count-upgrade cycle starts after its tier counter reset. Existing partial progress is not estimated.", "Attack and defense have separate counters at each tier and mutation group; never pool their attempts.", "One raw item is one one-attribute material of the required type. Attack and defense cannot be mixed.", "Retain one reusable base; craft one feed per failed attempt. Successful upgrades consume both inputs and retain the new output.", "Ordinary crafting has enough distinct affixes. Prices, desired precious affixes and special-result interactions are excluded.", "Mean route budgets require existing qualified stock, are long-run cycle allocations, and are not a guarantee for one player.", "Fresh budgets add four gate-stock pieces where needed, then a full 73/105 attempts. Upstream crafting uses means, so this is not an all-process upper bound or first-target expectation.", "Balanced budgets assume attack/defense raw materials arrive 1:1. Count 73/105 attempts for each type, share the four gate pieces once, and use one 3+3 reusable base per type. Each type is rounded up separately for displayed preparation quantities.", "Upstream 3+3/4+4 may already produce the target and build type-specific pity progress. Stop and reassess; no exact joint-process expectation is claimed." ], "unknown": [ "Per-attempt hazard / soft-pity curve and remaining-progress conditional mean", "Mutation-counter reset when declining a mutation result", "Joint distribution of count upgrades, mutation and ordinary quality upgrades", "Exact desired-affix inheritance and ordinary quality-upgrade chances" ], "targetRareExamples": [ { "conditionalRate": 0.05, "meanRareDrops": 20.0, "meanEligibleAttempts": 1025.6410256410256, "individualAffixPity": false }, { "conditionalRate": 0.2, "meanRareDrops": 5.0, "meanEligibleAttempts": 256.4102564102564, "individualAffixPity": false } ], "switchThresholdWithBase": 6, "switchThresholdFreshGate": 25 }