Mathematical analysis reveals Reliquary costs 19,200-25,600 primogems with 15-20% DPS boost for Nefer, while Luna III's December 2025 release offers 20-25% team improvements through Hexenzirkel mechanics and broader character synergies.
Understanding Genshin Impact Weapon Banner Mathematics
Here's the thing about weapon banners – they're brutal on your primogem stash, but the math isn't as scary as some players make it out to be. Let me break down exactly what you're getting into.
Pity System Mechanics
The weapon banner runs on 80-pull hard pity instead of the character banner's 90. That's already better odds. Soft pity kicks in around pulls 63-65, bumping that measly 0.7% base rate up significantly. Each 5-star has a 75% chance of being one of the featured weapons, with a 25% chance of trolling you with something like Aquila Favonia from the standard pool.
Your pity counter carries between banners – that's crucial to remember. So does the 75/25 guarantee. But here's where it gets tricky: Epitomized Path resets completely when the banner changes. You've got to manually select your target weapon before wishing, and each wrong 5-star earns you 1 Fate Point. Hit 2 points? Your next 5-star is guaranteed to be your selected weapon. That caps you at 160 total wishes maximum (25,600 primogems if luck completely abandons you).
Probability Calculations
The real success rate per 5-star pull sits at 37.5% (75% featured rate × 50% chance of getting the right featured weapon). Most players see success within 160 pulls – about 90% probability there. Within 120 pulls? You're looking at roughly 85% success rate.
Average acquisition costs hover between 120-150 pulls (19,200-24,000 primogems) when you factor in soft pity mechanics. Not cheap, but not the nightmare some make it out to be either.
Reliquary of Truth: Complete Analysis
Weapon Stats and Performance
At level 90, you're getting 542 Base ATK and 88.2% CRIT DMG. The passive Essence of Falsity is where things get interesting – 8% CRIT Rate baseline, +80 EM after using Elemental Skill (lasts 12 seconds), and +24% CRIT DMG after triggering Lunar-Bloom damage (4 seconds).
When both effects are active simultaneously, they amplify by 50%. That means +40 EM and +12% CRIT DMG during optimal rotations. Pretty spicy.
I've been running benchmark tests with C0 Nefer as the 100% performance baseline. A Thousand Floating Dreams hits about 86% of that performance, Nightweaver's Looking Glass R1 reaches 89%, and the craftable Blackmarrow Lantern R5 manages 88% effectiveness. Solid alternatives, honestly.
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Character Synergies
Nefer's obviously the star here – she sees a 15-20% DPS increase over her next-best alternatives. But the weapon isn't completely locked to her. Lauma, Nahida, and Mualani all benefit from that high Base ATK and CRIT DMG substat.
The catch? The passive is heavily optimized for Lunar-Bloom reactions. That limits its universal appeal compared to other 5-star catalysts that play nice with everyone.
Luna III: Comprehensive Overview
Weapon Specifications
December 3, 2025 – mark your calendars. Luna III drops with some genuinely impressive hardware.
The 5-star Sword for Durin packs 608 Base ATK, +33.1% CRIT Rate, and 16-32% Burst DMG bonuses. The 5-star Bow is even more impressive: 674 Base ATK, +44.1% CRIT DMG, and up to 120% damage scaling through its Time's Rhapsody passive. Even the 4-star Event Bow looks solid with 510 Base ATK, +45.9% Energy Recharge, and 28-56% ATK bonuses triggered by off-field hits.
What's really interesting is how these weapons emphasize off-field triggerable passives. They're clearly designed around support roles and the new Hexenzirkel mechanics, where characters like Albedo get +36% DMG bonuses when running Magic character teams. We're looking at a potential meta shift toward Mondstadt-focused compositions.
Character Pairings and DPS Calculations
Durin (5-star Pyro Sword) is the obvious primary target – he's built as a DPS/hybrid support with solid off-field Pyro application. Jahoda (4-star Anemo Bow healer) uses the new bow for coordinator summons that grant EM when HP exceeds 70%. And Venti? He's getting some serious buffs with piercing arrows post-burst and duration extensions.
Early calculations suggest 20-25% team DPS improvements when Hexenzirkel buffs activate. Unlike Reliquary's character-specific optimization, Luna III weapons show broader applicability. Those 36% damage buffs create multiplicative scaling that can exceed single-weapon improvements.
Mathematical Comparison: Pull Costs and Strategy
Expected Investment and Risk Analysis
Reliquary needs 19,200-24,000 primogems on average, with a 25,600 maximum guarantee. Luna III banking requires 24,000-30,000 primogems over 2-3 months – totally doable with F2P monthly income of 8,000-10,000 primogems from dailies and events.
The worst-case scenario for Reliquary? You hit that 10% probability of losing both the 75/25 rate AND getting the wrong featured weapon. That's 160 pulls of pain. Banking eliminates this risk entirely while giving you access to new characters and potentially superior weapons through Hexenzirkel synergies.
You can buy Genesis Crystals for weapon banner pulls through BitTopup's platform, featuring instant delivery, competitive rates, and 24/7 customer support for smooth resource access during your pulling strategy.
Player Type Strategies
F2P Optimization
Honestly? Skip weapon banners. That 25,600 primogem maximum equals 1-2 character guarantees. Use craftable alternatives like Blackmarrow Lantern – it hits 85-90% of signature weapon performance and costs you some mining time instead of months of savings.
Focus on character diversity. Banking for Luna III provides better long-term value, especially with those team-wide Hexenzirkel buffs.
Light Spender Approach
Monthly subscribers have more flexibility here. Keep 14,400 primogems for character guarantees, then consider weapons with your extra resources. Reliquary works if you've got established Dendro teams. Luna III appeals more for Pyro/Anemo expansion.
Whale Considerations
Go for both. No resource constraints mean you can focus on R1 breadth over refinement depth for maximum team flexibility. Just coordinate your weapon and character pulls to maximize synergies across all content types.
Decision Framework
Pull Reliquary if:
Nefer's your primary DPS and needs that immediate 15-20% improvement
Your current teams are struggling with DPS checks in Spiral Abyss
You've got 25,600+ primogems and zero interest in Luna III characters
You're running established Dendro compositions that need optimization
Bank for Luna III if:
You want roster expansion with Pyro/Anemo characters
Current weapons provide adequate performance (that 85-90% efficiency range)
Hexenzirkel mechanics and team-wide buffs sound appealing
You prefer long-term planning over immediate gains
Common Mistakes and Tools
Critical Errors
Sunk cost fallacy is the big one – players keep pulling after failures instead of cutting losses. Set strict budgets before you start. Remember that Epitomized Path requires manual activation and resets between banners. And don't misunderstand the probability – it's not 50/50 between featured weapons, it's 37.5% for your specific target.
Optimization Tools
Track your current pity through in-game Wish History (expires after 6 months, so screenshot if needed). Use weapon banner simulators for probability analysis with your specific situation. Calculate expected costs using that 37.5% per-pull success rate, and always budget for 160 pulls maximum at 90% confidence.
FAQ
How many primogems guarantee Reliquary of Truth? Maximum 25,600 primogems (160 pulls) with Epitomized Path. Average runs 19,200-24,000 primogems (120-150 pulls) based on probability analysis.
Should F2P players pull weapon banners? Generally no, unless both featured weapons provide significant upgrades and you've got 25,600+ primogems sitting around. Character acquisition provides better roster value.
When does Luna III release? December 3, 2025. You're getting a 5-star Sword for Durin (608 ATK, 33.1% CRIT Rate) and 5-star Bow (674 ATK, 44.1% CRIT DMG). Pre-installation starts December 1.
How does Epitomized Path work? Select your target weapon before pulling. Each non-selected 5-star earns 1 Fate Point. Hit 1 Point and your next 5-star is guaranteed to be your selected weapon. Points reset when banners change – don't forget this part.
Success probability in 120 pulls? About 85% chance within 120 pulls, accounting for that 37.5% per-pull rate and soft pity mechanics.
Is Reliquary worth it versus free alternatives? For Nefer users, you're looking at 15-20% DPS improvement over alternatives. Free options like Blackmarrow Lantern achieve 85-90% performance, so the decision comes down to your optimization priorities and available resources. Sometimes that extra 10-15% just isn't worth months of savings.