Short answer: guaranteeing a specific 5-star pull isn’t one price, it’s two. In Fate/Grand Order, the worst-case cash cost to force the featured unit through its 330-pull hard guarantee is about $440, but the probability-weighted average cost most players actually pay is closer to $152. That $288 gap between “worst case” and “expected value” is the real answer to whether a pull is worth the money, and the size of that gap changes dramatically depending on whether a game ramps your odds up as you approach the cap (soft pity) or keeps them flat until the guarantee hits. Below is the full pity-cost table, the step-by-step math behind both numbers, and how the same calculation plays out in Genshin Impact, Honkai Star Rail, and Goddess of Victory: NIKKE.
What “Guaranteed” Actually Means Across Gacha Games
Every gacha game promises a guarantee eventually, but “guarantee” means three different things depending on the title. The first type is a probability-based hard pity: the odds of pulling a top-rarity item climb with every failed pull (soft pity), then hit 100% at a fixed number (hard pity). Genshin Impact and Honkai Star Rail both work this way, with a hard pity wall at 90 pulls for any 5-star character. The second type is a flat-rate hard cap with no ramp at all: the odds stay exactly the same pull after pull until a fixed count is reached, at which point the result is simply forced. Fate/Grand Order’s Guaranteed Summon system, confirmed on its own official banner pages, works this way, with the odds locked at a flat rate all the way to pull 330. The third type isn’t probability-based at all: Goddess of Victory: NIKKE hands out one Gold Mileage Ticket per pull, and once you’ve banked 200 of them, you redeem the featured unit directly, no RNG involved in the final step.
These three designs produce wildly different relationships between the “worst case” number players quote online and the “expected” number most of them actually pay. A flat-rate system with a distant cap, like FGO’s, tends to resolve for most players long before the cap because the odds never get worse, just repeated. A ramping system front-loads the risk into the early pulls and backloads the certainty into the final ones. A ticket system has no variance at all once a player commits to the ticket path. Knowing which bucket a game falls into matters more than knowing the raw pull count, because the pull count alone tells you almost nothing about what you should expect to spend.
The Four Numbers Behind Any Guarantee-Cost Calculation
Every guarantee-cost figure in this piece comes from the same four inputs, each pulled from an official source or a current storefront listing rather than estimated. First, the base rate: the per-pull chance of the specific item being chased, not the combined chance of “any top-rarity drop,” since those two numbers get conflated constantly and produce very different math. Second, the guarantee mechanic itself: whether it’s a ramping soft-pity curve, a flat-rate hard cap, or a ticket counter, and the exact pull number where it resolves. Third, the in-game currency cost of a single pull, since multi-pull discounts change the real cost per roll. Fourth, the real-money price of that currency at the best available package rate, since the per-unit price drops as package size grows.
Miss any one of those four and the resulting dollar figure is fiction. A large share of the “cost to pity” numbers that circulate online skip the multi-pull discount entirely, which is exactly the mistake that inflates Fate/Grand Order’s guarantee cost from its true floor of 900 Saint Quartz to a commonly repeated 990, a nearly 10% overstatement that comes from pricing single pulls instead of the 11x Multi Summon. The table below uses the discounted rate throughout.
Case Study: Fate/Grand Order’s 330-Pull Guaranteed Summon
Fate/Grand Order’s summoning system is documented on its own official banner pages at webview.fate-go.us, with the rate structure also confirmed by GamePress’s NA summon simulator. A single summon costs 3 Saint Quartz, while the 11x Multi Summon costs 30 Saint Quartz for 11 rolls, an effective rate of 2.73 Saint Quartz per pull rather than 3. On a standard single-rate-up banner, the overall chance of any 5-star Servant is 1.0% per pull, split as 0.8% for the specific featured Servant and 0.2% spread across the rest of the standard 5-star pool. If a player reaches 329 pulls on that banner without naturally receiving the featured Servant, the 330th pull is forced to grant it, no exceptions.
Saint Quartz is sold on the US App Store in six tiers: $0.99 for 1 SQ, $3.99 for 5, $11.99 for 18, $23.99 for 41, $39.99 for 76, and $79.99 for 167, the best per-unit rate in the lineup at roughly $0.479 per Quartz. Buying the exact 900 Saint Quartz needed for 330 pulls through the cheapest real combination of those packages (five 167-Quartz packs plus one 76-Quartz pack, for 911 total) comes to $439.94 before tax. That is the true worst-case cash price to guarantee Fate/Grand Order’s featured Servant with zero free currency and zero natural luck.
The FGO Pity-Cost Table: Pull 1 to the Guarantee
Because the 0.8% featured rate never ramps, the chance of success by any given pull follows a simple compounding formula: 1 minus 0.992 raised to the number of pulls. Here is how that curve, and its cash cost at the 11x Multi Summon rate, looks at key milestones.
| Pulls | P(featured Servant by this pull) | Saint Quartz spent | Cash spent (best rate) |
|---|---|---|---|
| 1 | 0.8% | 2.7 | $1.31 |
| 30 | 21.4% | 81.8 | $39.19 |
| 75 | 45.3% | 204.5 | $97.97 |
| 116 (average) | 60.6% | 316.4 | $151.53 |
| 150 | 70.0% | 409.1 | $195.95 |
| 200 | 79.9% | 545.5 | $261.26 |
| 250 | 86.6% | 681.8 | $326.58 |
| 300 | 91.0% | 818.2 | $391.89 |
| 329 | 92.9% | 897.3 | $429.78 |
| 330 (hard guarantee) | 100% (forced) | 900.0 | $431.08 |
Read that middle column carefully: the probability only reaches 92.9% by pull 329, meaning roughly 7.1% of players would still be empty-handed at that point on pure luck. The guarantee doesn’t “kick in gradually,” it simply forces a result on pull 330 for whoever’s luck ran that cold. Everyone else gets there earlier, which is the entire reason the average cost sits so far below the worst case.
Step-by-Step Expected Value: Why the Average Isn’t $440
Expected value here means the probability-weighted average number of pulls a player actually needs, not the ceiling they might need. For a flat-rate system capped at a maximum of n pulls, that average is calculated as (1 minus the chance of total failure through n pulls) divided by the per-pull rate. Plugging in FGO’s numbers: (1 minus 0.992 to the power of 330) divided by 0.008 equals (1 minus 0.0706) divided by 0.008, which comes out to 116.2 pulls on average, less than a third of the 330-pull hard cap.
Converting that to Saint Quartz: 116.2 pulls at the 11x Multi Summon’s 2.73 SQ-per-pull rate comes to 317 Saint Quartz. At the best available package rate of $0.479 per Quartz, that’s $151.76, which rounds to the $152 figure quoted at the top of this piece. Compare the two numbers side by side: $440 is what a player should budget if they want a guarantee locked in before spending a cent. $152 is what the average player across a large enough sample actually ends up paying. Treating either number as “the price” of FGO’s featured Servant misses the point; they answer two different questions, and the gap between them is the actual measure of how much luck is worth in this specific system.
Why FGO Has No Soft Pity, and Why That Changes Everything
This is the detail that separates Fate/Grand Order’s math from almost every other major gacha game covered on this site: there is no soft pity ramp at all. GamePress’s summon simulator and FGO’s own banner pages describe a flat rate held constant from pull 1 all the way to pull 329, with the only escalation being the forced result on pull 330 itself. Compare that to Genshin Impact or Honkai Star Rail, where the base 5-star rate is published at a flat 0.6% but community-tracked data shows the rate climbing sharply somewhere around pull 74, well before the 90-pull hard cap.
A flat-rate system without a ramp sounds worse on paper, since there’s no “lucky zone” where the odds visibly improve. In practice, it produces a lower expected cost relative to its own hard cap than a ramping system does relative to its hard cap, for a simple reason: a longer runway at a constant rate gives the geometric distribution more room to resolve naturally before the ceiling. The lesson for players is that the hard-pity pull count alone is a poor predictor of what a banner actually costs. A game with a “worse” 330-pull ceiling can still produce a lower real-world average spend than a game with a “better” 90-pull ceiling, depending entirely on the base rate and whether that rate ramps.
How Genshin Impact and Honkai Star Rail’s Guarantee Compares
Genshin Impact’s Character Event Wish costs 160 Primogems per wish, with a 0.6% base chance of pulling any 5-star character and a hard pity guarantee at 90 wishes, confirmed directly in HoYoverse’s own Version 5.0 Event Wishes Notice. That’s 14,400 Primogems to force a 5-star outright. Genesis Crystals (which convert 1:1 to Primogems) are sold in the same tiered pattern as FGO’s Saint Quartz: $0.99 for 60, up to $99.99 for 6,480 plus a 1,600-crystal bonus, 8,080 total, confirmed on Codashop’s official US pricing page. Buying 14,400 Primogems through the cheapest real combination of those packages costs roughly $184 before tax. Honkai Star Rail runs an identical structure (Stellar Jade, the same 160-per-wish cost, the same 90-pull hard pity, the same package tiers under a different currency name), so the dollar figures track almost exactly.
That 90-pull number only guarantees a 5-star, not necessarily the specific featured one. HoYoverse’s own Capturing Radiance explainer confirms the consolidated chance of that 5-star being the promotional character sits at 55%, not a flat 50/50, a mechanic covered in detail in our separate Genshin Impact 50/50 breakdown. Using only the flat, pre-ramp 0.6% base rate (the conservative, officially-confirmed figure, since HoYoverse hasn’t published the exact soft-pity curve), the expected number of wishes to land any 5-star works out to about 70, putting the average cash cost at roughly $138, versus $184 to force it outright at pull 90. The real figure is almost certainly lower than $138 once the undisclosed soft-pity ramp, which only helps the player, is factored in, which is exactly why this piece treats it as a conservative estimate rather than a precise one.
Cross-Game Guarantee Cost Comparison
| Game | Featured-item rate | Guarantee type | Pulls to force it | Cash to force it |
|---|---|---|---|---|
| Fate/Grand Order | 0.8% (flat, no ramp) | Flat-rate hard cap | 330 | ~$440 |
| Genshin Impact / Honkai Star Rail | 0.6% for any 5-star; 55% of those are featured | Soft pity + hard pity | 90 (any), up to 180 worst case for featured | ~$184 (any 5-star) |
| Goddess of Victory: NIKKE | 2% per pull (half of the 4% SSR rate) | Deterministic ticket counter | 200 | 60,000 Gems (USD rate not independently verified) |
NIKKE’s row looks different from the other two because it is different: Level Infinite’s Gold Mileage Ticket system isn’t a probability curve at all once a player commits to it, it’s a straight currency exchange, 1 ticket per pull, 200 tickets for the featured unit, with zero variance in either direction. That removes the entire “worst case vs expected” question for the ticket path specifically, though it also means NIKKE has no path to a lucky early pull discount the way FGO or Genshin do.
Five Worked Examples: What Different Budgets Actually Buy
Example 1: Buying FGO’s guarantee outright from zero. A player with no free Quartz who wants certainty before spending a cent needs the full 900 SQ, bought as five $79.99 packs plus one $39.99 pack, for $439.94. This is the only way to remove all risk entirely.
Example 2: A cold-luck FGO player stuck at pull 200. With 130 pulls left before the guarantee, the remaining natural chance of still failing is 35.2%. Buying the rest of the way to pull 330 costs another 355 Saint Quartz, about $170, on top of whatever was already spent reaching pull 200.
Example 3: A $100 budget in FGO vs. a $100 budget in Genshin. $100 buys roughly 209 Saint Quartz, enough for about 77 FGO pulls, carrying a 45.9% chance of landing the featured Servant. The same $100 in Genshin buys roughly one $99.99 package’s worth of crystals, about 50 wishes, carrying roughly a 26% chance of a 5-star of any kind using the conservative flat-rate math. A flat dollar amount does not buy the same odds across games, even when both games are frequently described as “similarly generous.”
Example 4: Subscription currency vs. lump-sum currency in Genshin. Reaching 90 wishes requires 14,400 Primogems. Genshin’s Blessing of the Welkin Moon costs $4.99 per 30-day cycle and grants 300 Genesis Crystals instantly plus 90 Primogems daily, 3,000 total per cycle. Five cycles supply 15,000 Primogems, covering the full 90-wish guarantee, for $24.95 total, an 86% discount versus the roughly $184 it costs to buy the same 14,400 Primogems through one-off Genesis Crystal packages. The subscription is dramatically cheaper for anyone willing to wait five months instead of paying all at once.
Example 5: NIKKE’s deterministic floor. A player who decides in advance to grind straight to the 200-pull Mileage guarantee knows the exact cost on day one: 60,000 Gems, no more, no less, regardless of how the RNG behaves along the way, since any SSR pulled early simply ends the grind sooner without changing the ticket math for players who continue anyway.
Myths vs. Facts About “Guaranteed” Pulls
| Myth | Fact |
|---|---|
| Every gacha game ramps your odds up as you approach the pity cap. | Fate/Grand Order’s featured-unit rate stays completely flat at 0.8% all the way to pull 329, per GamePress’s documented rate table; the only jump is the forced result on pull 330 itself. |
| The hard-pity pull count tells you how expensive a banner is. | FGO’s 330-pull cap sounds three to four times worse than Genshin’s 90-pull cap, but FGO’s average expected cost (~$152) lands in the same range as Genshin’s worst-case cost (~$184), because the two systems distribute probability completely differently. |
| A 50/50 means a flat 50% chance every time. | HoYoverse’s own Capturing Radiance mechanic raises the consolidated chance of winning that coin flip to 55%, officially documented on HoYoverse’s site, not a flat 50%. |
| Buying currency in one lump sum is always the cheapest way to reach pity. | In Genshin, spreading the same spend across five months of Welkin Moon subscriptions costs roughly 86% less than buying one-off Genesis Crystal packages for the same total. |
| “Worst case” and “expected cost” are basically the same number. | In every system examined here, they differ by at least 20%, and in FGO’s case by nearly 190%; conflating them is the single most common reason players misjudge a banner’s real cost. |
Is a Pity Guarantee the Same Thing as Provably Fair?
No, and the distinction matters. A pity guarantee is a design choice that bounds the worst case; it says nothing about whether the published rate matches the rate actually running on the server. “Provably fair” in the strict sense requires a verifiable mechanism, typically a client-seed-plus-server-seed hash system common in casino-style RNG products, that lets a player independently confirm the outcome wasn’t altered after the fact. None of the three games examined here publish that kind of cryptographic verification for their gacha pulls; what they publish instead is a rate table and a guarantee mechanic, which is a weaker but still meaningful form of transparency. HoYoverse’s decision to publish the exact 0.018% trigger rate and 55% consolidated rate for Capturing Radiance, and FGO’s decision to display its guarantee counter directly in the summon UI, are both voluntary disclosures rather than cryptographic proofs. They’re worth taking seriously, but they’re a different category of “fair” than a provably-fair casino RNG, a distinction covered in more depth in our loot box disclosure laws explainer.
How to Budget for a Guarantee Without Overspending
The practical takeaway from all this math is simple: decide in advance which number to budget against, and don’t let the other one creep into the decision. If the goal is certainty, budget the worst-case figure and treat anything spent below that as a bonus, not a plan. If the goal is “probably get it without going broke,” budget the expected-value figure and accept that a meaningful share of players, roughly 7% in FGO’s case, will need more than that and should have a fallback plan rather than chasing sunk cost. Subscription currency (Welkin Moon, Express Supply Pass, and FGO’s own login bonuses) should almost always be the first dollar spent, since it converts into pull currency at a steep discount compared to one-off packages, as Example 4 above shows directly. And before spending anything, check whether the specific banner uses a flat rate or a ramping rate, because that single fact changes the expected-to-worst-case ratio more than any other input in the entire calculation.
Frequently Asked Questions
Is it cheaper on average to guarantee a 5-star in FGO or Genshin Impact?
Using the expected-value math above, FGO’s average cost to the featured Servant (~$152) and Genshin’s worst-case cost to any 5-star (~$184) land close together, but they aren’t measuring the same thing: FGO’s figure guarantees the specific featured unit, while Genshin’s hard-pity figure only guarantees a 5-star of some kind, with the featured character requiring a separate 55% roll on top.
Why does Fate/Grand Order’s pity cap sit so much higher than Genshin’s?
Because the two systems are built differently. FGO keeps the odds flat at 0.8% with no ramp, so it needs a much longer runway, 330 pulls, to make the cumulative failure probability acceptably small. Genshin ramps the odds sharply in the final pulls before 90, reaching the same kind of near-certainty in far fewer attempts.
Does buying the 11x Multi Summon actually save money in FGO?
Yes. A single summon costs 3 Saint Quartz per pull, while the 11x Multi Summon costs 30 Saint Quartz for 11 pulls, an effective 2.73 Saint Quartz per pull, roughly 9% cheaper per pull than buying singles.
What percentage of players actually need Fate/Grand Order’s full 330-pull guarantee?
Based on the flat 0.8% featured rate, about 7.1% of players will still be without the featured Servant after 329 pulls purely by chance, and will need the forced 330th pull to receive it.
Is NIKKE’s Gold Mileage Ticket system better than a probability-based pity?
It’s different rather than strictly better: it removes all variance once a player commits to the 200-pull path, so the exact cost is known in advance, but it also removes any chance of an early, lucky, cheap pull that probability-based systems allow.
Is Capturing Radiance the same thing as a guaranteed 50/50 win?
No. Capturing Radiance raises the consolidated chance of winning a 50/50-style roll to 55% rather than a flat 50%, and HoYoverse has stated that losing three consecutive 50/50s guarantees the next win, but it is not a guarantee on the first or second roll.
Does a higher base drop rate always mean a lower expected cost?
Not by itself. NIKKE’s 2% featured rate is more than double FGO’s 0.8%, but NIKKE’s guarantee is a fixed 200-pull ticket exchange rather than a probability curve, so the two systems aren’t directly comparable on rate alone; the guarantee mechanic matters as much as the base rate.
