A Tower of Fantasy Featured Weapon pull costs 150 Dark Crystal. The base SSR rate is 0.75% per pull. Pity guarantees an SSR by pull 80, and losing the 50/50 guarantees the next one is the featured weapon. Run those four numbers through the math and the worst-case cash cost to walk away with a specific featured SSR lands at $363.84, while the average (expected-value) cost across many players is closer to $206. That gap between “worst case” and “expected value” is the whole story of whether a gacha pull is worth the money, and it is the same math that applies to every banner in every gacha game, just with different inputs.
This piece walks through that math step by step using Tower of Fantasy’s currently published rates (Global version 6.3, live as of September 2026) as the worked example, because Level Infinite and Hotta Studio’s numbers are among the more clearly documented in the genre. The formula itself, though, works for any banner in any game, and we will show you how to plug in different numbers at the end.
The Short Answer: What a Tower of Fantasy Pull Is Actually Worth
A single pull has a 0.75% chance of landing an SSR weapon, and roughly half of the SSRs you get will be the featured one rather than a random one from the standard pool. If you spend nothing extra, you will get an SSR of some kind within 80 pulls, guaranteed, because Tower of Fantasy’s hard pity floor kicks in at exactly that number. If that SSR is not the featured one, the game guarantees your very next SSR is. That structure caps the true worst case for landing a specific featured weapon at 160 pulls, which is 24,000 Dark Crystal, which converts to 24,000 Tanium, which costs $363.84 if you buy currency at the best available rate.
Most players never hit that ceiling. Averaged across the probability curve, the expected cash outlay to land the featured weapon works out closer to $206. The $364 figure is what you should budget if you want a guarantee going in. The $206 figure is what you should expect to actually pay if you are willing to gamble. Neither number is the “real” price of a pull; they are two different answers to two different questions, and confusing them is the single most common way players misjudge whether a banner is worth their money.
How Gacha Expected Value Is Calculated, Step by Step
Expected value, in the statistical sense, is the probability-weighted average of every possible outcome, the same underlying concept that applies to any gacha-style randomized monetization system. For a gacha pull, that means multiplying the chance of each result by what that result costs, then summing across every outcome. In practice, gacha economics only needs four real inputs to build a usable expected-value model: the base drop rate for the item you want, the pity or guarantee mechanic that caps your worst case, the in-game currency cost of one pull, and the real-money price of that currency.
With those four numbers you can build two figures that matter far more than the headline drop rate: the expected number of pulls until you get what you want, and the guaranteed number of pulls it takes in the absolute worst case. Multiply either by the cost per pull and you get a dollar figure. The rest of this article is that calculation, done in full, using Tower of Fantasy’s confirmed rates so you can see every step rather than take a final number on faith.
Tower of Fantasy’s Pull Rates and Pity System, Confirmed
Tower of Fantasy’s Featured (Limited) Weapon banner runs on a base SSR rate of 0.75% per pull, a figure repeated consistently across player-maintained rate trackers and guides referencing the in-game probability disclosure. That is not a typo for the more commonly rounded 0.8% you will see quoted elsewhere; 0.75% is the more precise figure carried in detailed breakdowns of the banner’s own rate table. Every pull draws from that same 0.75% chance independently, with no reset, until one of two things happens: you pull an SSR by luck, or you hit the hard pity floor.
Base Rate and Soft Pity
Hard pity is confirmed at 80 pulls: if you have not received an SSR weapon by your 80th pull on the Featured banner, the 80th pull is guaranteed to produce one. Crucially, that pity counter does not reset when you pull an SSR early. It keeps counting toward 80 regardless of what you have already received, which means an unlucky run cannot “waste” progress. Community-run trackers such as pitycalculator.com also report that the effective rate climbs starting somewhere around pull 60, a soft-pity ramp similar to the one in other gacha titles, but Level Infinite has not published an official per-pull escalation curve the way some competitors have. We treat that ramp as real and directionally favorable to the player, without inventing exact percentages for pulls in the 60-79 range, because no verified official table for that range exists.
The 50/50 and the Featured Guarantee
When an SSR does drop, the Featured banner splits it 50/50: half the time it is the featured weapon, half the time it is a random SSR from the standard pool. If you lose that coin flip, the system guarantees your next SSR pull will be the featured weapon. That is the same “guarantee on loss” structure used across most of the genre, and it is what turns an 80-pull single-cycle pity into a 160-pull worst case for a specific featured item: one full cycle to force an SSR, a coin flip you might lose, and a second cycle that is now guaranteed to pay off.
The Currency Chain: From Real Money to a Single Pull
Tower of Fantasy uses a three-step currency chain that is easy to get lost in, so it is worth walking through once. Real money buys Tanium directly from the in-game shop. Tanium converts to Dark Crystal at a fixed 1:1 rate, meaning 1,000 Tanium always becomes exactly 1,000 Dark Crystal with no loss. Dark Crystal is then spent at a rate of 150 per pull on the Featured banner, technically purchasing a Nucleus that is immediately consumed for one draw. Because the Tanium-to-Dark-Crystal exchange is 1:1, you can treat Tanium and Dark Crystal as interchangeable for cost purposes, and that is what the calculations below do.
Tanium is sold in six standard tiers that mirror the usual mobile in-app purchase price points. Here is the full table, with the effective price per unit of Tanium worked out for each tier.
| Tanium Pack | USD Price | Price per Tanium | Pulls It Buys (150 Tanium each) |
|---|---|---|---|
| 60 Tanium | $0.99 | $0.01650 | 0 (partial pull only) |
| 300 Tanium | $4.99 | $0.01663 | 2 |
| 980 Tanium | $14.99 | $0.01530 | 6 |
| 1,980 Tanium | $29.99 | $0.01515 | 13 |
| 3,280 Tanium | $49.99 | $0.01524 | 21 |
| 6,480 Tanium | $99.99 | $0.01543 | 43 |
Notice that the biggest pack is not the best deal. The 1,980-Tanium pack at $29.99 has the lowest per-unit price of any tier, at roughly $0.01515 per Tanium, edging out even the $99.99 flagship pack. The 300-Tanium pack is actually the worst value in the entire lineup, worse even than the smallest $0.99 pack. If you are optimizing spend, stacking multiples of the $29.99 tier, topped off with the $0.99 tier to hit an exact number, beats simply buying the largest pack repeatedly.
Worked Probability Table: Your Odds by Pull Number
Using the confirmed flat base rate of 0.75%, the cumulative probability of landing at least one SSR by a given pull number follows the standard formula for independent trials: 1 minus (1 minus 0.0075) raised to the number of pulls. That formula holds cleanly through roughly pull 59, before any soft-pity boost would apply. Past that point, real odds are almost certainly higher than what a flat 0.75% rate alone predicts, because of the reported soft-pity ramp discussed above, but we are not going to invent numbers for a curve that has not been officially published. The only figure that is contractually certain past pull 59 is the one at the bottom: 100% by pull 80.
| Pulls Made | Cumulative Chance of at Least One SSR | Dark Crystal Spent |
|---|---|---|
| 1 | 0.75% | 150 |
| 10 | 7.25% | 1,500 |
| 20 | 13.98% | 3,000 |
| 30 | 20.22% | 4,500 |
| 40 | 26.00% | 6,000 |
| 50 | 31.37% | 7,500 |
| 59 | 35.86% | 8,850 |
| 80 (hard pity) | 100% (guaranteed) | 12,000 |
Two things stand out here. First, even at pull 50, your cumulative odds of having seen any SSR at all are barely above 31%, which is why pity systems exist in the first place: without a hard floor, a meaningful share of players would still be empty-handed deep into a banner. Second, the jump from pull 59 to the guaranteed 100% at pull 80 is doing a lot of quiet work, because the actual soft-pity curve in that 21-pull window is compressing a large chunk of probability that a flat-rate model cannot capture.
The Pity-Cost Table: What It Costs to Guarantee an SSR
This is the table that actually answers “how much do I need to spend to be sure.” It converts pull milestones into Dark Crystal, then into Tanium, then into a real dollar figure using the best available per-unit rate from the pricing table above (the $29.99 tier, topped off with $0.99 packs to hit an exact total).
| Milestone | Pulls | Dark Crystal / Tanium Needed | Cash Cost at Best Rate |
|---|---|---|---|
| Single pull | 1 | 150 | $2.27 |
| Hard pity: guaranteed SSR (not necessarily featured) | 80 | 12,000 | $181.92 |
| Expected cost for any SSR (probability-weighted average) | ~60.3 | ~9,048 | ~$137.05 |
| Expected cost for the featured SSR (probability-weighted average) | ~90.5 | ~13,572 | ~$205.60 |
| Worst case: guaranteed featured SSR (lose the 50/50 once) | 160 | 24,000 | $363.84 |
The hard-pity row of $181.92 uses six of the $29.99 packs plus two of the $0.99 packs, for exactly 12,000 Tanium with no waste. The worst-case row of $363.84 simply doubles that combination: twelve $29.99 packs and four $0.99 packs for exactly 24,000 Tanium. Those are not rounded estimates; they are the precise cost of buying exactly enough currency for the pull counts involved, at the best rate available in Tower of Fantasy’s own shop.
Expected Value Calculation: The Full Math
Here is how the expected-pulls figures in that table were derived, shown in full rather than asserted. For a pity system capped at N pulls with a flat per-pull success rate p, the expected number of pulls to first success is the sum of the “still haven’t succeeded” probabilities across every pull up to the cap, which simplifies to (1 – (1-p)^N) / p.
Plugging in p = 0.0075 and N = 80: (1 – 0.9925^80) / 0.0075. That works out to (1 – 0.5476) / 0.0075, or 0.4524 / 0.0075, which equals approximately 60.3 pulls. That is the expected number of pulls to land any SSR, using only the confirmed flat base rate. Because Tower of Fantasy’s real soft-pity ramp likely front-loads more probability into the 60-79 pull range than a flat rate would predict, this 60.3 figure is, if anything, a slightly conservative (higher) estimate of the true average, and we present it that way deliberately rather than guess at a lower number we cannot verify.
From there, the expected cost for the featured item specifically adds one more layer. There is a 50% chance the SSR you get in that first ~60.3-pull stretch is already the featured one, in which case you stop. There is a 50% chance it is not, in which case you are guaranteed the featured item on your next SSR, which arrives after a second cycle with the same 60.3-pull expectation. So the full expected value is 60.3 + (0.5 x 60.3) = 90.5 pulls. Multiply that by the best available cash rate of roughly $2.27 per pull (from the pricing table) and you land at $205.60, which is the expected-value dollar figure in the table above, rounded.
Five Worked Examples With Real Numbers
- The lucky pull. A player’s very first pull on a fresh Featured banner lands the SSR, and it is the featured one. Cost: 150 Dark Crystal, or $2.27 at the best rate. This happens roughly 0.375% of the time (0.75% base rate, split 50/50 for the featured result), so it is rare but not impossible.
- The single big pack. A player buys one $99.99 pack for 6,480 Tanium, good for 43 pulls. At the flat 0.75% base rate, that gives roughly a 27.7% cumulative chance of landing at least one SSR (using 1 – 0.9925^43), before accounting for any soft-pity boost that has not yet kicked in at pull 43. There is no guarantee at this spend level.
- Hitting hard pity, winning the coin flip. A player pulls 80 times without an SSR appearing early, hits the guaranteed SSR at pull 80, and wins the 50/50. Total cost: 12,000 Dark Crystal, or $181.92 at the best rate, for a guaranteed featured weapon. This is the “average bad luck” scenario.
- Hitting hard pity, losing the coin flip. A player pulls 80 times, gets the guaranteed SSR, but it is the standard-pool item, not the featured one. They keep pulling; the game now guarantees the next SSR is the featured weapon, which arrives at the latest by pull 160. Total worst-case cost: 24,000 Dark Crystal, or $363.84 at the best rate.
- The two-pack budget. A player buys two $99.99 packs for 12,960 Tanium, good for 86 pulls, comfortably past the 80-pull hard pity floor. They are guaranteed at least one SSR and have a 50% chance it is the featured one outright; if not, they are already six pulls into the second guaranteed cycle. Total spend: $199.98, which lands between the hard-pity cost and the worst-case cost in the table above.
Best Value vs Worst Value: Which Top-Up Pack to Buy
Why the Smallest Pack Isn’t Always the Worst Deal
The pricing table above shows a counterintuitive result: the $4.99 pack for 300 Tanium is worse value per unit than the $0.99 pack for 60 Tanium. Publishers often price mid-tier packs to nudge players toward specific purchase amounts rather than to reward volume evenly, and Tower of Fantasy’s Tanium tiers are a clean example. The lesson generalizes well beyond this one game: always check price-per-unit before assuming a bigger sticker price means a better rate, because gacha shops are not obligated to make every tier proportionally cheaper.
In Tower of Fantasy’s case, the $29.99 tier for 1,980 Tanium is the genuine best rate on offer, at roughly $0.01515 per Tanium. Stacking that tier and topping off with the $0.99 tier, as the cost calculations above do, gets you to any target pull count with the least amount of leftover, unspent currency.
Does Pity Carry Over Between Patches?
Yes, within the same banner category. Tower of Fantasy’s pity counter does not reset when a new patch or new Featured banner rotation goes live; unfinished pity progress on the weapon banner carries forward into the next weapon banner. That matters directly for the expected-value math above, because it means a player is never punished for banner timing the way they might be in a system that wipes pity at each rotation. Version 6.3, the Global build live through late September 2026, uses this same carryover structure, consistent with the pity mechanics that have applied to the Featured Weapon banner across prior versions.
Myths vs Facts About Gacha Expected Value
| Myth | Fact |
|---|---|
| Pulling an SSR resets your pity counter to zero. | In Tower of Fantasy, pity keeps accumulating toward 80 even after you pull an SSR early; it does not reset. |
| Losing the 50/50 means you’re back to a fresh 0.75% chance with no safety net. | Losing guarantees your next SSR is the featured item, capping the true worst case at 160 pulls rather than leaving it open-ended. |
| The most expensive top-up pack always has the best rate. | In this game’s shop, the $29.99 tier beats the flagship $99.99 tier on price per unit, and the $4.99 tier is worse value than the $0.99 tier. |
| Expected value and guaranteed cost are the same number. | They are different questions: expected value (~$206 here) is the probability-weighted average; guaranteed cost ($363.84) is the worst-case ceiling. |
| A 0.75% base rate means you need about 133 pulls on average. | That 1/0.0075 = 133 figure ignores the 80-pull hard pity floor; once you cap the distribution at 80, the real expected pull count drops to about 60.3. |
How Tower of Fantasy’s EV Compares to Other Gacha Games
The core mechanics here, a low single-digit-percent base rate, a hard pity floor somewhere between 70 and 90 pulls, and a 50/50 with a guarantee on loss, are close to an industry standard shape at this point. What varies from game to game is the pull cost in local currency and the real-money price of that currency, which is exactly why the same formula can produce very different dollar outcomes depending on the title. A game with a cheaper effective per-pull cash rate but a higher pity number can still end up more expensive in worst-case dollars than one with pricier pulls but a lower pity cap, and the only way to know which is true for any specific banner is to run the same four-input calculation shown above: base rate, pity cap, currency cost per pull, and real-money price per unit of currency.
That is also why headline drop-rate percentages, taken alone, tell you very little about what a banner will actually cost you. A game advertising a higher base rate than another can still be the worse deal in expected dollars if its pity cap is longer or its currency is priced less generously. Always run the full chain before comparing games on odds alone.
Is a Gacha Pull Ever “Worth It” in Expected-Value Terms?
That depends entirely on how you value the item you are chasing, which is a subjective input no probability table can supply for you. What the math above can tell you, objectively, is the range of what you are likely to pay: somewhere between $2.27 (extreme luck) and $363.84 (the guaranteed ceiling), with $205.60 as the mathematically expected middle if you are pulling without a top-up budget cap. If a featured weapon is worth less than $206 to your enjoyment of the game, the expected-value math says you are, on average, overpaying relative to what most players will spend to get it. If it is worth more than $364 to you, then even the worst-case outcome is one you would accept going in, which is the closest thing to a rational “this pull is worth it” threshold that pure probability can offer.
Regulators in several countries already treat these mechanics as a form of randomized paid content worth scrutinizing, which is part of why publishers increasingly disclose base rates at all. Still, what the math cannot do is tell you whether spending real money on a mobile game banner is a good use of your budget in the first place. That is a personal financial decision, not a statistical one, and no expected-value table should be read as encouragement to spend beyond what you have already decided you are comfortable with.
Frequently Asked Questions
What is Tower of Fantasy’s actual SSR drop rate?
The base rate for an SSR weapon on the Featured banner is 0.75% per pull, with a hard pity guarantee at pull 80 if no SSR has appeared by then.
Does Tower of Fantasy have soft pity like Genshin Impact?
Community-run rate trackers report the effective rate begins climbing around pull 60, similar in spirit to other gacha titles’ soft-pity ramps, but Level Infinite has not published an official pull-by-pull escalation curve, so exact percentages in that range cannot be verified.
What happens if I lose the 50/50 on the Featured banner?
Your next SSR pull on that banner is guaranteed to be the featured weapon, which caps the worst-case total at 160 pulls, or 24,000 Dark Crystal.
How much does it cost in dollars to guarantee the featured SSR?
At the best available Tanium rate in Tower of Fantasy’s shop (the $29.99 pack for 1,980 Tanium), the worst-case guarantee of 24,000 Tanium costs exactly $363.84.
Does pity carry over between game versions?
Yes, within the same banner category. Unfinished weapon-banner pity progress carries into the next weapon banner rather than resetting at each patch.
Is expected value the same thing as the guaranteed cost?
No. Expected value is the probability-weighted average outcome across many players (about $205.60 here); guaranteed cost is the fixed worst-case ceiling that covers every possible outcome, including bad luck ($363.84 here). They answer different questions and should not be swapped for each other.
Is the biggest top-up pack always the best value?
Not necessarily. In Tower of Fantasy’s shop, the $29.99 tier for 1,980 Tanium has a lower price per unit than the $99.99 flagship pack, and the $4.99 tier is actually worse value than the smallest $0.99 pack. Always compare price per unit of currency rather than assuming scale equals savings.
