Universal Tower Defense X Reroll Timing Calculator

Reroll Timing Calculator

How UTDX reroll math actually works

Trait rerolling in Universal Tower Defense X follows geometric distribution: the same probability model used in gacha games for banner pity math and in card games for rare card pulls. Each reroll is an independent event with a fixed probability of landing the target trait tier. That probability does not change based on how many rolls you have already done.

The expected number of pulls to hit a target with probability p is exactly 1/p. If your target trait has a 1-in-25 chance, expected pulls is 25. But expected is not the same as guaranteed: about 37% of sessions will require more than 25 rolls, and roughly 10% will require more than 58. That spread is why the calculator shows three numbers: mean, median, and 90th percentile: rather than just one.

Trait tier probability is not officially published by the UTDX developers as of May 2026. The values in this calculator are derived from community sampling data shared across Discord and the Stouts Studio group, supplemented by my own session logs across roughly 640 recorded trait rerolls since the game launched. They are the best available estimates, not confirmed developer figures. I update them if community data shifts significantly after a patch.

Trait tier reference

When to reroll: the 15% improvement threshold

The question I get asked most in UTDX Discord is "is it worth rerolling my trait?" The math answer depends on two things: how much better the target trait is, and how many rolls you have. My working rule: reroll when the target trait adds at least 15% improvement over the current trait, and you have at least 2× the expected pull count in reserve.

Below 15% improvement, the runs-saved versus rerolls-spent ratio tends to go negative unless the unit is your primary carry. A 10% damage improvement on Water God is worth less than a 10% improvement on First Emperor, because Water God's value is in its slow duration rather than raw damage. Role matters as much as the stat number.

The 2× reserve rule protects against unlucky sessions. If you start a reroll session with exactly the expected pull count and no buffer, roughly 37% of sessions end before the target is hit. That is a real-money or real-time loss if the session outcome was supposed to upgrade your main carry before the next map attempt. Two times the expected count gives you roughly 86% session completion probability: better odds than a coin flip on whether your session plan actually works out.

Co-op rerolling: support traits matter more

In solo play, trait value is isolated to your own units. In co-op Endless Mode: which is where team composition guides like this one get tested: the same support aura applies to every teammate's units in range. A Water God with an aura-strength Legendary trait is also 30% better for your own units; it is 30% better for every unit inside its radius across all four players.

That scales the effective value of support trait upgrades considerably. When I run four-player Endless Mode sessions, I prioritize trait upgrades on Water God, Virtual Idol, and Love Goddess before chasing damage trait improvements on the carry units. The co-op multiplier on support traits is real and it changes the worth-it calculation.

Optimal reroll budget timing by unit type

Different unit types justify different reroll budget sizes because the value of hitting the target trait varies by how much that unit contributes to run outcomes.

Mythic boss-killers like First Emperor (Greatest) and Alpha Devil (Omega) are the highest-value reroll targets. These units are already expensive to acquire, and the performance difference between a Common trait and a Legendary trait on a boss-killer is visible within a single run: the boss-contact window is fixed, so any trait that increases burst during that window translates directly to whether the boss dies before exiting your firing line. Budget 3× expected pulls before starting on Mythic boss-killer trait sessions.

Legendary carries like Crow Shinobi (Reanimated) and Ichiko (Rage) sit one level below in reroll priority. The improvement curve is real but less dramatic: these units fire during extended lane segments rather than narrow boss windows. Budget 2× expected pulls. The 2× rule gives you enough runway for an Epic trait run without draining your entire reserve.

Support units: Virtual Idol, Love Goddess, Mimicry Sorcerer: justify rerolling for specific trait types (aura radius or aura strength) but not for generic damage trait improvements. A damage trait on a support unit is nearly worthless in practice. Reroll supports only when targeting the correct trait category, and stop at Rare or Epic rather than chasing Legendary. The probability math and gem cost for Legendary on a support unit are better spent on your primary carry.

Farm units such as Bulmo and Fastcart should receive economy relics and economy traits, but chasing Legendary economy traits is rarely the best use of reroll budget. The gold-per-wave difference between an Epic and Legendary economy trait is modest, and the probability cost is high. Reroll farm units last, after carries and support units have been addressed.

Session discipline: stop rules and common waste patterns

The most common waste pattern I see in UTDX reroll sessions is rolling past a good result. A player hits an Epic trait on roll 18, keeps rolling because Legendary is theoretically possible, and ends the session with a Common trait at roll 31 after burning through the reserve. The Epic on roll 18 was better than the final result, but by that point the reserve was gone.

Define the stop condition before the first roll. Write it down: "I will stop at the first Epic or better result, and I will not exceed 40 rolls regardless of outcome." That sentence makes the session auditable. If you deviate from it, you know exactly which decision lost you the resource.

The stop rule embedded in the calculator output is my recommendation based on your specific inputs: target tier, reserve size, and unit role. Follow it unless the run is for a unit that definitively changes whether you can clear the next map checkpoint. In that case, you may extend to P90 as the hard ceiling: not as a soft guideline.

Patch timing also interacts with reroll decisions. Rolling for a Legendary trait on a unit that is likely to be rebalanced in the next update is a lower-EV session than rolling on a stable unit. After Update 2.75 in May 2026, several DPS units saw minor stat adjustments. Units that had been rerolled to Legendary pre-patch were fine; units that had not been rerolled were not suddenly worse, just unchanged. Stability of the unit's role is a reasonable factor to consider before committing a large reserve.

Using free rerolls from codes: timing the spend

Active UTDX codes hand out meaningful reroll reserves. As of May 2026: GiftFromMiniking! gives 100 Trait Rerolls plus 3 Exclusive Shards, 40kInterestedWano! gives 200 Trait Rerolls, and 20KInterestedWano! gives 250 Trait Rerolls. That is 550 trait rerolls from codes alone: enough to cover roughly 9 full Epic-tier sessions or 2 Legendary-tier sessions within P90.

The timing question is whether to spend code rerolls immediately or hold them until the right unit is available. My answer is to hold them until you have a clearly identified target: a specific unit, a specific trait category, and a defined stop condition. Spending 550 rerolls across six different units without a stop condition on any of them produces random results on all of them instead of a good result on one.

Redeem codes from the codes page before any reroll session, not during it. The codes are time-limited and expiring mid-session while you are watching trait results is an avoidable frustration. Check for new codes at the same time: update windows often drop additional code strings alongside patch notes.

Which trait categories to target by unit role

Trait categories in UTDX are not published in a clean list, but from 640 recorded rolls I can map the trait outcomes reliably enough to guide reroll targeting. Trait results fall into roughly five categories: damage amplifiers, fire-rate boosters, range extenders, support multipliers (aura strength/radius), and economy accelerators.

For boss-killers, target damage amplifiers and fire-rate boosters. Boss windows are time-limited and the units with the most contact time inside those windows see the highest return from either category. Range extenders are secondary: useful on maps with short contact zones, neutral on maps with long lanes.

For carry units, both damage amplifiers and fire-rate boosters improve sustained output. The choice between them depends on the unit's base attack pattern: units with slow, heavy attacks gain more from fire-rate; units with fast attacks gain more from damage amplifiers. In practice, either category at Epic or higher is a meaningful upgrade on a Legendary or Mythic carry.

For support units, target aura strength and aura radius. Damage amplifiers on a support unit that provides team buffs rather than personal damage are nearly worthless: the amplifier applies to the support's own small damage number, not the team buff magnitude. Always check what the trait category does to the specific unit, also what the category name implies.

For farm units, economy traits (gold output rate, income interval reduction) are the only meaningful category. Rolling for combat traits on Bulmo or Fastcart is a category mistake: those units do not contribute combat value even with a Legendary damage trait.