NTE Warp Planner

A pull-planning calculator for Neverness to Everness (NTE).

Tell it what you own (Annulith, Solid Dice, Tri-Keys, Warp Pieces) and what you're aiming for, and it returns your exact probability of reaching that goal plus the average number of pulls it takes.

Inspired by the HSR Optimizer Warp Planner, re-derived from scratch for NTE's gacha rules.

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Features

• Character banner (Scarborough Fair / Limited Board) — chance to reach any Awakening level (A0 → A6).
• Arc banner (Arc Research Program / Miracle Box) — chance to reach any Mixing Intensity level (T1 → T5).
• Resources entered as raw currency; conversions and compounding refunds are folded in automatically.
• Pity-aware: start the calculation from your current pity counter.
• Exact probabilities — same result every time, no simulation variance.
• Reactive UI: every number recomputes instantly as you type.

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How it works — the gacha rules modelled

All figures below come from NTE's in-game rule pages (Scarborough Fair → Board Details, Arc Research Program → Miracle Box, Mall → Warp Exchange).

Currencies

Currency	Role	Conversion
Annulith	Premium currency (flexible)	160 Annulith = 1 pull
Solid Dice	Character-banner pulls	1 die = 1 roll
Tri-Keys	Arc-banner pulls	10 Tri-Keys = 1 box (1 Limited Issue)
Warp Pieces	Recycle currency (flexible)	24 Warp Pieces = 1 die / Tri-Key

Character banner (Limited Board)

• One roll = one Solid Die. The board-game layer (rolling 1–6, landing on tiles) is cosmetic for probability purposes — the game publishes a clean per-roll featured rate.
• No 50/50. The featured S-Class character is always guaranteed; there is no off-banner loss to model.
• Pity is a flat staircase, shared across all Limited Boards:

Roll # (since last featured)	Featured rate	Board state
1 – 70	0.99 %	Baseline
71 – 89	19.59 %	Modified (after 70 consecutive misses)
90	100 %	Hard pity

• The blended effective rate is 1.87 % per roll.
• Board tiles passively refund dice/Warp Pieces (Roll Again, Multiple Surprises, Hero Chest) — modelled as a ~5.1 % compounding refund.

Arc banner (Miracle Box)

• One pull = one Limited Issue box = 10 Tri-Keys = 10 Arcs. Pity is counted in boxes, shared across all Limited Issues.
• Per-Arc drop rates: S-Class 3 % base (4.19 % w/ pity), of which the featured Arc is 1.68 %; A-Class 7 % (13.47 % w/ pity); B-Class 90 %.
• Pity guarantees: any S-Class within 6 boxes, the featured Arc within 8 boxes (hard pity).
• Unlike the character banner, an S-Class Arc can be off-featured. The planner targets the featured Arc only, so off-featured S-Class pulls are ignored (they don't advance Mixing Intensity and don't reset the featured pity).
• Arc Warp-Piece bonuses (40 per S-Class, 4 per A-Class) are modelled as a ~9.2 % compounding refund.

Awakening & Mixing Intensity

Concept	HSR analogue	Levels	Copies needed
Awakening (character dupes, via Mind Shards)	Eidolon	A0 → A6	A_n = n + 1 copies
Mixing Intensity (Arc dupes)	Superimposition	T1 → T5	T_n = n copies

So A6 = 7 character copies; T5 = 5 Arc copies.

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The math

The engine (src/lib/warp-engine.ts) is pure and side-effect-free:

1. Per-pull distribution — buildDistribution(rateFn, cap) produces the PMF dist[i] = P(a single copy lands exactly on pull i+1) for a fresh pity counter.
2. Pity adjustment — pityAdjustedPmf(dist, pity) slices off the pulls already spent and renormalises (the conditional cost given the current pity).
3. Multiple copies — multiCopyCostPmf convolves the per-copy PMFs (first copy from current pity, every later copy from a fresh pity, since pity resets on a success).
4. Summarise — summarize(costPmf, budget) returns successChance = P(total cost ≤ budget) and average = Σ k·P(cost = k).
5. Budget — currencies are converted to pulls/boxes and inflated by the compounding refund as a geometric series (raw / (1 − refundRate)).

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Assumptions & limitations

• ARC_FEATURED_PER_ARC = 1.68 % is taken from the in-game rules and used to derive the per-box featured rate (~15.6 %). If real player data shows a different value, this is the single constant to retune.
• Refund rates (5.1 % character, 9.2 % Arc) are estimates of the average passive income from board tiles / Arc Warp-Piece bonuses, compounded geometrically.
• One banner at a time. Each calculation uses one currency pool. Annulith and Warp Pieces (flexible) are fully assigned to the targeted banner; Solid Dice feed only the character banner and Tri-Keys only the Arc banner.
• Featured Arc only. Off-featured S-Class Arcs are not counted toward Mixing Intensity.
• Action advances, energy, board minigames (Slumberland, etc.) and non-pull rewards are out of scope — this is a pull planner.