Every cast written out as equations, with the slot number under each term. ( ) multicasts, [ ] trigger payloads, { } copies from Divide By and the Greek letters.
Wand
Always casts
Spells
ProjectileStaticModifierMulticastMaterialUtilityOtherPassive~ random or player-dependent part
Spell stats
All 393 spells, including unlockables, read from the game's own spell and projectile files. Edit mana, cast delay or recharge if a patch changed them. Spells whose behavior is handled by special rules (Divide By, Greek letters, Requirements, Add Trigger and so on) show their stats read-only.
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Rules this calculator uses
The draw engine follows the game's wand rules: cards move from the deck to the hand to the discard pile, modifiers draw one more card, multicasts draw several, and triggers start a new shot that draws its own payload.
Wrapping: when a modifier, multicast or trigger needs a card and the deck is empty, the discard pile (spells from earlier casts, not this one) is shuffled back in order and the wand recharges after this cast. The cast's own first draws never wrap.
Cast delay belongs to the cast that fired. Cast delay from spells inside a trigger payload goes to the payload and is ignored (struck through). Chainsaw sets the running total to 0, written as × 0.
Recharge adds up across every cast in the cycle, starting from the wand's base, and applies once when the wand runs out.
Mana is paid when a card is drawn, in slot order. A card the wand can't afford is skipped and the next one is drawn. Copies made by Divide By, Alpha and the rest are free.
Divide By copies the next card; only the first copy is blocked from drawing. Its copies' cast delay and recharge are undone, then the copied cards are discarded. Mu, Phi and Sigma also undo their copies' cast delay, recharge and mana.
Modifiers apply to every projectile in the same shot. Speed multipliers stack by multiplying and cap at 20×. Projectiles also cap at their terminal velocity (usually 1000 px/s).
Distance is speed × lifetime in a straight line. It ignores gravity, air friction and walls, so it's the most a projectile can travel. Nolla cuts lifetime to about 3 frames. A payload on an expiration trigger (like Long-Distance Cast) starts where its carrier ends.
Limited-use spells lose a charge each cycle they fire. With Unlimited Spells, only spells the game marks as never unlimited still run out.
Spell data comes from the game's files (stable branch, March 2023). Damage shows projectile damage only, ×25 as in the game's tooltips; other damage types aren't counted.