Magic Formulas

Magic in Utopia runs on wizards and runes. This page explains how your wizards are trained, what makes a spell last longer or land more often, what a spell costs, and gives the formulas and full spell tables behind it. If you only want to know what each spell does, read Mystics first; come here for the numbers.

In short

Wizards are not bought with gold. Your Guilds train them slowly: 0.02 wizards per Guild per day.
Percent Guilds (Guilds divided by acres) makes your spells last longer. At 20% Guilds, spells reach their maximum duration.
Wizards per acre (WPA) decides whether offensive spells succeed. What counts is your modified WPA divided by your opponent's.
Self spells never depend on WPA. Their success depends on Percent Guilds.
Every spell costs runes. The cost grows with your land size and the spell's cost multiplier.
The spell tables at the bottom list every spell with its bonus, difficulty, cost, duration and who can cast it.

How magic works

Unlike footmen or thieves, wizards are not trained with gold. Your ascendant wizards study in Guilds before they can serve you, which makes Guilds an absolute necessity for Mages.

Guilds and wizards

Guilds train 0.02 wizards daily (a 2% chance to train a wizard per Guild).
Guilds are unaffected by Building Efficiency (BE), both for spell duration and for wizards trained.
Guilds also increase the duration of your self spells and offensive spells.
Guilds train wizards only while your number of wizards is below the maximum allowed. See the training limit.

What Percent Guilds does

Percent Guilds (% Guilds) is the share of your land that is Guilds. The higher it is, the longer a spell lasts, until the spell reaches its own maximum duration. You reach every spell's maximum when 20% of your land is Guilds (unaffected by Building Efficiency). Some Races or Personalities have a bonus or penalty to spell duration. Destabilize Guilds lowers spell duration.

Self spells

A higher Percent Guilds gives a greater:

Spell duration
Chance of a successful cast

WPA does not influence self spells.

Offensive spells

A higher Percent Guilds gives a greater spell duration. Success also depends on wizards per acre, below.

Wizards per acre and success

The ratio of your WPA to your opponent's WPA determines how often your offensive spells succeed. Magic Effectiveness raises your WPA without changing your number of wizards; the result is called mod WPA (see the formulas below). The higher your mod WPA is compared with your opponent's, the greater your:

Chance of a successful cast
Chance of preventing an opponent's spell

Formulas

Numbers last updated 25 Nov 2024.

Percent Guilds

Divide your Guilds by your acres.

% Guilds=Total Number of Guilds÷Total Acres

Wizard training limit

Guilds train wizards if it is allowed and your current number of wizards is less than the maximum allowed.

Maximum Wizards Allowed to Train=Peasants×2

Raw WPA

Divide your wizards by your acres.

Raw WPA = Number of Wizards /Acres

Modified WPA

Modified WPA is raw WPA multiplied by each modifier that applies. Use the offensive version when you cast and the defensive version when you are the target. The modifier values follow the two formulas.

Offensive Modified WPA=Raw WPA×Channeling Science×Race Mod×Honor Mod×Mage's Fury Mod×Dragon Mod

Defensive Modified WPA=Raw WPA×Channeling Science×Race Mod×Honor Mod×Mage's Fury Mod×Magic Shield Mod×Dragon Mod

Modifier Type	Active	Otherwise
Race: Dark Elf	1.1	1
Race: Elf	1.25	1
Race: Human	0.7	1
Mage's Fury: Mage's Fury	1.25 (off) / 0.75 (def)	1 / 1
Magic Shield: Magic Shield	1.2 (def)	1
Ritual: Havoc	1.25 (off)	1
Dragon: Sapphire	0.7	1

Numbers last updated 25 Nov 2024. Changed? Help keep it current.

WPA ratio for offensive spells

Your chance of success depends on this ratio. Higher is better for you.

Modifier=Your Mod WPA÷Opponent's Mod WPA

Runes cost

The runes a spell costs depend on your land size and the spell's cost multiplier (see the spell tables).

Runes cost = ROUNDDOWN ( (0.6 * Size + 200) * Spell Cost Multiplier * 1.5 )

Spell tables

Each row is one spell. Spell Bonus is the effect size, and Difficulty, Cost Multiplier and Duration (Average) are the spell's cast difficulty, runes cost multiplier and typical length. The last columns show, for each race and personality, whether it can cast the spell. Click "Details" for what the spell does. For full descriptions see Mystics.

Self spells

Spell	Description	Spell Bonus	Difficulty	Cost Multiplier	Duration (Average)	Support Spell	Av	DE	Dry	Dw	Elf	Fa	Ha	Hu	Or	Art	Cle	Her	Mys	Rog	Shep	Tact	WH	Warr
Minor Protection	Details Increases Defensive Military Efficiency by 5% (multiplicative). Stacks with Greater Protection.	105%	0.017	0.35	12	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Greater Protection	Details Increases Defensive Military Efficiency by 5%. Stacks (multiplicative) with Minor Protection.	105%	0.019	0.45	24	Yes	Yes	No	No	No	No	Yes	No	Yes	No	No	No	No	No	No	No	No	No	No
Magic Shield	Details Increases Defensive Magic Effectiveness by 20%.	120%	0.022	0.5	14	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Mystic Aura	Details Makes the next spell cast on you fail automatically.		0.022	0.5	N/A	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No
Fertile Lands	Details Increases Food production by 25%	125%	0.022	0.5	16	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Nature's Blessing	Details Grants immunity to Storms and Droughts. Has a 33% chance to cure the Plague on a successful cast.	100%	0.023	0.6	16	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Love & Peace	Details Increases Birth Rate by +0.85% and War Horse production rate by 40%.	+0.85%	0.024	0.7	14	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Divine Shield	Details Decreases Instant Spell Damage taken by 20%.	80%	0.024	0.8	12	Yes	No	No	No	No	No	No	No	No	No	No	Yes	No	No	No	No	No	No	No
Quick Feet	Details Decreases Attack Time by 10%.	90%	0.026	0.8	2	No	No	No	No	No	No	Yes	Yes	No	No	No	No	No	No	No	No	No	No	No
Builder's Boon	Details Reduces Construction Time by 25%.	75%	0.027	1	12	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Inspire Army	Details Reduces wages by 15% and decreases training time by 20%.	85%/80%	0.028	1.1	12	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Hero's Inspiration	Details Reduces Military Wages by 30% and Training Time by 30%.	70%/70%	0.017	1.1	14	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No
Scientific Insights	Details Increases Science Efficiency by 10%.	110%	0.019	1.25	9	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No
Anonymity	Details Hides province name in the next attack, but reveals Kingdom location. No Honor gains when active. Reduces attack gains by 15%. Grants Ambush Immunity for this attack.		0.04	1.3	N/A	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Illuminate Shadows	Details Reduces Damage taken from Thievery Operations by 20%.	80%	0.02	1.3	8	Yes	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No
Salvation	Details Reduces All Military Casualties by 15%.	85%	0.02	1.3	8	Yes	No	No	No	No	No	No	No	No	No	No	Yes	No	No	No	No	No	No	No
Wrath	Details Increases the Military Casualties of attacking provinces by 20%.	120%	0.021	1.35	8	No	No	No	No	No	Yes	Yes	No	No	No	No	No	No	No	No	No	No	No	No
Invisibility	Details Increases Offensive Thievery Effectiveness (Offensive TPA) by 10%. Reduce Thieves lost during Thievery Operations by 20%.	110%/80%	0.032	1.35	12	No	No	Yes	No	No	No	Yes	No	No	No	No	No	No	No	No	No	No	No	No
Clear Sight	Details Gives a 25% chance to catch enemy thieves.	75%	0.033	1.4	16	No	No	Yes	No	No	No	Yes	No	No	No	No	No	No	No	No	No	No	No	No
Mage's Fury	Details Magic Effectiveness 25% higher for Offense, 25% lower for Defense.	125%/75%	0.033	1.4	6	No	No	Yes	No	No	No	Yes	No	No	No	No	No	No	Yes	No	No	No	No	No
War Spoils	Details While the spell is active, you immediately take control of Land gained on Attacks.		0.034	1.45	4	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Mind Focus	Details Increases Wizard production by 25%.	125%	0.033	1.475	12	No	No	No	No	No	No	No	No	No	No	No	No	No	Yes	No	No	No	No	No
Fanaticism	Details Increases Offensive Military Efficiency by 5%. Decreases Defensive Military Efficiency by 5%.	105%/95%	0.034	1.5	6	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Guile	Details Increases Instant Spell Damage and Sabotage Operation Damage by 10% for the duration.	110%	0.039	1.5	8	No	No	Yes	No	No	No	Yes	No	No	No	No	No	No	No	No	No	No	No	No
Revelation	Details Increases the Spawn Rate of new Scientists by 20% while the spell is active.	120%	0.035	1.55	10	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No
Fountain of Knowledge	Details Increases the Science Book production by 10% while the spell is active.	110%	0.033	1.55	10	No	No	No	No	No	No	Yes	No	Yes	No	No	No	No	No	No	No	No	No	No
Tree of Gold	Details Instantly generates 26.66% to 53.33% of daily Income.		0.025	1.6	N/A	No	No	No	Yes	No	No	Yes	No	No	No	No	No	No	No	No	No	No	No	No
Town Watch	Details Every 5 Peasants defend with 1 strength, but suffer high Casualties.		0.037	1.6	10	No	Yes	No	No	No	No	Yes	Yes	No	No	No	No	No	No	No	No	No	No	No
Aggression	Details Soldiers are +2/-2 strength for the duration of the spell.	+2/-2	0.037	1.625	12	No	No	No	No	No	No	Yes	No	Yes	No	No	No	No	No	No	No	No	No	No
Miner's Mystique	Details Peasants generate an extra 0.3gc per tick.	+0.3	0.038	1.65	14	No	No	No	No	Yes	No	Yes	No	No	No	No	No	No	No	No	No	No	No	No
Ghost Workers	Details Lowers Jobs required for maximum efficiency by 25%.	75%	0.038	1.65	14	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No
Animate Dead	Details In your next defensive battle, 50% your Military Casualties are returned as Soldiers.	50%	0.038	1.7	N/A	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	Yes	No
Mist	Details 10% lower resource losses in battle.	90%	0.038	1.7	4	No	No	No	No	No	Yes	Yes	No	No	No	No	No	No	No	No	No	No	Yes	No
Reflect Magic	Details 20% chance to reflect Offensive Spells back upon casters.	20%	0.4	1.8	12	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	Yes	No	No	No
Shadowlight	Details Reveals the origin Province for the next Thievery Operation on you. Makes the next Sabotage Operation targeting you fail automatically.		0.042	1.9	N/A	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Bloodlust	Details Increases Offensive Military Efficiency by 10% and Enemy Military Casualties by 15%, but suffer 15% higher Military Casualties.	110% 115%/115%	0.04	2.0	6	No	No	No	No	No	No	Yes	No	No	Yes	No	No	No	No	No	No	No	No	No
Patriotism	Details Increases draft speed by 30%. Lowers Propaganda Damage taken by 30%.	130%/70%	0.045	2.0	12	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Paradise	Details Creates a few acres of land. Consumes explore pool. Not available during War or Protection.		0.5	3.0	N/A	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Cast Ritual	Details Increases progress towards the chosen ritual for each cast. Only available on the Ritual tab.		N/A	6.0	N/A	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Spell	Description	Spell Bonus	Difficulty	Cost Multiplier	Duration (Average)	Support Spell	Av	DE	Dry	Dw	Elf	Fa	Ha	Hu	Or	Art	Cle	Her	Mys	Rog	Shep	Tact	WH	Warr

Numbers last updated 25 Nov 2024. Changed? Help keep it current.

Offensive spells

Spell	Description	Spell Bonus	Difficulty	Cost Multiplier	Duration (Average)	Av	DE	Dry	Dw	Elf	Fa	Ha	Hu	Or	Art	Cle	Her	Mys	Rog	Shep	Tact	WH	Warr
Crystal Ball	Details Reveals target's Throne, displaying Troops and Resources. Fully accurate. Costs 1 Mana.		0.004	0.35	N/A	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Storms	Details Kills Peasants equal to 1.5% of total Population. Cancels Drought. Increases Tornado damage taken by 15%.		0.009	0.8	12	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Drought	Details Food production reduced by 25%. Draft Speed reduced by 15%. Kills some War Horses. Cancels Storms. Increases Arson damage taken by 15%.	75% / 85%	0.01	1.0	12	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Magic Ward	Details Unfriendly + Hostile + War: Increases the Rune Costs of target province by 100%.	200%	0.02	1.15	6	No	No	No	No	No	No	No	No	No	No	No	No	Yes	No	No	No	No	No
Gluttony	Details Increases Food required by 25%.	125%	0.014	1.2	12	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Vermin	Details Destroys on average about 50% of target's Food.	50%	0.014	1.275	N/A	No	No	No	No	No	Yes	Yes	No	No	No	No	No	No	No	No	No	No	No
Greed	Details Increases Military Wages and Draft Costs of target province by 25%.	125%	0.016	1.3	12	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Expose Thieves	Details Unfriendly + Hostile + War: Reduces target province's Stealth by 5% of current Stealth level every Tick.	0.95	0.024	1.4	6	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Chastity	Details Reduces Birth Rate by 50%.	50%	0.024	1.4	6	No	No	No	No	Yes	Yes	No	No	No	No	No	No	Yes	No	No	No	No	No
Sloth	Details Unfriendly + Hostile + War: Reduces Drafting Rate of target province by 50%. Increases Draft Cost by 100%.	50% / 200%	0.024	1.4	6	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No	No
Fireball	Details Unfriendly + Hostile + War: Kills ~6% of opponent's Peasants.	94%	0.02	1.5	N/A	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Fool's Gold	Details Unfriendly + Hostile + War: Destroys up to 25% of target's Gold.	75%	0.02	1.5	N/A	No	No	No	No	No	No	No	No	No	No	No	Yes	No	No	No	No	No	No
Lightning Strike	Details Unfriendly + Hostile + War: Destroys up to 65% of opponent's Runes.		0.02	1.55	N/A	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Explosions	Details When sending aid if either the donor or the receiver are under the explosions spell, there is a 50% chance that the shipment will be reduced to 55%-80% of what it would have been otherwise.		0.02	1.8	12	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Blizzard	Details Reduces the building effectiveness of target province by 10%.	90%	0.02	1.8	6	No	Yes	No	No	No	Yes	No	No	No	No	No	No	No	No	No	No	No	No
Pitfalls	Details Causes opponent to suffer 15% higher Defensive Military Casualties.	115%	0.024	1.8	12	No	No	No	No	Yes	Yes	No	No	No	No	No	No	No	No	No	No	No	No
Nightmares	Details Unfriendly + Hostile + War: Roughly 1.5% of target's Troops are put back in Training over 8 Ticks.	98.5%	0.039	2.2	N/A	No	No	No	No	No	No	No	No	No	No	No	Yes	No	No	No	No	No	No
Tornadoes	Details Unfriendly + Hostile + War: Destroys several of your opponent's Buildings.		0.03	2.5	N/A	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Mystic Vortex	Details Unfriendly + Hostile + War: For each active spell your opponent has, there's a 50% chance it's removed.	50%	0.031	2.8	N/A	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Amnesia	Details War: Temporarily removes ~5% of target's total allocated Science Books. These return over 48 ticks.	0.95	0.034	2.8	N/A	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Meteor Showers	Details Hostile + War: Kills Peasants and Troops every Tick.		0.04	3.5	8	No	No	No	No	No	No	No	No	No	No	No	No	Yes	No	No	No	No	No
Abolish Ritual	Details Unfriendly + Hostile + War: Reduces enemy ritual strength by 2%. Limited to 10 casts on a single enemy province; see Ritual tab for more details.	-2%	0.032	2.8	N/A	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Land Lust	Details Unfriendly + Hostile + War: Captures between 1 and 1.25% of opponents Acres.		0.04	4	N/A	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Spell	Description	Spell Bonus	Difficulty	Cost Multiplier	Duration (Average)	Av	DE	Dry	Dw	Elf	Fa	Ha	Hu	Or	Art	Cle	Her	Mys	Rog	Shep	Tact	WH	Warr

Numbers last updated 25 Nov 2024. Changed? Help keep it current.

Who can cast what

For full information on all of the current spells refer to Mystics. The first table lists the races and personalities used in the spell tables; the second lists every spell in the spellbook by type.

Races & Personalities
Races	Avians • Dark Elves • Dryads • Dwarves • Elves • Faeries • Halflings • Humans • Orcs • Undead
Extinct Races	Bocans • Gnomes
Personalities	The Artisan • The Cleric • The General • The Heretic • The Mystic • The Rogue • The Tactician • The Warrior
Extinct Personalities	The Freak • The Paladin • The Raider • The Undead • The Necromancer • The Merchant • The Sage • The Shepherd • The War Hero

The spellbook

The Spellbook
Self Spells	Army Spells	Defensive Spells	Animate Dead • Greater Protection • Minor Protection • Town Watch • Wrathful Smite • †Fog
		Offensive Spells	Aggression • Anonymity • Bloodlust • Fanaticism • Quick Feet • War Spoils
		Army Spells	Inspire Army • †Hero's Inspiration • Patriotism
	Civil Spells	Mystic Security Spells	Divine Shield • Mage's Fury • Magic Shield • †Mystic Aura • Nature's Blessing • Reflect Magic
		Thievery Spells	Clear Sight • Illuminate Shadows • Invisibility • Shadowlight
		Economy Spells	Builders' Boon • Fertile Lands • Fountain of Knowledge • Love & Peace • Mind Focus • Paradise • Tree of Gold • Revelation • †Scientific Insights

Combat Spells	Economy Damage Spells	Friendly	Blizzard • Droughts • Explosions • Greed • Gluttony • Vermin
		Unfriendly	Amnesia • Fool's Gold • Land Lust • Lightning Strike • Magic Ward • Nightfall • †Sloth • Tornadoes • †Barrier of Integrity
	Population Damage Spells	Friendly	Storms
		Unfriendly	Chastity • Fireball • Nightmares
		Hostile	Meteor Showers
	Interaction Spells	Friendly	Crystal Ball • Crystal Eye • Pitfalls
		Unfriendly	Expose Thieves • Mystic Vortex

How magic works

Guilds and wizards

What Percent Guilds does

Self spells

Offensive spells

Wizards per acre and success

Formulas

Percent Guilds

Wizard training limit

Raw WPA

Modified WPA

WPA ratio for offensive spells

Runes cost

Spell tables

Self spells

Offensive spells

Who can cast what

The spellbook

See also