The Insane Mathematics of Mystic

Battle resolution

The Die Is Cast

Every battle is two six-sided dice: overall strength = strength modifier + roll, highest total wins. That is 36 equally likely outcomes, few enough that we can simply count them. No simulation anywhere on this page: every probability is exact.

The 36 outcomes, at equal strength

Rows are the attacker’s roll, columns the defender’s. Win by 4 or more and the loser is destroyed; win by less and the defender retreats (the attacker must advance). Notice how much of the grid is not lethal.

A triangular battlefield

The margin of victory (attacker roll − defender roll) follows a triangular distribution: a dead heat is six times likelier than a rout. The coloured tails are the only cells where anyone dies at equal strength.

Three uncomfortable facts

8.3%of equal-strength battles destroy anything. The kill line (margin ≥ 4) sits near the edge of the dice.
16.7%of equal-strength battles end in a draw. The attacker must exceed the defender to win, so every draw is a failed attack: defenders hold 58.3% of parity battles.
33.3%end in a retreat: the most common decisive result is a shuffle, not a kill.

The ladder of advantage

What a strength edge is worth, from −3 to +4. Each +1 shifts the whole triangular distribution one step sideways, which is why biome buffs are effectively dice surgery.

Ninety creatures

The Roster, Weighed

The roster is a perfect 9 × 10 matrix: each of the 9 biomes contributes exactly 10 creatures, covering each of the 10 classes once. But the strength budget each biome spends is anything but equal.

Strength distribution

An approximately bell-shaped curve from 1 to 6, summing to 311 (mean 3.46). Only four creatures in the game reach strength 6.

Class averages

Nine creatures per class. Dragons and Giants are the heavyweights; Undead are cannon fodder by design, fitting for a class with its own resurrection spell. Only Dragons and Undead have class-specific spells at all (see R2).

The biome budgets

Total strength per biome (10 creatures each). Mountain and Tundra field armies 57% stronger than Desert and Forest. Remember this chart when we get to biome buffs: one of these biomes also holds the strongest combat buff in the game.

Nine realms, nine deals

Biome Equity

Every biome pays its natives and taxes its visitors, but in three different currencies: dice (strength), gold (economy) and actions (tempo). Each deal is priced out below.

What a buff is worth

Combat buffs, measured as the shift in an even-strength battle; economic buffs, measured in gold per trigger. Tundra’s Acclimatized is the outlier: the largest dice shift in the game, active on attack and defence, with no trigger condition.

Biome	Match buff	Buff value	Mismatch debuff	Debuff value

Swamp and Cave deal in tempo, which resists pricing: Stuck can eat two-thirds of a turn; Trapped can turn a retreat into a death sentence.

Gold flow

The Economy

Gold enters through harvesting, biome tricks and selling creatures; it leaves through summoning and spells. Every player starts with 4 gold and a safety net of 1 gold for any turn ended creature-less.

Harvest yields by biome

Four tiles per biome. Eight biomes run 1–4 gold (mean 2.5); Desert alone runs 2–5 (mean 3.5), the richest soil in the game. The ±1 gold crossing effect is a smaller matter than it looks: each crossing costs an action, and actions are the scarcest currency in the game (see R4).

The price of power

Ability costs from the master tables (mean 3.3 gold), against a mean harvest of 2.61 gold per action. Selling a creature returns its strength in gold: mean 3.46.

The implied price list

Creatures_tbl has no cost column, but the north star Ice Elemental prints strength 4, cost 6, ability Freeze: exactly cost = strength + ability cost, with the unlisted Freeze priced at 2 gold. Applied to the roster, the formula implies costs from 2 to 12 gold (mean 6.75).

Exchange rates

1 action≈ 2.61 gold when harvesting an average tile
1 move= 1 action, i.e. the harvest not taken (opportunity cost ≈ 2.61 gold)
1 spell= 1 gold, no action: the cheapest tempo in the game
1 creature= its strength in gold when sold (mean 3.46)
1 summon≈ 6.75 gold implied (strength + ability cost), about 2.6 harvest actions
1 Ocean entry= 0.67 gold in expectation for a native; a 1-in-6 double discard for a stranger

The shuffle

Deck & Draw Math

Two decks: 90 creatures, and a Lands & Spells deck of 71, with 36 lands against only 35 spells. Every draw from it is a coin flip.

The Lands & Spells deck

50.7% of the deck is land. Your opening hand holds two of these cards, so the chance you can summon at all on turn one (gold permitting) is 76.1%. Nearly a quarter of players open without a deed.

Reactions & triggers

Lightning-bolt density: 12 of 27 abilities and 8 of 35 spells can be played in response. Most triggered abilities ask for a roll above 3 (a coin flip) or above 4 (one in three).

The biome lottery

Pair a random creature with a random land card and the biomes match only 11.1% of the time. Eight times out of nine, a summoning sends a creature into hostile terrain; the debuff chart is not an edge case but the default state of the board.

The win condition

The Chain

Control 3–7 connected tiles, in any configuration, and hold them for a full round. “Any configuration” hides a combinatorial explosion. This page enumerates every free polyhex (winning shapes, up to rotation and reflection) live:

Every winning shape, sizes 3 and 4

Three trihexes and seven tetrahexes, drawn exactly as enumerated. By size 7 there are 333 distinct winning silhouettes.

The growth of choice

Free polyhexes by chain size. Longer chains are not just slower to build: the shape space explodes, which is why large-N games sprawl.

Holding the line

An attack at equal strength flips a tile 41.7% of the time (kill or retreat; the attacker must advance either way). Survival of a chain through a round of k such attacks is 0.583^k, unless you defend on buffed ground, where Forest/Tundra’s +2 cuts the flip rate to 16.7%.

The recommended chain length is 8 − players, a rule of thumb that dips below the 3-tile minimum at six players (8 − 6 = 2). Creators: consider max(3, 8 − n) in the next rulebook pass.

Combinatorial scale

Every Possible Mystic

How large is this game? Before anyone rolls a die, the board itself is drawn from a combinatorial ocean, and every battle multiplies it further. Exact where the data allows, honest estimates where it does not.

Continents

The map is 36 unique tiles in any connected shape. This page enumerated the small winning shapes exactly (3 trihexes, 7 tetrahexes, 333 at size 7); the counts are known to size 25 (about 6.5 × 10¹⁴) and grow by about 5.2× per cell. Extrapolated, roughly 10²³ connected continents of 36 hexes exist, and each admits 36! ≈ 3.7 × 10⁴¹ tile assignments: about 10⁶⁴ possible maps.

Battle situations

90 attackers × 89 defenders × 9 tile biomes × 36 dice outcomes = 2,595,240 atomic duels. Count which subset of the 35 spells is in play (2³⁵) and the tally reaches roughly 10¹⁷ distinct battle situations.

The league table of universes

State spaces on a log scale: each bar is roughly ten times the one before it. Mystic lands between Chess and Go, mostly because its board is rebuilt every game. (Approximate state spaces, for fun: Tic-tac-toe 10⁴, Connect Four 10¹³, Checkers 10²¹, Chess 10⁴⁴, Go 10¹⁷⁰.)

Try it yourself

The Battle-Odds Calculator

Pick any two creatures from the real roster and the tile they fight over. Biome effects are applied from the master data; the odds are the exact count of the 36 outcomes. Spells and abilities are excluded; they are the wildcard.

Attacker

Creature

vs Battle tile

Only Tundra (±2), Forest (+2, defender only) and Plains (−1, non-natives) move the numbers.

Defender

Creature

All 36 roll pairs, coloured by outcome.

For the creators

Recommendations

Eight adjustments, each motivated by the numbers above. Daniel, Don: the dice have spoken.

R1

Tundra: Acclimatized +2 → +1

At equal base strength, +2 turns a battle into 72.2% wins with a 27.8% kill rate (3.3× the baseline) and a flat 0% chance of being destroyed. Worse, it stacks on the roster’s second-largest strength budget (43, mean 4.3): a Tundra native on home ice fights at an effective 6.3 against a world average of 3.46, roughly a +3 differential, or 83.3% wins and 41.7% kills before spells are considered. The biome’s strongest native (Okami, strength 5) defends home ice at an effective 7: a typical strength-4 attacker wins 8.3% of the time and is destroyed 41.7% of the time, while the holder cannot be destroyed at all.

At +1 the buff stays the best combat deal in the game (58.3% wins, 16.7% kills) without making home ice unwinnable for visitors. Alternative: keep +2 but pull Tundra’s strength budget down toward the 33–34 median.

R2

Give every class a spell

Only 2 of 35 spells reference a creature class: Alliance fetches a Dragon and Reanimate returns an Undead. The other eight classes (Orc, Elite, Elemental, Angel, Demon, Giant, Mermaid, Dwarf) have no spell support at all, so class identity is expressed almost entirely through strength and abilities.

Design a class-spell cycle: one targeted spell per class at the flat 1-gold rate raises class coverage from 2 of 10 to 10 of 10 and gives the spell deck a second axis of counterplay.

R3

Mind the kill line (margin ≥ 4)

On two d6, a 4-point kill margin means equal creatures destroy each other only 8.3% of the time; 33.3% of battles end in a retreat. The game is positional by design: creatures die to buffs and focus-fire, not to fair fights.

If that grind is the intent, keep it; it is elegant. If you want bloodier battles, margin ≥ 3 doubles the parity kill rate to 16.7%. Do not do both this and keep Tundra at +2.

R4

Reprice the harvest outliers, not the Desert crossing

A first draft of this section flagged the Desert’s ±1 gold crossing effect as an exploit. It is not: every crossing costs 1 of the turn’s 3 actions, so pacing in and out yields 1 gold per action, strictly worse than harvesting even an average tile (2.61) and far behind the best tiles (4 gold anywhere, 6 on a Mountain-buffed 4-tile). The genuine outliers are tile-based: Desert’s 2–5 spread (mean 3.5, +40%) and Mountain’s Resourceful, which lifts its tiles to an effective 3–6 (mean 4.5, +80%).

Leave the crossing trigger as printed. Trim Resourceful to +1, or drop Desert’s 5-tile to 4, to bring peak harvests back toward the 2.5 mean.

R5

Balance Ocean in one currency

Lucky pays gold (EV +0.67 per entry); Unlucky taxes cards (1-in-6 chance to discard two). Buff and debuff live in different economies, so the matchup is impossible to price and feels swingy rather than risky.

Mirror the currencies: either both gold (e.g. Unlucky: on a 1, lose 2 gold) or both cards. The current EV asymmetry also makes Ocean the only biome whose debuff can be wholly avoided by simply having no cards, a perverse incentive to empty your hand.

R6

Formalise the summoning-cost formula

The north star card implies cost = strength + ability gold cost (Ice Elemental: 4 + 2 = 6). Two inconsistencies follow. First, the data assigns Ice Elemental AOE (cost 3), which would price the card at 7 rather than 6; the unlisted Freeze belongs in Abilities_tbl at 2 gold. Second, selling a creature returns its strength, so under the formula a sale refunds the body and writes off the ability (mean write-off 3.3 gold). Smaller gaps remain: AbilityID 23 is missing, and spell cost is flat-1 in the rules but per-spell in the renders.

Add a Cost column to Creatures_tbl computed as strength + ability cost (mean 6.75 gold, range 2–12), add Freeze at 2 gold, and decide whether selling refunds strength or full cost. Then re-run this page.

R7

Reprice the 1-gold abilities

Ability costs run 1 to 6 gold (mean 3.3), but the 1-gold tier punches far above its price: Poison makes a creature undestroyable when initiating an attack, and Invisibility makes it unattackable in its native biome. Under the cost formula (R6) these add a single gold to a summon. Three creatures carry Poison (Zirax, Mordecai, Swamp Elemental).

Move Poison and Invisibility to the 3-gold tier alongside Stun and AOE, or scope them down (for example, Poison protects against destruction but not repulsion).

R8

Guarantee an opening line

Summoning requires a creature card and a matching land card, yet the opening hand holds only two cards from a deck that is 50.7% land: 23.9% of players open with no land at all and cannot summon on turn one. They spend their first actions drawing while opponents develop.

Deal each player one land card before the opening draw, or allow a landless hand to be mulliganed.