Mechanics

The formulas below are the ones the game uses. Exact values for each producer or upgrade are in the reference pages.

Tempo

Tempo is the currency. The game tracks three counters:

Counter	Meaning	Reset on prestige?
Bank tempo	what you can spend	yes
Run tempo	everything earned since the last prestige; it unlocks upgrades	yes
All-time tempo	everything earned since the beginning; it sets Elo and crowns	no

The click and the hero pawn

Each click on the board (not on a rival piece):

earns the click value:
```
click = (click multiplier × crown bonus + production/s × % of production per click) × temporary click bonuses
```
- click multiplier: 1 at the start, ×2 for each of “Touch-Move Rule”, “J’adoube”, “Snap Move”, and ×2 for the “Golden Fingers” legacy;
- % of production per click: +1% for each of the 10 upgrades from “En passant” to “Absolute click” (10% at most);
- the production used includes temporary bonuses: during a ×7 Zeitnot, clicks are worth much more too.
moves the hero pawn one square. It starts on the 2nd rank and is promoted on the 8th, so after 6 clicks (5 with “Two-Square Advance”, which moves it two squares on the first step, as in real chess).
On promotion you earn:
```
promotion = click × 10 × promotion multiplier + production/s × promotion seconds
```
- promotion multiplier: ×3 (“Eighth rank”) and ×5 (“Extra queen”);
- seconds: +15 (“Underpromotion”) and +60 (“Lightning promotion”).
The pawn then reappears on a random file.

On average, a click is worth about click × (1 + 10 × promotion multiplier / 6).

Producers

20 producers, from Pawn to Caïssa (full table: Producers).

Price of the n-th copy: base cost × 1.15^(n−1) (the same 1.15 factor as Cookie Clicker).

Output of one copy:

base output × 2^(tiers bought) × (1 + 0.10 × training level) × total multiplier

Total multiplier (applied to every producer):

openings × full army × production legacies
× (1 + 0.01 × trophy count)
× (1 + 0.01 × crowns)            ← 0.015 with “Laurel crown”
× Π (1 + fervor × k) for each supporter bought
× date bonuses (calendar cheats)

A producer is revealed when you own one, when run tempo reaches 40% of its base cost, or when you own at least one of the previous producer.

The army on the board

The first 6 producers are chess pieces. Up to 16 of them appear on the board (8 pawns, 2 knights, 2 bishops, 2 rooks, 1 queen, 1 king) and play legal moves. Pawns that reach the 8th rank get a decorative promotion and return to the 2nd rank. It is visual only: production is continuous, and the number shown on each move is the real production that piece accumulated since its last move. Lining up all 16 pieces unlocks “Full army” (+50%) and a trophy.

Upgrades

317 upgrades, bought with tempo and lost on each prestige (list: Upgrades).

Family	Count	Effect
Producer tiers	13 × 20 = 260	×2 on one producer; they appear at 1, 5, 25, 50, 100, 150… 500 copies
Click	13	3 × “click ×2”, then 10 × “+1% of production per click”
Promotion	5	multipliers and seconds of production for each promotion
Openings	25	+5% to +29% global production, getting more expensive (×60 each time)
Full army	1	+50% when all 16 pieces are on the board
Supporters	7	multipliers that grow with your trophies (see below)
Events	5	puzzles and rival pieces more often, longer, or more rewarding
Grand œuvre	1	the end of the game

Supporters and fervor

The equivalent of Cookie Clicker’s “kittens”: fervor = 0.04 × trophy count (×1.25 with the “Trophy cabinet” legacy). Each supporter multiplies production by 1 + fervor × k, with k between 0.10 and 0.20. With 150 trophies (fervor 6), all 7 supporters together give about ×100.

Rival pieces

The equivalent of golden cookies.

Appearance: once run tempo reaches 40, a timer starts (90 s the first time), then a rival appears every 3 to 7 minutes. The delay is divided by 2 with “Provocation” and by 1.5 with the “Flair” legacy.
Duration: it stays 13 s (×2 with “Poisoned piece”, ×2 with the “Instinct” legacy). The timer is drawn around the square.
Capture: click its square. An effect is drawn at random:

Effect	Chance	Effect	Base duration
Zeitnot	45%	production ×7	77 s
Fork	40%	instant gain: `min(15% of the bank, 15 min of production) + 13`	—
Blitz	10%	click ×777	13 s
Discovered check	5%	production ×66	6 s

Durations are multiplied by 2 with “Time trouble” and by 1.5 with “Instinct”.
Different bonuses stack (they multiply). The same bonus does not stack: it is restarted at full duration.

Mate-in-1, 2 and 3 puzzles

You need the “Tactics Study” upgrade (25,000 tempo), or the “Pattern Memory” legacy, which turns them on at the start of every run.
The first arrives after 2 min, then every 6 to 12 minutes (twice as often with “Exercise book”). The “Puzzle!” button stays for 45 s.
White to move and mate in 1, 2 or 3 moves. In a mate in 2 or 3, Black answers on its own (its best defence), then it is your turn again.
A real rules engine checks every move: a mating move is always accepted, even by another route. Before the mate, you must play the solution’s move. Any other move, or a window closed before the end, counts as a failure. The game then shows the line.
Progression:
- for the first 5 puzzles, easy mates in 1;
- up to the 25th, 70% mates in 1 and 30% mates in 2, of medium difficulty;
- after that, 40% mates in 1, 35% mates in 2 and 25% mates in 3, of every difficulty.

Reward:

(min(20% of the bank, 20 min of production) + 50 clicks + 100) × multiplier (×2 with “Exercise book”)

multiplied by ×1.6 for a mate in 2 and ×2.2 for a mate in 3.

340 positions: 10 classics and 330 puzzles from the free Lichess database, checked by Stockfish and checked again by the game. Each can appear mirrored. Solutions are in Puzzles.

The chess clock (automatic clicks)

A chess clock taps the board on its own; it shows up in the corner of the board with its rate.

Unlock: the “Chess Clock” upgrade (2,000 tempo) appears once the run has earned 1,500 tempo.
Rate: 1 click/s, then +1, +2, +4, +4 and +8 with “Classical Time Control”, “Rapid”, “Blitz”, “Bullet” and “Ultrabullet” (up to 20 clicks/s).
Value: a clock click is worth the base value of a click (crown and click bonuses included), without the production-based part, at 50% to begin with. “Weighted Clock” ×2, “Swiss Movement” ×2, “Atomic Clock” ×3. Very useful early in a run, more modest later: the big gains stay with your own clicks.
Its own pawn: the clock promotes an invisible pawn every 6 clicks. It does not touch your hero pawn, so it never steals a promotion from you.
“Arbiter’s Clock” (7.7e8): the clock captures rival pieces after 2.5 s if you haven’t.
Clock clicks do not count as your clicks (click trophies), but have their own trophies (1,000, 100,000 and 10 million clock clicks). The clock stops while the game is closed (offline gains: the army only).

Prices in Upgrades.

Analyses and training

The equivalent of Cookie Clicker’s sugar lumps: a resource tied to time, not money.

You earn 1 analysis every 11 minutes of play (tab open).
Offline, they accumulate at the same reduced rate as production: 25% by default, 50% or 90% with legacy, within the same time cap.
A producer’s analysis button (the green eye followed by the level; gold frame from 10) trains it. Level n costs n analyses, and each level gives +10% to that producer (additive: level 10 is +100%, that is ×2).
Analyses and levels are kept after a prestige.
Taking one producer from level 0 to 10 costs 1 + 2 + … + 10 = 55 analyses. For all 20 producers you need 1,100, which is 201.7 hours of play. That is what guarantees the minimum length of the game.

Checkmate (prestige)

Total crowns = ⌊ ∛(all-time tempo / 10¹²) ⌋: 1 crown at 1e12, 10 at 1e15, 100 at 1e18, 1,000 at 1e21…
The button turns on as soon as there is at least 1 crown to gain. The panel shows the all-time tempo required for the next crown.
Each crown gives +1% production and click forever (+1.5% with “Laurel crown”).
Crowns are also spent in Legacy (list), then in the skill tree. Spending crowns does not reduce their bonus.

Reset	Kept
bank tempo, run tempo, producers, upgrades, active bonuses, hero pawn, run counters	all-time tempo (Elo), trophies, crowns, legacy, skill tree, analyses, training levels, record book, settings, play time, lifetime statistics

The “Prepared opening” and “Grand preparation” legacies give free producers at the start of each run.

When to checkmate?

The panel gives advice under the button, tuned with the simulator:

Advice	Next mate	What to do
◔ Too early	less than a quarter of your crowns	keep going: you would restart for almost nothing
◑ Soon	less than your crowns	a little more patience
● Good time	1 to 4 times your crowns (you double)	checkmate: the button glows
▲ Too late	more than 4 times your crowns	checkmate right now: every minute slows what follows

For your first mate, aim for at least 3 crowns. Measured: checkmating as soon as you double your crowns gives the fastest ending (201.7 h); waiting to quadruple them pushes it to ~215-220 h, and mates that are too frequent delay the economic goal (Strategy).

The skill tree

When the legacy is almost complete (15 of the 17 legacies), crowns get a new use.

4 branches of 7 nodes: Clock (clock rate and value, capturing rivals), Army (production, producer prices, offline gains, free producers every run), Tactics (rivals and puzzles), Crown (crowns earned, bonus per crown, achievement fervor).
Prices: from 10 million to 10 billion crowns depending on the tier. Each node requires the node above it and a number of checkmates (12 to 30). Spending does not reduce the crown bonus, as with the legacy.
Masteries: at the end of each branch, an endlessly upgradable node (+3 to +10% per level), from 30 checkmates. First level: 1e11 crowns, then ×10 per level.
The tree is kept at every checkmate. The button appears from the first checkmate, locked until the 15 legacies are bought.
Bonuses are deliberately measured: the tree extends the game past the ending without shortening it (the ending stays at ~200 h, locked by analyses).

Full list in Skill tree.

Offline gains

When you open the game, time since the last save is compensated:

gain = base production (without temporary bonuses) × seconds away × offline rate

Situation	Rate	Maximum duration
Default	25%	8 h
“Blindfold analysis” legacy	50%	8 h
“Correspondence game” legacy	90%	24 h

Analyses, however, only advance while the game is running (a background tab counts): the device clock has no effect on them. A message summarizes the gains at startup. The boost (see below) counts offline for the time it was still running: those hours earn double.

A tab left open (even in the background) counts as active play: when you return, the game catches up at 100%, up to 8 hours at once.

The shop: boost, gems and time warps

The BOOST ×2 button, under the bank, opens the shop. Nothing in it is required: the game can be finished without paying, and the end (≈ 200 h, tied to analyses) does not move with purchases. They only make things faster.

Item	Effect	How to get it
Boost	production ×2 for 2 h, stacks up to 8 h ahead	watch an ad (website and apps, never on Steam), 20 gems, or one click with “Boost at will”
Time warp	1 h, 4 h or 24 h of your current production, at once	15, 50 or 250 gems
Gems 💎	shop currency	5 per checkmate, or in packs of 100, 600, 1,500
Boost at will	the boost with no ad and no gems	one-time purchase
Lifetime production ×2	all production ×2, permanently	one-time purchase

The boost runs in real time, even while the game is closed, and doubles offline gains while it runs.
It multiplies production (and so the production-based part of a click), not analyses or crowns.
A time warp counts base production, without temporary bonuses (rival pieces, boost).
Gems and perks are kept through checkmate, Erase everything and importing a save.
Prices and terms: terms of sale. On the website, a purchase code brings your purchases to another browser; on iOS and Android, the Restore purchases button; on Steam, perks are DLC.

Elo and titles

Elo = 400 + 200 × log10(all-time tempo + 1)

Each factor of 10 in tempo is worth 200 points. The final title, Caïssa, arrives at 7,400 Elo, which is 1e35 all-time tempo (table).

Trophies

214 trophies (list): all-time tempo, production per second, clicks, promotions, rivals, puzzles, counts of each producer (1, 50, 100, 200, 300, 400, 500), total producers, prestiges, crowns, analyses spent, clock clicks, skill tree nodes and masteries, finishing the game. Each gives +1% production and 0.04 fervor. Cheats are a separate record book, with no bonus.

The grand œuvre: the end of the game

“Solving chess” requires three conditions, tracked on the panel of the same name:

1e37 tempo in the bank (it will be spent);
at least 1 Caïssa recruited;
all 20 producers at training level 10 (1,100 analyses, about 200 h).

The final button opens the ending screen (statistics, play time, Elo) and the trophy “Chess is solved”. You can then keep playing: nothing is locked.

The referee and the record book

Each cheat you trigger is a yellow card, and every third card is red (purely decorative). Discovered cheats fill the record book. Details are in Cheats.