Classic games

Every strategic situation you'll meet is some blend of six archetypes. Learn them once and you start seeing them everywhere — in pricing pages, treaties, and group chats.

Each game below is solved the same way: read the best-response marks column by column, row by row, and ring the cells that earn both. Every equilibrium stated here — pure and mixed — is what the site's own engine computes on the same numbers.

Prisoner's Dilemma

One move always wins, and everyone loses because of it.

Walk the marks. Fix the column player on Cooperate: Defect pays 4 against Cooperate's 3, so the red corner sits on Defect. Fix them on Defect: 1 against 0, red corner again. Switch chairs — against a cooperator the column player defects (4 beats 3), against a defector it still defects (1 beats 0). Green corners land on the same column, and one cell carries both marks.

Equilibrium: (Defect, Defect) — the only cell nobody wants to leave, paying (1, 1) while (3, 3) sits one diagonal away.

The tension. Defect dominates, so two self-interested players talk themselves into 1 each when 3 each was on the board. Nobody errs; the arithmetic is airtight. That's what makes the dilemma durable — it needs no villains, only incentives. Cartels that cheat, arms races that build, and climate pledges that slip are this grid in different clothes.

Where you'll meet it: price wars, arms races, and climate agreements — anywhere private temptation beats collective payoff.

Stag Hunt

Together you could eat well. Alone you'll still eat — barely.

Walk the marks. Against a partner hunting stag, your best reply is stag — 4 beats 3. Against a partner hunting rabbit, your best reply is rabbit — 2 beats 1. The same two checks from the other chair land on the same two cells, and both carry double marks.

Equilibrium: (Stag, Stag) and (Rabbit, Rabbit) — plus a third in mixed strategies, where each hunter picks stag with probability ½ and expects 2.5.

The tension. The rich equilibrium needs faith; the safe one needs none. Hunt stag while your partner quietly downsizes to rabbit and you come home with 1 — the board's worst meal. Enough people expecting hesitation get the mediocre outcome for free. Trust is the whole game, and the grid can't supply it — it can only price it.

Where you'll meet it: group projects and alliances — anywhere the good outcome needs everyone to show up.

Chicken

Whoever blinks lives well; nobody blinking ends badly.

Walk the marks. If the other driver swerves, your best reply is straight — 4 beats 3. If they go straight, your best reply is to swerve — 1 beats the crash at 0. The same checks from the other chair produce the mirror, so the double-marked cells are exactly the two where one driver swerves and the other doesn't.

Equilibrium: (Swerve, Straight) and (Straight, Swerve), plus a mixed equilibrium where each driver goes straight with probability ½.

The tension. Both pure equilibria require exactly one player to blink, and the game is silent about who. The mixed equilibrium is worse than it sounds: with both drivers flipping coins, both go straight a quarter of the time — the crash cell, on schedule, at 25%. Nerve is rewarded, symmetry is punished, and everyone privately wishes the other were more predictable.

Where you'll meet it: traffic merges and standoffs — anywhere two forces meet and both would rather not.

Battle of the Sexes

You want to be together. You just want to be together somewhere else.

Walk the marks. Against a partner choosing opera, your best reply is opera — 2 beats 0. Against football, it's football — 1 beats 0. Both checks run the same from the other chair, so the two matching cells carry double marks.

Equilibrium: (Opera, Opera) and (Football, Football), plus a mixed equilibrium — row picks opera with probability ⅔, column with probability ⅓ — that pays each only ⅔.

The tension. Coordination is easy to want and hard to split. Each player's favorite outcome is the one built around their own preference, and the mixed equilibrium — the no-negotiation fallback — puts both partners in the same place less than half the time: 4 meetings in 9. Real couples solve this with a conversation; the matrix only records the standoff.

Where you'll meet it: any two-sided standard choice — one evening, two events, one shared dislike of missing each other.

Coordination

Any agreement beats no agreement — so how do you agree?

Walk the marks. Against System A, your best reply is A — 2 beats 0. Against B, it's B — 1 beats 0. Both chairs agree: match, always. The only double-marked cells are the two matches.

Equilibrium: (System A, System A) and (System B, System B) — plus a mixed equilibrium (A with probability ⅓ each) that pays just ⅔ and nobody plays on purpose.

(A, A) pays both more, and with these numbers it is also the safer rendezvous — a mismatch costs everyone 0 either way, and the richer meeting point has the wider pull. The genuinely hard case is when the rich equilibrium and the safe one are different cells; that's the Stag Hunt two sections up, and it's where selection stops being polite.

The tension. The fight isn't over whether to coordinate but over which equilibrium to coordinate on. Standards battles, keyboard layouts, group-chat migrations — everyone wants the same thing, to be on the same thing, and still end up split.

Where you'll meet it: the group chat that has to switch apps together — coordination with no villain in sight.

Matching Pennies

Being predictable is the only way to lose.

Try the marks anyway. In the Heads column, the row player's best reply is Heads — matching wins — red corner on the top-left cell. In the Heads row, the column player's best reply is Tails, green corner one cell over. The pattern holds around the whole board: every cell carries exactly one mark, which means exactly one player wishes they'd chosen differently. No cell passes the test.

Equilibrium: none in pure strategies. The unique equilibrium is mixed — Heads with probability ½ for both players — which the derivation in Mixed strategies finds in three lines of algebra.

The tension. This is the only game in the set where having an answer is the mistake. Every other classic rewards finding the right move; pennies punishes being findable at all. It's also the purest demonstration of why mixed strategies exist — not confusion, but armor.

Where you'll meet it: shootouts and poker nights — anywhere reading you is beating you.