# Mastermind

A hidden code of coloured pegs, and a fixed number of guesses to break it.

## Played as a duel

The pencil-and-paper game is one person setting a code and another breaking it,
which makes a poor two-handed game: one player would sit and watch.

Here **both players are set a code and both are breaking one**, a guess each in
turn. Whoever cracks theirs first wins.

That symmetry is why the game ends at the foot of a round rather than the moment
somebody gets it. If the player who went first breaks the code on their sixth
guess, the player who replied still gets a sixth guess of their own — and
equalling it is a draw. Ending it any earlier would make going first worth half
a guess.

## The answer

Each guess is answered with pegs:

- a **dark** peg for a colour in the right place;
- a **light** peg for a colour that is in the code but somewhere else.

**A colour is never counted twice.** Three reds guessed against a code with one
red is worth exactly one peg, however they are arranged. The pegs say how many,
never which, and they are deliberately not lined up under the code they answer —
a tidy row would invite reading a position into them that is not there.

## Options

| | |
| --- | --- |
| **Colours** | 6 or 8 |
| **Pegs** | 3, 4 or 5 |
| **Guesses each** | 8, 10 or 12 |
| **Repeated colours** | on by default; off makes every peg a different colour |
| **Opponent** | Casual, Club or Strong |

The setup screen shows how many codes are possible, which is the honest measure
of how hard a game will be: 1,296 for the standard four pegs and six colours,
32,768 for five pegs and eight.

## Ending

- One player breaks it and the other does not — that player wins.
- Both break it in the same round — a draw.
- Neither breaks it before the guesses run out — a draw.

## Keeping the codes secret

This is the only game here with anything to hide, and it is the only one whose
`viewFor` does real work. The host holds both codes and sends each device **only
its own**: the code you are trying to break is never on your device in the first
place, so there is nothing to find by digging through what arrived over the
network.

A guess is scored by the host, which is the only machine that can score it. A
device asked to score a guess against a code it was never given refuses rather
than quietly answering "nothing" — tested, because that failure would look like
a very hard code rather than like a bug.

Both codes are revealed when the game ends. There is nothing left to protect,
and a code breaker wants to see what they were up against.

## What the computer does

There is no tree to search — a guess cannot be answered badly, and the opponent
makes no reply — so the whole game is in choosing what to try next.

- **Casual** guesses anything it has not tried, ruled out or not.
- **Club** never guesses a code the answers have already eliminated. That one
  rule is most of the strength, and it cracks a standard code in about five.
- **Strong** is Knuth's idea one ply deep: among the codes still standing, it
  plays the one whose *worst* possible answer leaves the fewest candidates
  behind, so it cannot be handed a reply that tells it little. Both lists are
  sampled when they are large — the full calculation on a fresh game is over a
  million scorings for a choice a sample makes just as well.