# Penney's game — the second chooser wins

- From: Penney's game, a coin game by Walter Penney
- Players: 2 players
- Time: 5 min
- Made by: Walter Penney, 1969

Made with boardgameBuilder 0.14.4. To design from it, open boardgameBuilder and choose Open game: its blocks go on the canvas, and the feelings are left for you to pick.

Each player picks a run of three coin tosses, such as heads-heads-tails. A coin is tossed until one of the runs appears. It looks like a fair bet, but whoever picks second can always choose a run that comes first more often.

## What it shows a designer

A game that looks fair and isn't. It shows how probability can surprise players, and why designers test balance instead of trusting how a rule looks.

## What you need

- one coin
- paper and a pen

## How to play

1. **Choose.** The first player names a run of three, like HHT. The second player, having heard it, names a different run of three.
2. **Toss.** Toss the coin again and again, writing each result in a line.
3. **Win.** Whoever's run appears first in the line, as three tosses in a row, wins the round.
4. **The trick.** The second player can always choose well: take the opposite of the first player's middle toss, then add their first two. Against HHT, choose THH.
5. **Play.** Play ten rounds, swapping who chooses first, and count the wins.

## After playing, talk about

- Did the results look fair or not, before you knew the trick?
- Why does the second player have the advantage?
- Where else might a fair-looking setup hide an advantage?

## Where the rules are written down

- https://en.wikipedia.org/wiki/Penney%27s_game
- https://doi.org/10.2478/rmm-2020-0002

## Its blocks

- Chance or skill: mostly chance
- Theme: educational
- Information visibility: full information
- Timing: take turns

## Saved state

boardgameBuilder reads this part back when the file is opened.

```json
{"mechanics": {"chance-skill": "mostly-chance", "information": "full-information", "theme": "educational", "timing": ["take-turns"]}, "chosenFeelings": [], "previousMechanics": {}, "previousFeelings": [], "turnNumber": 0, "locked": false, "turnHistory": [], "answers": {}, "tests": {}}
```