Penney's game — the second chooser wins
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.
From Penney's game, a coin game by Walter Penney.
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.
Credits
- Made by
- Walter Penney, 1969
- Sources
- en.wikipedia.org/wiki/Penney%27s_game
doi.org/10.2478/rmm-2020-0002
What you need
- one coin
- paper and a pen
How to play
- Choose. The first player names a run of three, like HHT. The second player, having heard it, names a different run of three.
- Toss. Toss the coin again and again, writing each result in a line.
- Win. Whoever's run appears first in the line, as three tosses in a row, wins the round.
- 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.
- 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?
Its blocks
Download it as a design (.md)In boardgameBuilder, Open game puts its blocks on the canvas. Changed, the same file can come back here from Propose a game.