flip 3 coinsFlip 3 coins

Flip three coins at once

Three coins, tossed together. Tap them, press Flip or hit the Space bar, and each coin lands heads or tails on its own. The result appears as a count, such as “2 heads, 1 tails”, and the bar at the bottom keeps the tally. There are eight possible sequences, all equally likely.

Casting the I Ching with three coins

The most common way to consult the I Ching, the Chinese Book of Changes, uses three coins. Each toss builds one line of a hexagram, starting from the bottom, and you toss six times. In the usual convention, heads count 3 and tails count 2, so each toss totals 6, 7, 8 or 9:

• 6 (three tails): an old yin line, broken and changing. Chance: 1 in 8.
• 7 (two tails, one head): a young yang line, solid. Chance: 3 in 8.
• 8 (two heads, one tail): a young yin line, broken. Chance: 3 in 8.
• 9 (three heads): an old yang line, solid and changing. Chance: 1 in 8.

Some traditions swap the values of heads and tails; check the convention of the book you use. Note the six results in order, from the bottom line up, and keep the history open to look back.

Best of three, in one toss

Want a decision a little more solid than a single coin? Flip three at once and go with the majority. There is always a winner, since three coins cannot tie, and each side still has exactly a 50% chance. It is the same as a best-of-three series, settled in a single tap.

In a classroom, three coins are a classic first example of a sample space: list the eight sequences, HHH to TTT, then check against a hundred flips.