1. Call it: the classic guessing game
One player flips, the other calls heads or tails while the coin is in the air (or before the flip, as the NFL now requires). It's the oldest coin game there is, and the odds never move: every call is a 50% shot, whatever came before.
To play solo, use the Call it buttons on the simulator (or press H / T) and it keeps your score. Play 50 rounds and you'll probably finish somewhere between 18 and 32 correct. That's the normal spread, and it shows how hard it is to feel the difference between luck and skill.
2. Best of three (or five)
"Best of three" is the usual answer when one flip feels too final. It doesn't change the odds for a fair coin, since each player still has exactly a 50% chance of winning the series. It does make a biased coin's edge bigger: a coin that lands heads 51% of the time wins a best-of-three for heads about 51.5% of the time. If someone suggests best of three after losing, they wanted a different answer, which is useful to know.
3. Penney's game: the coin game with a winning strategy
Penney's game, described by Walter Penney in 1969, is the best-known coin game with a strategy. Each player picks a sequence of three flips, such as HHT. The coin is flipped repeatedly, and whoever's sequence appears first wins. It sounds even, but it isn't: the second player can always pick a sequence that wins more often.
The rule for player two: take player one's middle result, flip it to its opposite, put it at the front, then add player one's first two results. Against HHT, player two picks THH.
| Player 1 picks | Player 2 should pick | Player 2 wins |
|---|---|---|
| HHH | THH | 7 in 8 |
| HHT | THH | 3 in 4 |
| HTH | HHT | 2 in 3 |
| HTT | HHT | 2 in 3 |
| THH | TTH | 2 in 3 |
| THT | TTH | 2 in 3 |
| TTH | HTT | 3 in 4 |
| TTT | HTT | 7 in 8 |
The game is non-transitive, like rock-paper-scissors: there is no best sequence, only a best reply. It works because sequences overlap. Once HH has appeared, THH can only lose if HHH appears first, which needs three heads from the very start. It's a great classroom demonstration, so try it on the simulator with a friend.
4. Matching pennies
Two players each secretly turn a coin to heads or tails and reveal at the same time. If the coins match, player one wins; if they differ, player two wins. Matching pennies is a standard example in game theory because it has no pure strategy that wins. Any pattern you fall into can be exploited, so the best strategy is to choose completely at random, 50/50. A digital coin is an easy way to do that. The game is about reading the other player and staying unpredictable.
5. Two-up
Two-up is a traditional Australian gambling game. A "spinner" tosses two coins in the air from a small wooden paddle called a kip. Players bet on the result: two heads or two tails wins for whoever backed it, and one of each ("odds") means toss again. Each toss has a 1/4 chance of heads-heads, 1/4 tails-tails and 1/2 odds. Two-up is closely tied to Australian soldiers in the First World War, and in most states it's legal to play publicly only on Anzac Day (25 April) and in licensed casinos.
6. Streak challenge
Pick a target, such as five heads in a row, and count how many flips it takes. The expected number of flips to reach n heads in a row is 2n+1 − 2:
| Target streak | Average flips needed |
|---|---|
| 2 heads in a row | 6 |
| 3 heads in a row | 14 |
| 4 heads in a row | 30 |
| 5 heads in a row | 62 |
| 10 heads in a row | 2,046 |
The simulator's longest streak counter tracks your record for you. Players often find the waits feel too long, then too short. More on streak odds in the probability of a coin flip.
7. Classroom experiment: real vs. fake sequences
A well-known probability exercise: half the class flips a real coin 100 times and writes down the sequence. The other half invents a 100-flip sequence that looks random. The teacher can usually tell which is which at a glance. Real sequences almost always contain a run of six or more, while invented ones rarely do, because people avoid streaks. Use the bulk flipper to generate many real sequences quickly, then compare the heads percentages with the ranges on our law of large numbers page.
Frequently asked questions
What is a coin toss game?
Any game where a coin flip decides the outcome or is the main mechanic. That includes simple guessing games like calling heads or tails, betting games like two-up, and strategy games like Penney's game and matching pennies, where the maths decides who wins over time.
Is there a strategy for winning a coin toss?
Not for calling a fair flip. Heads and tails are each 50%, and no calling pattern changes that. In Penney's game, though, the second player can choose a sequence that wins up to 7 out of 8 times.
How many flips does it take to get 5 heads in a row?
On average, 62. The expected number of flips to see n heads in a row is 2n+1 − 2: 6 flips for two in a row, 14 for three, 30 for four and 62 for five.
Can I play these games online?
Yes. The coin toss simulator has a built-in Call it mode that keeps score, a streak counter and a bulk flipper for experiments. For two-player games, take turns flipping on one screen or each open the simulator on your phone.