Alice needs to decide between buying a strawberry cake or an apple cake, but she really can't make up her mind. So, she tries to decide by...flipping a coin. Heads, strawberry. Tails, apple.
Flipping coins to decide on an action has been a practice that, according to The Other Wiki, dates at least back to Ancient Rome. In fiction, it usually happens in the following situations:
A character is unsure whether the option they are considering is the correct one, so they leave it up to fate.
A third party is trying to solve a dispute between two other people or factions. Often happens in contests when there is no clear winner.
Note that this trope can be used when deciding between two characters, things, or virtually anything.
A Born Lucky character will almost always get the result they want in this. A staple feature of The Gambler and The Trickster, who frequently settle their disputes this way. Occasionally a character will pick a course of action with a coin flip because he wants to prevent his enemies from figuring out what he'll do—they can't predict it if he doesn't know himself. Cheaters tend to use a Two-Headed Coin. Heads Tails Edge is a subtrope.
A 1990 PSA from the Canadian organization Companies Committed to Kids encourages kids to not play games when making important decisions and to "use their heads" instead. Flipping a coin is one of the games depicted.
In the Pokémon anime, Dawn has a Poketch app to flip a coin which she sometimes uses to make decisions, for example the episode in which she got the Poketch she used it to decide whether to go left or right at a forked road.
Two-Face's signature item in Batman is a double-headed coin, except one side is all scratched up. This lets him easily identify which side landed.
In a Donald Duck story by Carl Barks, "Flip Decision", Donald is conned by a charlatan into believing in Flipism: the idea that all of life's choices can be made on the flip of a coin. Hilarity Ensues, of course, though the coin does show uncanny predictive power.
In a Richie Rich story, the same coin ends up deciding whether Mr. Rich should invest a billion dollars in a new company, and whether a hobo or tramp ("I can't decide...let's toss a coin!") should buy a soda or a candy bar. (The actual tosses' results are unknown, but they each read the result of it flying out from under the moped seat and into the window of the mansion.)
In Coming to America, Prince Akeem flips a coin to choose between traveling to New York or Los Angeles to find himself a bride.
In The Sentinel, the Secret Service, aware that an assassination attempt on the President is imminent and that there is someone in the Secret Service helping, are trying to take every precaution possible. The President's personal bodyguard Montrose suggests a coin toss. That is they create two plans for how the President travels, and right before they leave he tosses a coin to decide which one they do. That way, no one has advanced knowledge.
While the midshipmen are trying not to be captured, Horst Staley proposes flipping a coin when deciding what to do so his Mediator Fyunch(click) can't predict his decisions.
When the human expedition prepares to leave the Mote system, the Moties send them a gift ship full of alien technology. The human leadership decides to randomly cut up the technology into pieces in case the Moties designed any of it for nefarious purposes. While Lady Sally is directing the procedure she flips a coin to decide how many times to cut.
No Country for Old Men: The main villain flips a coin to decide whether to kill a potential victim. Those that choose not to take the chance are killed anyway, because they refuse to submit to the Powers That Be.
In the book Q and A Ram flips a 'lucky coin' to make important decisions throughout his life. As it turns out, Ram's coin was a trick coin and he was fully aware of what life-changing choices he made throughout the story.
I flipped a coin to decide, and of course won since I had palmed the coin before the toss. It was going to be action.
Isaac Asimov wrote a short story called "The Machine that Won the War", where scientists gather around MULTIVAC, the computer used to calculate their army's strategy, and celebrate their victory. Then the scientist who programmed data into it admits that he just blindly guessed on every decision. The scientist who fed him the data admits that he fudged the results based on his intuition because he couldn't understand any of it. The scientist who gathered the initial calculations then confesses that he couldn't make out the readings and made stuff up. And the scientist who gave him those initial readings reveals his method of making the first call: "Heads or tails, gentlemen?"
In The Wheel of Time books, Mat, and sometimes Rand, uses this method to make decisions. Since they both have luck-bendingreality powers, this has extra significance. Mat in particular has a tendency to get coins landing on their edge.
In Barefoot Boy With Cheek by Max Shulman, the protagonist decides to flip a coin to answer the question vexing him: "Yetta or Noblesse?" The coin disappears in a snowbank.
In Andre Norton's Storm over Warlock, Shan and Thorvald are trapped in mists, with no sense of direction. They have an artifact rather like a bone coin, which has shown strange powers before, and decide to flip it as they have really no other alternative — heads this way, tails that way. It flies off through the air, and they chase it instead.
In the Known Space novel Protector, a superintelligent alien (sort of...) needs to fight a space battle with similarly intelligent aliens. He knows what the ideal weapon is for the circumstances—but also knows that the enemies would know what that ideal weapon is, and could use countermeasures. So instead, he comes up with four pretty-good weapons which would each require different countermeasures, and rolls a die to pick which one to use. (The enemies would be able to predict that he'd do that, too, but they wouldn't know which way the die came up.)
The Mentalist: An episode of season 2 features the protagonist winning a bet this way. It landed heads 20 times in a row. No wonder they thought he was cheating.
Subverted in an episode of Gilligan's Island. Gilligan was slated to duel with a native by throwing spears. Skipper had a coin to toss to determine who went first. He kept trying to get Gilligan to pick heads (it was a 2-headed coin) but Gilligan kept insisting on tails. In the end, the native (translated by the Professor) told Gilligan he could go first.
In an episode of Scrubs, J.D. and Kim can't decide if they want to keep their baby, so they leave it up to a coin toss. It landson its edge.
Although jokes involving such a show have come up before on sitcoms, there actually was a real Heads or TailsGame Show.
In international soccer/football, the referee does a coin toss with the captains of both teams before the game. The winning captain decides which half of the field his team will defend, and the other team kicks off to start the first half.
Euro 1968. Italy, against the Soviet Union, won by this after none having scored in the semi-final match. It was the first and only time that this method was used.
In American Football in general and the Super Bowl in particular, a coin flip decides who gets to choose one of the following first: which goal to defend and whether to kickoff or receive. The winner usually decides to receive and the other team gets to choose which goal to defend; but sometimes the winner will decide which goal, leaving the choice to receive or kick to the loser. At the start of the 2nd, 3rd & 4th quarters the direction of play reverses, and at the top of the 3rd quarter whoever received at the beginning of the game now kicks off. If there's overtime they have another coin toss.
The league has a long list of tiebreaks for two (or more) teams with equal records attempting to secure a playoff spot (or, in some cases, a specific playoff spot). In the unlikely case the teams make it all the way to the end of a tiebreaker list, the final tiebreaker is a literal coin toss.
This is very common in the Pokémon Trading Card Game. Each player has a coin of his or her own. Players flip to see who goes first. Then there are several cards where the player flips his or her coin to determine the number of cards they draw from their deck or the amount of damage a move will do etc.
Dante picks up this quirk in the second installment of Devil May Cry for unexplained reasons, using his coin to determine whether or not he'll help Lucia and Matier, most notably when deciding who between him and Lucia will go into Demon World and slay the recently-revived devil king Argosax and most likely be trapped there for eternity. Lucia notices in the epilogue that it's a trick coin and the coin itself later comes in handy when Dante switches his own lucky coin with the Arcana Medaglia to fool Arius near the end of the game. Dante retains this trait during his guest appearance in Shin Megami Tensei III: Nocturne. Savvy players can actually recruit Dante for only one Macca if they know about the trick coin.
In Final Fantasy VI Edgar and Sabin flip a coin to determine who will be king of Figaro. Edgar won, by using a Two-Headed Coin, in order to not keep the burden off his brother's shoulders. Later, Celes borrows the same coin against Setzer. He falls for it. If you bring both Figaro brothers to that cutscene, Sabin is rather appalled to learn the truth about the coin.
Celes: Heads, you take us to the Empire's capital. Tails, I agree to marry you.
Subverted in the ending of the game. When faced with two paths, Setzer flips a coin, and the group starts down the path it bounced. Setzer stops them and decides to go the other way, which turns out to be correct.
Setzer: Sometimes you just have to feel your way through life.
In BioShock Infinite, Booker DeWitt runs into Robert and Rosalind Lutece for an obligatory "heads or tails" coin flip, in which Booker chooses "tails" and flips the coin, only for it to come up heads. Rosalind records on the sandwich board Robert carries, showing that all previous (127) attempts have always come up as heads.
Played with in Homestuck. Terezi will sometimes make decisions with a coin flip. (The coin is two-headed, but one side is scratched) However, she more often than not ignores the result and just does what she wants.
In Freefall, Florence tries this more than once. Once Sam catches the coin in midair, and another time she thinks as she throws that if she really wanted it to be fair, she wouldn't use one of Sam's coins.
In an episode of Futurama , the main characters enter an alternate universe where coin flips have opposite results causing decisions to be different.
The Scooby-Doo, Where Are You! episode "Haunted House Hang-Up" had Shaggy flip a piece of baloney with one side covered in mustard to decide which side of a forked road the gang should take. Scooby promptly ate it before it landed.
"Which Witch Is Which?" zig-zagged this with Shaggy flipping a coin to decide who would enter a spooky shack. Shaggy's options were "heads I win, tails you lose."
The "heads I win, tails you lose" trope also appeared in an episode of Speed Buggy between Speed Buggy and Tinker. Tinker lost when the coin came up tails.
At least one U.S. state has it written into its constitution that, in the event of a perfect tie during an election, the outcome may be decided by a coin flip if other alternatives (run-off, voting by state legislators) are unfeasible or likewise deadlocked.
In 1845, pioneers Asa Lovejoy (of Boston, Massachusetts) and Francis Pettygrove (of Portland, Maine) both wanted to name a new city after their hometown. They flipped a coin and the city has been known as Portland, Oregon ever since. The coin they used, now known as the "Portland Penny", is on display in the Oregon Historical Society Museum.