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Heads or tails

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Pile_ou_faceHeads or tails is a game of chance played with a coin. The principle of the game is to throw up a balanced coin and wager on the side that will remain up. The spinning coin falls to the ground and it stabilizes, or it is caught with one hand and laid flat in the other hand.

The name “heads or tails” comes from the names of the two sides of the coins.

The first use of this game in this form dates from the creation of metallic money. However, other forms existed previously using objects having two distinct sides, a shell for example. The goal is to do a binary random selection. Even today, playing “heads or tails” means to let a decision be taken at random, depending on the side of the coin that will appear after the launch.

The heads or tails is always used in sports, for example. It provides support for many problems in probability, some remain open as the problem of Sleeping Beauty.

This is an important tool in game theory as well as in probability theory.


Heads or tails lets help the decision of a binary choice. The most common method to flip a coin is positioned horizontally on the tip of the thumb and the portion of the index. It then suffices to exert an extension of the thumb to provide a rotational movement to the workpiece, the workpiece must perform at least one full rotation in the air. According to a statistical study, the average number of coin flips of a coin to a specific side of the piece is 19. It leaves the coin to fall to the ground or you catches up and positioned horizontally on the back of the other hand. In any case it is the upper side of the part that gives the outcome.

It is common to bet on heads or tails before the coin toss. One can also bet while the play is in the air, avoiding any attempt of cheating on the part of the launcher.

Gambling game

You can play heads or tails betting by betting on the outcome. The game is often present in probability exercises. The study then focuses on independent simultaneous or successive throws. Several rules and betting strategies exist.


Example of strategy:

Consider a classic game of heads or tails: a player bets on the head or tail outcome, if he gets the right result then he wins his bet (in addition to its setting), otherwise he loses his bet. Then again another coin is flipping. There is a strategy allowing the player to always win in the long run: the player bets 1 unit for the first draw. If he loses, he bets 2 units in the second run, if he loses, he bets 4 units in the third run, and so on. If he did not win, he bets 2n-1 up to n-th throw. The player stops playing when he wins.

This game strategy is winning for the player. Indeed, if he wins the nth run, he will have wagered 1 + 2 + 4 + … + 2 ^ {n-1} = sum_ {k = 0} ^ {n-1} 2 ^ k = 2 ^ n – 1 units and will have earned 2n units. Its total gain is 1 unit. The game ends this way in finite time. The limit for using this technique is that the game is not limited in time, that is to say it can last very long time. To win, one must thus assume that the player has a purse infinite, that is to say it can even bet 2n for a big n.

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