Coin toss

The coin toss is a very old and popular way to choose between two options. The principle is based on a throw whose outcome is unpredictable for the players in advance. This method was used for decision-making in Ancient Rome, where it was called “Navia aut caput”, which literally translates to “Ship or head”, because one side of the coin bore the image of the emperor, and the other a ship. In Czech, it is most commonly called “Panna nebo orel” (“Heads or tails”).

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Game rules

Each coin has two sides, so the result of a toss is always just one of two options. In a game with two players, one’s win simultaneously represents the other’s loss. The chances of both players winning are equally balanced from the beginning. The coin must be thrown into the air so that it spins and it is not possible to predict which side it will land on. In some cases, it is allowed to fall to the ground or it is caught during the fall, while in others it is caught in mid-air and slapped onto the other hand. The result of the toss is then read from the side facing up.

How to play Coin toss

First of all, players decide which outcome they want to bet on and how much their bet will be. The next step is the actual toss. This is done by one of the two players (they can take turns) or a third independent person (or a computer). During the toss, it is not possible to place additional bets or change the initial decision. After the coin lands, the result can be immediately read based on which side of the coin is facing up and visible to everyone.

Probability of winning

The chance of winning in the basic game is 50 to 50, which represents a 50% chance of success; expressed in betting odds, it is a ratio of 1:2. In the long run, this is a so-called fair bet, where each player can win and lose the same amount they put into the game. The probability of achieving the same result in a coin toss, however, decreases proportionally by a multiple of 0.5 with the number of repeated tosses, as shown in the table below:

Same side of the coin	Probability ratio
1x	1 : 2
2x	1 : 4
3x	1 : 8
4x	1 : 16
5x	1 : 32
6x	1 : 64
7x	1 : 128
8x	1 : 256
9x	1 : 512
10x	1 : 1,024

Bernoulli’s scheme

According to this formula, it is possible to calculate the probability with which the same side of the coin will fall repeatedly (or not fall) in a given number of tosses. It can be calculated how likely it is that the chosen side will fall exactly that many times (e.g., exactly 4 times) or at least that many times (e.g., at least 4 times). The probability of repeating a given result in 10 tosses can be read in the table below:

• p = probability
• k = k-times (how many times a certain side falls)
• n = number of attempts
• (1 – p) = probability of failure

Number of same results (k)	Probability of exact number of results	Probability of at least number of results
0	1 : 1,024
1	1 : 102	1 : 1.000978
2	1 : 23	1 : 1.0109
3	1 : 8.53	1 : 1.058
4	1 : 4.88	1 : 1.21
5	1 : 4.06	1 : 1.61
6	1 : 4.88	1 : 2.65
7	1 : 8.53	1 : 5.82
8	1 : 23	1 : 18
9	1 : 102	1 : 93
10	1 : 1,024	1 : 1,024

Betting methods

Bets can be placed in coin tosses in several ways. Players can bet on the specific outcome or make the game more interesting by betting on the repetition of the selected outcome in a certain number of tosses. In practice, this means that one player commits to tossing, for example, heads or tails six times in 10 tosses with the offer that if they succeed, they will win €20 from the opponent. Conversely, if they lose, they will pay €1 for each unsuccessful toss.

How you can play Coin toss

Coin toss is most often played among players with a physical coin. However, it can also be played using virtual coins on various online portals or in mobile apps that simulate the toss. Nowadays, no company offers Coin toss as a gambling game on which bets can be placed. However, with available resources, players can freely modify this game themselves and customize the betting method and the minimum bet amount.

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2️⃣ What can you bet on in a Coin toss?

Players can bet on which side of the coin will land after the toss or how many times the selected side of the coin will land in a certain number of tosses.

3️⃣ What is the probability of winning?

When betting on a specific outcome in one toss, the chance of winning is 50 to 50. The probability of achieving the same result in a given number of tosses can be read from the tables above.

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