Calculating Probability for single events

In the last post we figured out how to calculate the number of possible outcomes for coin tosses (or any game).  Now we'll look at the probability.

We can calculate the number of possible outcomes using the following formula

number of combinations ^ (number of tosses)

otherwise known as

number of combinations to the power of number of tosses.

So to calculate the probability of an event, we are basically saying the following

the number of times the desired outcome can occur / the number of possible outcomes

Coin Toss (2 sided coin)

So for a 2 sided coin (heads or tails).  there are 2 possible outcomes.

H, T

So there is 1 in 2 chance of flipping a head (as shown in blue below)

H, T

1 instance of the desired outcome within a set of 2 possible outcomes.  Giving a 1/2 chance (50% chance),

Coin Toss (3 sided coin)

So for a 2 sided coin (heads, tails or body).  there are 3 possible outcomes.

H, T, B

So there is 1 in 3 chance of flipping a head (as shown in blue below)

H, T, B

1 instance of the desired outcome within a set of 3 possible outcomes.  Giving a 1/3 chance (33.3333333% chance),

Dice Throw (6 sided dice)

So for a 6 sided dice throw there are 6 possible outcomes.

1,2,3,4,5,6

So there is 1 in 6 chance of rolling a 3 (as shown in blue below)

1,2,3,4,5,6

There is also a 1 in 6 (16.6666666%) chance of hitting any specific number

And there is a 3 in 6 (otherwise known as 1 in 2 (or 1/2 or 50%)) chance of hitting an even number

1,2,3,4,5,6

And the same for hitting an odd number

1,2,3,4,5,6

Specific Number in European and American Roulette

Now that we know how to calculate probability.  Let's look at roulette (we will have bigger discussions on this later).

However in European Roulette, we have the following numbers (note the number zero)

0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36

So in European Roulette, the probability of predicting a specific number is 1 in 37, i.e. 1 desired outcome in 37 possible outcomes (2.7% chance)

Specific Number in American Roulette

And in American Roulette, we have the following numbers (not the extra number, the double zero)

0,00,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36

So in American Roulette, the probability of predicting a specific number is 1 in 38, i.e. 1 desired outcome 38 possible outcomes (2.63% chance)

Red or Black in European Roulette

In European Roulette, the zero number is green.   And every other number (1 to 36) is evenly split between red and black (will explain the exact wheel in another post).   That means there are:

18 reds in 37 possible outcomes

18 blacks in 37 possible outcomes

1 zero (green) in 37 possible outcomes

Which means if you were to bet red or black, you would have an 18 in 37 (18/37 or 48.6% chance)

Red or Black in American Roulette

In American Roulette, the zero and double zero numbers are green.   And every other number (1 to 36) is evenly split between red and black (will explain the exact wheel in another post).   That means there are:

18 reds in 38 possible outcomes

18 blacks in 38 possible outcomes

2 zero numbers (green) in 38 possible outcomes

Which means if you were to bet red or black, you would have an 18 in 38 (18/38 or 47.36% chance)

Okay, so now you know how to calculate probabilities in single events.

In future posts, I'll discuss the following

• Calculating Odds from Probabilities
• How to make a book and calculating edge and over round
• Calculating probabilities for sequenced events and multiple outcomes (double dice throws, lottery numbers etc).