## Monte Carlo Simulation
# Tossing a Coin
Monte Carlo simulation is particularly useful when you want to predict the overall outcome
of a series of related events when you only know the statistical probability of the
outcome of each component event.
The simplest such situation must be the tossing of a coin. Any individual event will
result in the coin falling with one side or the other uppermost (**heads** or **tails**).
However, common sense tells us that, if we tossed it a very large number of times, the
total number of **heads** and **tails** should become increasingly similar. We could
simulate this by using a random number between 1 and 100 to decide which side would be
uppermost, giving a 50% chance of it falling on either side by making **heads** any
number below or equal to 50 and **tails** any above 50.
This element of chance at each event is where the name *Monte Carlo*,
synomymous with games of chance, comes from.
## The working simulation
Here is a working example of the coin-tossing simulation with lots of information in
addition to which side the coin lands.
Click on one of the option **buttons** to select how many times you want the coin
tossed - I have limited the range to 100 000 times simply because Javascript is not too
fast.
If you select the **whole series** option, the program will work through 100,000 tosses
and will eventually display the running totals it recorded for the smaller samples on the
way.
Source and permission for noncommercial use: **Monte Carlo Introduction** |