Weak Law of Large Numbers Simulator

What is this chart for?

The weak law of large numbers is best visualized with line chart.

This website, as one example, simulates throwing a coin several times, and calculating its relative frequency to the total of throws. Along the x-axis, you'll see the amount of throws that have already gone. The y-axis represents the relative frequency of each coin side. Each line in the graph represents one of the coin sides, 2 in total. Every roll is random, however, after enough amount of rolls, every time, the relative frequency converges to 1/2, or 0.5.

We have also plotted a black line corresponding to that ideal probability.

How do I use this site?

This website is very simple. There are four main things you can change to see the effect of the theorem. Since we are simulating dice and coin throws, the first input is the dropdown, right next to the Help button, called "Coin/Dice". Click and choose which one you'd like to simulate.

The second input is the amount of rolls the computer should do. Lower this to stop the graph earlier, or leave it at a large number to see the effect even more.

The third input is the "Start from". It starts the graph at that number. If you're playing with large numbers at the "Amount of rolls", increment this number so that it'll already start at a big amount of rolls/throws already done.