Random dice throw and the law of large numbers

If you throw a dice, the possible outcomes are

1, 2, 3, 4, 5, 6

Throw the dice once you might get 6, throw it again you might get 4 etc. This seems pretty random. The average of these two throws is 5.

But what happens if you throw the dice a hundred times or even a thousand times? This is where the law of large numbers comes into play.

The theory describes that when you perform the same task a large number of times, the average of the results should be very close to the expected result.

For a dice throw this would be

(1+2+3+4+5+6)/6 = 3.5

Proof:

$nrOfTries = 100000;
$total = 0;
for($i = 0; $i < $nrOfTries; $i++){
    $total += random_int(1,6);
}
echo number_format($total/$nrOfTries,2);

The result of this experiment will always be close to 3.5

Let's flip a coin. When we apply this law, then the average will be

(0+1)/2 = 0.5


Tags: math


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About the author

human, software engineer, tech enthusiast, security researcher

E-Mail: blog@cipher.digital

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