February 18, 2018
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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