For a coin toss, the probability of getting a head 50%. But this doesn't mean that for a given number of tosses, the percentage will be exactly 50% or even close.
Theory states that the larger the number of tosses, the closer the percentage will be to 50%.
This is known as the law of large numbers. See http://en.wikipedia.org/wiki/Law_of_large_numbers
Test this out experimentally, with the virtual coin toss below. Let the computer do all the work.
Wait a few minutes and look at the results. Then see what happens after a few hours. For the really curious, leave it running for a few days. Then take cold showers for a month to make up for the electricity used by your PC.
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The theoretical number of heads, is calculated as the number of coin tosses divided by two. This gives values with 0.5 for odd values of tosses (1->0.5, 3->1.5, 5->2.5, 7->3.5 ...). Which isn't really accurate, but reduces to an insignificant percentage for large number of tosses.
Theory states that the accuracy of the result is proportional to the square root of the number of tries.
This means that if the number of tries is multiplied by 100, the accuracy increases by only 10 times (or, the error decreases by 10 times).
History of the coin tosses above, is shown in this table, for tosses of 100, 10000, etc. The error should decrease by about 10 times for each entry.
| Coin Tosses | square root (Coin Tosses) | Heads Error |
|---|---|---|
0 |
0 |
0 |
Convinced? This is why casinos don't believe in luck, and believe in probability. In the long run, "the house always wins". Or, "gambling is a tax on people who are bad at math."
Unfortunately, gamblers sometimes do experience a "run" of "luck" due to the small number of tries. If they did record their winnings over the long term, they would realize the futility of their efforts (for games of pure chance, not for games where some skill is involved).
Note: the realism/accuracy of the results above, depends on how truly random the web browser's JavaScript psuedo-random number generator, is. That's a whole other topic.