For example, when I flip a coin, I have a 1/2 chance of getting head, and the same chance at getting tails. With that theory, if I toss a coin 50 times, I should get 25 heads, and 25 tails.
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However, I did 3 rounds of 50 coin flips, with results of:
1. 28 heads, 22 tails
2. 27 heads, 23 tails
3. 27 heads, 23 tails.
I assumed that perhaps the coins weren’t “true”. Maybe the sides are waited different, maybe I tossed with different height/force each time. So I went virtual, and switched to having a computer roll a dice.
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I should have a 1/6 chance at rolling a number between 1-6. So 60 rolls, should have each number come up 10 times. But in practice my results were:
1. 14
2. 9
3. 8
4. 13
5. 6
6. 10
So how come practice/reality, doesn’t align with theory, even when we take human error out of the equation?
In: 34
Consider this: if you flipped a coin exactly once, with a 50% chance of heads and a 50% chance of tails, would you expect to get half of heads and half of tails in that one flip? No, you would get either heads or tails, with an equal probability of each. This result, with your sample size of 1, would be either 100% heads or 100% tails. You can flip a coin once more to see if you end up with the other result to balance it out, but you might also end up with the same heads or tails result again. The previous flip does not force the next flip to balance out the odds, it has the same equal probability for each result. This is because the probability of the result just applies for the one, current coin flip or dice roll. It does not take past flips into account to influence the odds of your next flip.
When we track lots of coin flips or dice rolls, we find that the results tend to converge towards the underlying probability, but nothing forces the results to align once you have enough flips. The only point at which results are forced to converge is when you flip an infinite number of coins, which you are not going to do. Before that, the results will be close but are not guaranteed to be exact, and will tend to get closer as you flip more coins. You can somewhat see this with your coin flips: while at first the results were 100% on one side, you ended up with results of 56% and 54% weighted towards heads, which is closer to the underlying probability. As you flip more and more coins, that number will, with some wiggles, move closer and closer to 50%.
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