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
Many answers here are saying you will get closer to 50/50 if you flip more coins, which is correct.* But perhaps one way to grasp this concept is by thinking about it the other way. What if you flipped *fewer* than 50 coins? In the extreme, you can flip a coin once, and it will be either heads or tails. There’s no magic in probability that will force it to somehow be 1/2 heads and 1/2 tails. That would make the rate of heads in your experiment *extremely* off what you were expecting no matter what.
Flipping 2 coins gives you some chance of having 50/50 with 1 heads and 1 tails, but it’s definitely not impossible to flip a heads (or tails) twice in a row. You surely did this many times during your experiment. Once again, there’s no magic in the coin that looks at the last flip and says “Ah, so that was a heads, which means I have to flip tails the next time”. So with just 2 flips, we also have a pretty good chance of being very far away from the probability, though it’s not as bad as with 1 flip.
As you keep adding flips, you end up with more and more “typical” outcomes and fewer and fewer extreme outcomes, so you move towards the theoretical probability. However, you’re never guaranteed to reach it. In some sense, the whole field of statistics is just about characterizing that process and being able to say precisely whether results like yours (because sometimes you only have 50 observations!) are unusual.
*In the sense of the average number of heads. If you flipped a coin a million times and got 500,010 heads, that’s a rate of 0.50001, so very close to 1/2, but the absolute deviation is 10 flips, much higher than in any of the experiments you did.
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