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
There’s one thing called probability and there’s another thing, distribution.
Probability applies to the single event, like the coin toss. If you do several coin tosses (let’s say 6 of them), you will get different outcomes. You may get 3+3, but you may also get 4+2 or 5+1. You even have some little chance to get a straight run of 6 of tails or 6 of heads.
If you count all possible unique outcomes, there will be 64 different cases. I call it a unique outcome if the order of the heads and tails are different.
So for example HHHTTT is different from HTHTHT, however both of them gives you exactly 3 H’s and 3 T’s.
Out of the 64 possible cases, there’s exactly one that has 6 H’s (HHHHHH), and exactly one that gives you 6 T’s. You will also get 6 different cases of 1H5T (such as HTTTTT or TTHTTT), and another 6 of 5H1T. There will be another 15 cases of 2H4T and 15 of 4H2T. And the remaining 20 gives you 3H3T.
This thing is called *binomial distribution*. What it says is that even though the two outcomes have the same probability, only 20 of 64 cases will give you the expected 3+3 outcome. 15 of 64 will be 2H4T and so on.
Now imagine you have 64-sided “dice” (I’ll call it d64). This imaginary object has 64 sides and when you roll it, they all have equally possible probabilities to come. On each side you can have one unique outcome of a 6-coin toss.
So instead of tossing 6 coins you can roll a d64, and you can get, for example, HHTHTT or so. If you are only interested in the amount of H’s and T’s, then you will see that 20 of 64 sides of d64 give you 3+3. Basically what you did is you “packaged” the outcomes of the binomial distribution. It’s interesting to notice that although the 3+3 outcome is the most abundant, it’s only less than 1/3rd of all possibilities, so in most cases you will get one of the non-expected outcomes.
If you toss let’s say 24 coins, you expect 12+12, but because of the binomial distribution, 16-million sided dice to roll, and there will be a lot of non-expected outcomes such as 11+13 or 10+14.
If you go higher with the number of coin tosses, two things will happen:
One is that you will get results very close to the 50% expected outcome, and there will be virtually no huge deviations such as 30% and 70%.
Two is that the exactly 50% (like exactly 5000 of 10000 and not 5001) will be super rare, as this will be a very small portion of the all possible outcomes.
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