LogFAQs > #887242467

Dash_Harber posted...

Isn't charting it like that a perfect example of the gambler's fallacy? Doing it multiple times doesn't actually change the percentage of it happening each time.

no, it's measuring something else. the first graph is "how many tries does it take to 'win'" with 100,000 data points.

ex: each roll of a (fair) die is always 1/6 but "how many rolls will it tend to take to get a 6" is a different question. chart for that looks like:



the second graph is almost the same data except accumulating which I then divided by 100,000 to get "what is the accumulated chance of it taking this many tries".

for a die, that looks like this:



notice that it very quickly soars towards 100% chance of having rolled a 6. if you roll a die 4 times you have a roughly 50/50 chance of getting a 6 or not. roll it 8 times and you have about a 75% chance of getting a 6. very likely with 20 or more rolls and almost 100% guaranteed with 30+ rolls.

note that there are probably better ways to calculate this kind of thing, but I'm a programmer not a mathematician/statistician. (though I'm learning to like statistics more and more and wouldn't mind learning a lot more about it.)

here it is calculated that the chance of rolling a 6 in 4 rolls is about 52% which matches my graph
https://math.stackexchange.com/questions/1000488/throw-a-dice-4-times-what-is-the-probability-6-be-up-at-least-one-time
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