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12.07.2019 , 06:40 AM | #5
Quote: Originally Posted by PatT View Post
[...]. If you buy 10 lottery tickets with a 1 in 500 million chance, you are not getting 5 in a 5 hundred million chances. [...]
bad example, because actually you do get the 5 in 500 mil chance (since you're covered 5 unique possibilities... assuming you didn't pick the same numbers 5 times (because it's a single roll against 5 chances, not 5 rolls against 1 chance each)

people really misunderstand how flat odds works, but actually the simple intuition is correct... an X% chance does mean that, on average, it takes (100 / X) tries... the problem comes from the fact that lower X is the bigger the number of tries you need to get that average....

you can think of it more simply as a tray with 100 slots for 100 marbles.... if you only have 1 marble (chance) there's lots of places it can go, and so it feels a lot more random how often it "hits" the spots you want. but if you have a bunch of marble (chances), the "hits" will be pretty evenly spread out over the tries and it feels more regular. as a general rule, the lower the odds, the more random it will behave, and the more tries it takes to get a true average. reverse it for high odds. It tends to match short terms expectations at around 50%

a fun way to hack your perceptions is to always look at the higher odds side... 5% success = 95% failure... so if you are are expecting 95% failure, you are less surprised by the randomness of lower odds.
If it moves, shoot it.
if it stops moving... shoot it again.
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