How many times do I have to try for winning something if my chances are 20%?
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A lot of other answers are giving the odds, but to apply those answers to your original question “how many times do I have to try”, the answer is related to how “sure” you want to be. Most people mean, “how many times to I have to try before I can win ‘consistently’?” But “consistent” could mean a number of things.
From the answer of /u/chillbo-swaggins:
>so after 1 try, the odds of not winning is 0.8. so the odds of winning are 20%
>
>after 2 tries the odds o not winning is 0.82 = 0.64 = 64%. So the odds of winning are 36%
>
>after 3 tries the odds of not winning are 0.83 = 0.512 = 51%. So the odds of winning are 49%
In other words, if you took 100 people and had them each try 3 times, around 49 people would win at least once, while around 51 people wouldn’t win anything. But a lot of people probably wouldn’t count a 49% overall chance as good enough to be a consistent win and wouldn’t accept “You have to try 3 times” as an answer.
So maybe a more than half chance is good enough for you? In this case, 4 tries will give you a 59% chance of at least one success. If you prefer 75%, 6 tries will get you odds of about 75% for one success. Maybe you want around 90% chance? You’d have to go up to 10 or 11 tries. As you can see, the price of increasing our confidence is that we have to prepare for trying at lot more (to account for “bad luck” cases). The extreme version of this is, as many stated, that 100% confidence is literally impossible.
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