According to https://www.yours.org/faq/, first quarter of voters always profit. This is not wrong but a very engineery answer to a simple mathematics problem that can be much more accurately answered using calculus.
The more accurate statement should be:
The first third of voters always profit.
The most precise statement is "The first 36% of voters always profit".
Explanation
Suppose you voted according to the below order:
Your payment and earnings are below as described in https://www.yours.org/faq/
In order to break even, the following must hold:
Here is where we stand on the shoulders of the giants. Above sum can be approximated very accurately. See https://en.wikipedia.org/wiki/Harmonic_number.
What you get is the below equation which can be solved easily

So there it is. The true for breaking even is 1/e. That is, if 10 people voted before you, then in order for your vote to break even there must be a total of at least 28 voters.



 

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Comments
  earned 20.0¢
Beautifully explained and 100% correct. I was trying to be conservative when I wrote that the first quarter of votes make money. As you point out it is better than that: you must be in the first 1/e = 36% of voters to make a profit. Will be corrected on the faq.
By the way it gets more complicated when users vote multiple times. The thing is that you never pay to yourself when you vote, so it's not a harmonic series anymore. I have not completely thought through how that changes the math. Would be very interested in case you want to think about that...
Let me add that you do not have to understand the math to make money from voting. Just vote on good content early and you will make money :)
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