Any investement into a HYIP has to be treated like any other investment like stocks, bonds or currencies. There are obviously two things to consider: The risk you are taking and the potential profit you might gain. This is something most of us do intuitively, but let's apply some math!
Here's an example: Let's assume someone offers you the following deal: You flip a coin - head means you receive $1, tails means you lose $10. Intuitively no one would ever accept that, rightly so.
To prove that mathematically, we take the probability for each outcome and multiply that by the financial impact:
50% x -$10 = -$5
50% x $1 = $0.50
Now we add the two possible outcomes together:
-$5 + $0.50 = -$4.5
We now have calculated the average result of this "deal": You lose $4.50 on average each time you flip the coin.
Which is obviously negative, so you wouldn't want to do that.
Note: This is the statistical average: You could of course get lucky, do 5 coinflips and win each time! It is just very unlikely that that happens. And unlikely is nothing you should ever base real investments on.
But how is that related to HYIP investment?
Let's just assume that we have no idea if an HYIP is running long enough to reach ROI (even though HYIP Rotation System helps with that). With that assumption we can treat investing into an HYIP just like a coin flip: 50:50 chances. So we already have the probabilites for our formula.
But how are we calculating the financial impact?
In case the HYIP collapes before we can get our money out, we lose everything (not quite correct, see below). For our calculations let's assume that we invest $100. So the impact of that outcome is -$100.
But what's the impact when we reach a later phase of the HYIP-RS? Assume that we successfully did two
in phase 3 and then pulled everything out. That means we have our ROI from phase 2 and 2x2 the principal from phase 4. With an $100 initial investment that's a total of $500.
Adding the two together:
50% x -$100 = -$50
50% x $500 = $250
-> -$50 + $250 = $200
So in this scenario our statistical average result would be $200. Or 100% profit on the $100 initial investment. That's positive, so it's a good investment from a mathematical point of view
Naturally this is just an example: All variables have to be calculated (or often guestimated) for each HYIP and each situation individually - which leads to different results.
A few details that we've left out for simplicities sake:
Investing into a HYIP is not as black and white as a coinflip. They might collapse half way to ROI for example. In this case you don't lose 100% of you investment, but only 50% (you've pulled out the other half during phase 2)
If you are investing into a program which converts you deposit to USD and then back to BTC when withdrawing: You have to take changes in the conversion rate into account
Any obviously greatly change the outcome in your favor