This makes me realize that I never totally understood how this works--so when someone invests say 1 BTC to the bankroll, their portion of the bankroll is 0.98 BTC and the other 0.02 BTC is divided proportionally among all existing investors?
Imagine the existing bankroll is 1 BTC, and you are going to invest 1 BTC.
You are given a stake of:
($yourInvestment * 0.98) / ($bankroll + ($yourInvestment * 0.98))
= 0.98 / 1.98
= 49.49%
But the bankroll increases by 1 BTC (AKA the new bankroll is 2 BTC)
So your stake is worth 0.98989 BTC. (AKA you only lost ~1% even though the dilution fee was 2%)
---
The high-level reasoning behind it is that if you didn't recoup some of your own dilution fee, it would incentivize people to "fragment" their large investment into tiny ones (possibly over multiple accounts?). So the dilution fee is split amongst all investors (including yourself), so that the smart way to invest a lot of money is just simply invest a lot of money.
Ok thanks this is very helpful. I'm still not quite there yet, what I'm not exactly clear on is how the dilution helps the existing investors. In your example, let's say that the bankroll was previously split between two people with 0.5 BTC each, so they each previously had a 50% stake. Without any dilution they would expect to have stakes of 25% after the new investment of 1 BTC.
Are their stakes now instead 0.5/1.98 = 25.2525...%? Since the bankroll is actually 2 BTC, this would give them 0.505050... BTC each, in other words their personal stake increased by 0.005050...BTC upon the new 1 BTC investment.
Indeed 2*0.005050... = 0.0101... which is how much the new investor had deducted from his investment so that works out, so I'm guessing this must be what happens.