I agree on your calculations for our compounding, but I think the (1 + 0.02*0.9)**8 for other sites is not correct.
For instance, week 2 should actually be 1 + (1.018*1.02 - 1)*0.9 = 1.034524 instead of (1 + 0.02*0.9)**2 = 1.036324
No, other sites only take 10% commission on new profits.
At the end of the 1st week, the profit is 2% of 1, or 0.02. 10% of that is 0.002. that leaves an investment of 1.018
At the end of the 2nd week, the profit is 2% of 1.018, and the profit is (1.018*1.02 - 1.018), not (1.018*1.02 - 1) as you wrote.
That can be simplified to 1.018 * 0.02, and after commission is removed as 1.018 * 0.02 * 0.9.
Each week the investment will grow by a factor of 1 + 0.02*0.9, compounding.
The formula you provided is for compound growth and that is what win88 would see if we were to used 10% fee.
Growth at other sites *does* compound. The formula I gave is correct for other sites, and would be correct for win88 if you used 10% fee and charged it every week, like the other sites do.
The fact that you can't understand this gives me cause for concern.
Are you sure you want to be running a site where the mathematics matters?