My analysis agrees with Deprived.
[...]
If there's essentially no difference, then this new feature is just a fancy way of divesting a portion of your balance.
(sorry for cutting up your post, by the way)
The problem is that you and dooglus calculated different things. He showed the relative change in your *invested* bankroll:
>>> a=500
>>> for i in range(20): a *= (1-0.0025); print "%.2f" % (a*100/500,),
99.75 99.50 99.25 99.00 98.76 98.51 98.26 98.02 97.77 97.53 97.28 97.04 96.80 96.56 96.31 96.07 95.83 95.59 95.36 95.12
>>> a=125
>>> for i in range(20): a *= (1-0.0100); print "%.2f" % (a*100/125,),
99.00 98.01 97.03 96.06 95.10 94.15 93.21 92.27 91.35 90.44 89.53 88.64 87.75 86.87 86.01 85.15 84.29 83.45 82.62 81.79
while you calculated the total of invested bankroll *plus* uninvested portion:
>>> a=500
>>> for i in range(20): a *= (1-0.002500); print "%.2f" % (a),
...
498.75 497.50 496.26 495.02 493.78 492.55 491.32 490.09 488.86 487.64 486.42 485.20 483.99 482.78 481.57 480.37 479.17 477.97 476.78 475.58
>>> a=125
>>> for i in range(20): a *= (1-0.0100); print "%.2f" % (a+375),
...
498.75 497.51 496.29 495.07 493.87 492.69 491.51 490.34 489.19 488.05 486.92 485.80 484.69 483.59 482.51 481.43 480.37 479.31 478.27 477.24
The problem in this unequal comparison arises when you start calculating, as you did in the end, what happens when several big losses are followed by wins (for the investor).
Take an extreme example: Several big losses drive the *invested* bankroll of the 1% investor to 0, while the <1% investor still has a non-zero amount invested. That's a possible scenario, and that's what dooglus' percentage calculation describes.
In that case, any further profits are going entirely to the <1% investor,
unless the 1% investor "refilled" his investment. But in that case, your calculation isn't applicable anymore, because you assumed fixed initial investments.
So I don't think your example calculations already sufficiently show what you want them to show, but I admit they did make me think about the relevance of the new system as well.
I'll have to think about it some more, but I'm not sure anymore either if it makes a difference whether you invest, say 400 btc @ 0.25% or 100 btc @ 1%, assuming the 1% investor "refills" his investment up to the total of 400 btc.