Thanks. I plugged your numbers in a spreadsheet and can verify the exact total NBT and NSR but only to the 4th digits for the sent amount. I also notice there is more than 1NSR left undistributed.
I did some math and find some interesting results -
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Calculated based on the averaged price, everyone’s profit is exactly 0.
Suppose a participant puts in S1 NSR and B1 NBT and gets S2 NSR and B2 NBT back. The averaged price is P.
Then profit is S2-S1in NSR and B2-B1 in NBT. Based on the average price, total profit is S2-S1 + (B2-B1)/P
Since by the distribution rules B2=S1P and S2=B1/P, we have **total profit = B1/P - S1 + (S1P-B1)/P = 0**
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Calculated based on one’s own price, no one makes a loss. The more one’s own price deviates from the average price, the greater profit becomes.
Using definitions made above, the profit is S2-S1 in NSR and B2-B1 in NBT. Based on the participant’s own price P’, defined as B1/S1, the total profit is S2-S1 + (B2-B1)/P’. Still by the distribution rules B2=S1*P and S2=B1/P, we have
total profit = S1 * (P’-P)^2 / P1 /P2 = S1 * (P/P’ + P’/P - 2)
Since (P’-P)^2 is always positive, unless P=P’ when the profit is 0, therefore the profit is always non-negative. P/P’ + P’/P - 2 is another way to show the symmetry between P and P’. The more P’ differs from P, the more P/P’ + P’/P is greater than 2.
There are two ways to increase total profit with the same amount input NSR. One is increase input NBT so P’ >> P. One is decrease input NBT so NBT becomes more precious in participants own terms, and the distributed NBT will be worth a lot at price P’. Apparently the latter isn’t what people usually want.
