Not sure I understood the initial post, but I'm pretty sure I understand what happens longer term.
Assuming that the dev is trustworth and doesn't run away with BTC or STD... the price guarantee simply puts a lower bound (GER or "price guarantee") on the price, as well as an upper bound (the price you can currently buy from the remaining 50% reserve). The lower bound is at 1/4 of the value invested by early investors and hence they have to accept a possible 75% loss.
The upper bound can be derived as follows:
F = fraction of stored STD available, where 0 <= F <= 1
F/2*MMS = stored STD available
(1/AMC) * F * (MMS/2) = STD's received for one additional BTC invested (there's a tiny rounding approx in here)
(2/F) * (AMC/MMS) = (2/F) * GER = price in BTC/STD to buy from stored STD's
Hence, after the IPO the upper bound is 2*GER. As more people buy from the stored STD the GER goes up and the upper bound increases much faster than the GER.
In other words, after IPO at price z BTC/STD the market price will be between [0.25,0.5]*z BTC/STD or equivalently [1,2]*GER. Whilst it is traded between these bounds NOBODY will buy from the stored STD, but rather from a normal exchange.
Problems:
1) The initial investors in the IPO overpay - they could buy the coin for half of what they paid right after the IPO!
2) The price guarantee is useless as/if more people buy from the stored STD. If 90% of the stored STD were sold the price would be bounded between [1, 20]*GER.
3) The coin cannot go up easily! In addition to the coins generated by the miners there are 50% (!) of the total coins available for sale. Their marginal price is 2x the price paid be the initial investors and goes up slowly as the stored STDs are depleted.
4) The price can actually fall below GER if there are concerns that the dev is trustworthy. See Mt Gox.
Dear initial investors: your only hope can be that more people do not understand the mechanics.
You understand the system correctly. But there is a small mistake in your calculation.
(1/
(AMC+1)) * F * (MMS/2) = STD's received for one additional BTC invested (there's a tiny rounding approx in here).
Re-calculate with the new formula, you will see that: The initial investors who join the Price Valuation Phase are the ones that buy at the best rate.
And you also forgot that, when someone dump their STD at GER, the stored STD will increase, which mean more STD for new investors, more profit.
To be honest, it feels like I'm the only one on this forum that understands the system and the math behind it correctly... either I'm a genius or there are a lot of high school kiddies on here.
Regarding your comment: no, the initial investors buy at a bad price. I think someone on the forum also already noticed it that buying after the price valuation phase gives you STD's at roughly half price.
Here are the details: the +1 in 1/(AMC+1) does not make a difference, it is a quantisation effect, as it relates to 1 additional BTC invested. However, to get the true marginal rate for buying STD's you'd have to consider an (infinitesimal) small additional investment of x BTC from the reserve. The accurate formula then is:
S STD's received for x BTC invested:
S = (x/(AMC+x)) * F * (MMS/2)
S = F*x*MMS/(2*(AMC+x))
Hence the price paid in BTC/STD is:
x/S = 2*(AMC+x) / (MMS*F)
simplifying yields:
x/S = (2/F)*(AMC/MMS + x/MMS)
x/S = (2/F) * (GER + x/MMS)
Obviously x can be very small, as a buy may choose to buy 0.01 BTC worth of STD's etc.
Taking lim(x/S) for x->0 (i.e. an infinitesimal small buyer) we get the result I stated initially:
x/S ~= (2/F) * GER
It is possible to fix this, but I can't be bothered going through that now. You can make me a partner, though and I'll think about it again.
Oh well, I guess the simplest fix would be to half the number of STD's received in the S = ... formula.
