you seem to have an incorrect understanding of fractional reserve, more specifically, of what the 'reserve' percentage means.
in the case you describe, having 100btc deposit, and lending out all 100btc, you end up with 0% reserve, not 50%. A bank cannot lend out more btc than it actually has.
Not really. My example just simplifies a little bit. When looked at from the perspective of the banking 'system,' the end result is the same. This thread seems to touch on the difference:
http://mises.org/Community/forums/t/22490.aspx . Banks don't have to lend out the hard reserves - particularly when all the banks form one system. Khan Academy describes the difference between 'modern' (banks working as one system) and 'primitive' (single bank's perspective) fractional reserve banking:
http://www.youtube.com/watch?v=ZyyaE3DIxhc (3 to 6 minute mark)
My argument, though, is that it will be difficult to sustain a fractional bitcoin banking system because:
a) Any given bitcoin bank's on-demand deposits (what you see on the bank's database) will not circulate as equivalent to or as widely as hard BTC (what you see through Bitcoin software)
b) The decentralized nature of the protocol prevents cartelization of bitcoin 'banks'
c) Nobody can act as a central bank to 'inject' artificially created BTC to prop-up liquidity
End result: runs cannot be prevented or forestalled. Bitcoin banks will have to be honest to depositors that their funds cannot be both on-demand
and lent out.
