- we have formally defined nothing-at-stake attack(again, using Buterin's informal definition) and made initial simulations. We haven't included their results in paper as they are seems to be too raw, but I can reveal them here: N@S attack could happens only in short-range, e.g. for within 20 blocks for 10% stake, so with 30 confirmations we haven't observed the successful attack. Also please note the attack has pretty unpredictable nature for attacker, so he can hardly enforce it, even in theory(in practice it's even harder to get it done properly). The correlation with stake size is still the open question, but it's nearly impossible to attack a proof-of-stake currency with "1% stake even" as stated by Buterin