We analyze “coin-wallet” and “balance-wallet” under
partial real-time audit, and compute upper bounds on theft due to the fact that not all the transactions are audited in real time,
assuming that every- thing else is perfect. In particular, we assume that the audit regime holds for innocent players. Let
v be the maximum allowed balance in a wallet, 0 ≤ μ ≤ 1 be the fraction of transactions that are audited in real time in an
audit round that includes overall n transactions. Assume one unit transactions. We show that for μ << 1 the upper bound on
expected theft for coin-wallet is

(which if
v << μ
−2 becomes

), while for plausible parameter choice the bound for a balance-wallet is
O(
exp(
v
2/
n)). This last bound can become huge in some cases, implying that partial audit, while suitable for coin-wallets with low denomination
coins, may be too risky for balance-wallet. Some implications to the design of anonymous and non-anonymous systems are discussed.