  Nakamoto double spend strategy, described in Bitcoin foundational article,
leads to total ruin with positive probability and does not make sense from the
profitability point of view. The simplest strategy that can be profitable
incorporates a stopping threshold when success is unlikely. We solve and
compute the exact profitability for this strategy. We compute the minimal
amount of the double spend that is profitable. For a given amount of the
transaction, we determine the minimal number of confirmations to be requested
by the recipient such that this double spend strategy is non-profitable. We
find that this number of confirmations is only 1 or 2 for average transactions
and a small hashrate of the attacker. This is substantially lower than the
original Nakamoto numbers that are widely used and are only based on the
success probability instead of the profitability.
