Further thoughts: Alice and Bob must each choose an actual policy for how many confirmations they need before they actually commit to attack. We can number the

Further thoughts: Alice and Bob must each choose an actual policy for how many confirmations they need before they actually commit to attack. We can number the messages like this: 1. Alice's first message 2. Bob's first message 3. Alice's second message 4. Bob's second message ... Alice's policy can only commit to attack after receiving some even-indexed message n. Bob can only commit to attack after receiving some odd-indexed message m. So n and m cannot possibly be equal. Therefore the possibility exists that a message fails between n and m, and either Alice or Bob ends up attacking without the other's support.