How Does the Cost of Acquiring the Necessary Hash Power Relate to the Potential Profit from a Double-Spend?

The attacker must ensure the potential profit from the double-spend significantly exceeds the cost of acquiring and operating the necessary 51% hash power. The cost includes renting mining equipment, electricity, and any lost opportunity cost.

If the cost of the attack is higher than the value of the double-spent coins, the attack is economically irrational. This economic barrier is the primary defense for high-hash-rate coins.

Low-hash-rate coins have a much lower barrier, making the profit potential higher.