[AgentME]

If you had 1/4 the hash power, it's true that you have 1/4 chance of creating a block before anyone else, but to be clear, doing that once isn't enough to do a double-spend attack of a transaction with some N confirmations (usually people would aim for N=6). There's only a 2% chance an individual attempt would pull that off for 6 confirmations in a row when using 1/4 the global hash power, and the whole time you're attempting this, your hash power isn't making money mining unless you succeed. On average, you would make $144,000 just from the block rewards from mining for that much time with 1/4 global hashpower, so the expected amount of failures are very expensive in opportunity costs. If I'm doing probability right, then at a 2% chance, you could expect to fail about 25 times on average before succeeding, so 25 failures adds up to $3.6 million of expected opportunity cost. (This isn't counting the cost in acquiring 1/4 global hashpower to begin with.) You would have to double-spend a lot of transactions to make that worth it, and people are probably going to wait for more than 6 confirmations on bigger transactions, which means a much larger attack would have to be done to target those.

[labawi]

If you add opportunity cost and renting cost, you are double counting.

Assuming you can repeat your "totally legit" setup transactions until you succeed, with minimal cost other than rent, you would need to take more than either the opportunity cost (otherwise it's better to just mine), or the renting cost (otherwise you're still losing money).

[Rodyland]

Adding opportunity cost and renting cost isn't double counting.

Opportunity cost is the foregone block rewards that you lose because you didn't submit your blocks, because you were holding them hoping to build a long enough chain to double spend. When you fail, that reward that you would have earned is gone forever.

Renting cost is the actual $ outlay that it costs you to rent the hash power necessary to perform the attack.