“Well, in our country,” said Alice, still panting a little, “you’d generally get to somewhere else — if you run very fast for a long time, as we’ve been doing.”
“A slow sort of country!” said the Queen. “Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!” 
Through the Looking Glass, Lewis Caroll
A Red Queen’s race is any conflict situation where any absolute advances are equal on all sides such that the relative advantages stay constant despite significant changes from the initial state.
In other words … Much Ado/efforts and pains About Nothing; all for naught.
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Literally, pay the devil what you owe him. Used figuratively to mean ‘give back what you owe’, either money or favours.
From Shakespeare’s Henry IV Part 1, 1597:
Constable: I will cap that proverb with ‘There is flattery in friendship.’
Orleans: And I will take up that with ‘Give the devil his due.’