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The phrase "maximize their gains" is correct and usable in written English.
You can use this phrase to refer to a situation in which someone or something is striving to obtain the greatest possible benefit from a particular situation or circumstances. For example, "The investors were eager to maximize their gains by diversifying their portfolio."
Exact(13)
But what about those who invest more broadly or do so to maximize their gains?
Thus, buyers attempt to maximize their gains and minimize their losses from purchase situations.
Apart from the Islamists, who understandably saw a chance to maximize their gains, every last one of Egypt's political factions opposed this plan.
This article uses negotiation examples in real life to offer negotiating skills tips on how bargainers can maximize their gains at the negotiation table by tailoring their style to the negotiation scenario at hand.
Residents said the intensity of the strikes has increased since the announcement of the cease-fire agreement, perhaps as Russia and its allies seek to maximize their gains ahead of its possible implementation.
With Robert Keohane, Nye developed the influential "neoliberal model" of international relations (which posits that international cooperation is possible because states are rational actors that seek to maximize their gains, and though there are opportunities for conflicts and cheating, institutions and regimes generally keep the system in check).
Similar(47)
Lacking these conditions, consensual exchange cannot occur, and rational individuals will try to cheat others to maximize their gain.
2d at 200 ("A Rule 10b5-1 trading plan may give rise to an inference of scienter because a clever insider might maximize their gain from knowledge of an impending price drop over an extended amount of time, and seek to disguise their conduct with a 10b5-1 plan".) (internal quotations omitted).
"Class action plaintiffs lawyers are indeed independent entrepreneurs driven by the desire to maximize their gain, even at the expense of class members' compensation," she wrote.
One might begin instead with a competitive betting situation, in which it is given that both sides attempt to maximize their gain.
They are assigned specific characteristics that control their action such as moving in a neighborhood, making rational choice to maximize their gain while minimizing the risk of apprehension from interaction with other residents of the neighborhood.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com