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We studied the gain of Raman-assisted fiber optical parametric amplifiers (RA-FOPAs) both theoretically and experimentally. We investigated the relationship between the overall gain and different combinations of Raman and parametric pump powers using contour maps. We derived a normalized phase-matched model to determine the general behavior the peak gains of RA-FOPAs operating in the small signal region. The contour maps of the combined gain enhancement can be used to optimize both indirect and direct Raman gain of the signal/idler in RA-FOPAs. We showed that, in a given fiber, it is possible to optimize the Raman and parametric pump powers in RA-FOPAs for high gain and high efficiency.