The specific formula you are describing, where every six months served after five years counts as a full year, does not reflect any standard federal or state sentencing policy that exists in writing. It is likely a version of prison yard math, the informal calculations and rumors that circulate inside facilities and get passed along as fact. Inmates spend a lot of time thinking about their release dates and informal theories about how time works tend to spread and evolve the longer they circulate.
That said, there are real mechanisms that reduce time served and some of them do reward longevity and consistent behavior.
Good time credits accumulate throughout a sentence. In the federal system, that is up to 54 days per year under the First Step Act. Over a five-year sentence that adds up to a meaningful reduction. The longer a sentence runs the more total good time can accumulate, which is likely where the idea behind what you heard comes from.
Earned time credits under the First Step Act are another layer on top of good time. Inmates who complete approved rehabilitative programming generate additional credits that can move them toward prerelease custody or home confinement earlier than their projected date. The more programming completed the more credits earned, and longer sentences create more opportunity to stack those credits.
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