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A capped range has a clear upper bound

What is the term for a range with a clear lower-bound?

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Not sure why you don't want to just say "range with lower-bound". Depending on the scenario, "overcards" (the high hands of a polarized range) or "top-range" / "medium-top-range" are candidates that, while not matching the nuance of the capped ranges, works.

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A pure value range. The value range is the part of the range where you want your opponent to call. There is also a "merged range," which is a range that consists of medium strong to very strong hands, and only a few bluffs.

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