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No matter if the losses are long or short term - they get applied to whatever gains are made (long or short) ?

The losses do retain their character as long or short term. So the loss carryovers will offset their own kind first (long term carryover offsets long term gains, short term carryover offsets short term gains), but then they will offset whatever gain remains.

In effect, the capital loss carryovers act just like an additional current year loss. They just get tossed into their appropriate pile and netted out.

Here's a pretty ancient post I wrote explaining the process of netting capital gains and losses. The only caveat is that the tax rate on long-term gains has changed since then. Otherwise, the methodology is still correct.

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