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i.e 2. $13,000 in long term gains in a given year against $10,000 in long term losses in the same year, $3,000 offsets ordinary income. Gains that exceed $3,000 would be taxed at the capital gains rate.

The way you've stated it - $13k in LT gains and $10k in LT losses, you would actually have $3k in LT gains, and no offset for ordinary income. In order to have a $3k offset for ordinary income, you would need to have $16k in losses if you had $13k in gains.

If I’ve got this right, is there anything else that needs to be taken into consideration?

You kind of missed a step in between the capital gains and the offset against ordinary income. After offsetting long term gains against long term losses, and short term gains against short term losses, you then net the long term against the short term - so if your total long term are gains, and your total short term are losses, the short term losses would offset the long term gains. Only after that calculation, if you still have a net loss, would the loss offset ordinary income. You can seen the calculation where the long term and short term are netted together on line 16 of Schedule D

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