I think you understand but you wrote it wrong. Its not that you only carryover 3,000. You carryover the rest after the 3,000.
You get to first offset the loss against any gains you have each year so that can use more of it up. Then after applying the loss to the current gains you can take a max loss of 3,000 (1,500 MFS)per year.
The rest you have to carryover to next year. You have to report the carryover every year until it's used up. You can't skip a year.
