Credit scores play a large roll in determining whether you’ll be approved for a credit card or offered the best rate on an auto loan. But credit scores remain a mystery to most consumers, who typically have to pay to see their score.

Now borrowers who are denied a consumer loan or are offered a higher interest rate will be entitled — at no cost — to see a credit score that was used to make that decision.

Until now, consumers were only entitled to free credit reports from each of the three major credit bureaus annually through www.annualcreditreport.com — not a free credit score.

“The new rule represents a major victory for openness and consumer financial literacy,” said Darryl Dahlheimer, program director at LSS ­Financial Counseling Service.

But the rule isn’t perfect.

“It’s as clear as mud,” said John Ulzheimer, the president of consumer education at SmartCredit.com, of the new rule, which is complex, written in regulator-speak and is riddled with exceptions.

For example, if the lender used two scores to make its decision, it is required to share only one score. If the bank uses a proprietary score that factors in data beyond what’s found on a credit report, the lender doesn’t have to show it to you. And if you qualified for the best rate, you don’t get a free peek at your ­credit score.

Confused yet? Maybe the new Consumer Financial Protection Bureau can create a rule requiring free credit scores for the applicants of all consumer loans.