Screenshot by Emily Dreyfuss

"If they go to 10 cents, I'll go to 9 cents," Overstock CEO Patrick M. Byrne told CNET on Monday about his plan to continue to undercut Amazon on books.

On Thursday of last week, Overstock sent out a daring press release announcing that it would beat Amazon by 10 percent on its books.

On Friday, Amazon appeared to match those prices.

"Not true," CEO Byrne insisted. Byrne explained that Overstock dropped the prices of 360,000 titles ("three times the size of Barnes & Noble's stock") by 10 percent below Amazon. According to Byrne, Amazon matched those prices on a few thousand. "On the books that people look at, they dropped their prices below ours. But on Friday, we dropped our prices even on those 10 percent again. So we're back to 10 percent below [Amazon]."

Amazon has not replied to requests for comment.

If you've been waiting for Dan Brown's "Inferno" to come out in paperback, you might want to check out how much the hardcover is selling for on both Overstock and Amazon on Monday. Discounted from the list price of $29.95, you can grab the book for $10.48 right now. That's a 65 percent savings on a relatively new best seller.

I went searching for more obscure titles to put Byrne's assertions to the test. The book I just finished, "Beautiful Ruins" by Jess Walter, is selling for $8.10 on Amazon and $7.29 on Overstock. Ridley Pearson's mystery "The Risk Agent" is going for $8.99 on Amazon, but only $8.09 on Overstock. Not quite 10 percent, but close. What about a slightly older book? One of my all-time favorites, "The History of Love" by Nicole Krauss, goes for $20.07 on Amazon and $19.66 on Overstock.

So though I found that while Overstock does consistently beat Amazon on many book prices right now, it's not necessarily 10 percent. Byrne said Amazon updates its prices more often than Overstock, "but we'll know tomorrow. If they drop the prices, we'll just keep going."

Screengrab by Emily Dreyfuss

If you're like me, you may not have realized Overstock even sold books. I thought the Web site was strictly about home goods. "That's a problem," Byrne told me. "What you say does not fall on deaf ears. We've sold books for 10 years. Maybe this event will get people to change their thinking."

How long does Overstock plan to undercut Amazon on books this way? "It well might be permanent," Byrne said.

When asked if the promotion was worth it to Overstock's bottom line, Byrne reported that the company has more than doubled its book sales in the last four days. Although he wouldn't share the absolute numbers of those sales, he said book sales are an eight-figure number annually.

So is Overstock losing money on this promotion? Executives aren't sure yet. I was told they are "evaluating the economics of it, but so far, it looks good."

Picking this fight with Amazon is a risky business, of course, but, as Byrne said, "It's all part of the game.

"As my old football coach used to say, it's not the size of the dog in the fight, but the size of the fight in the dog," he said.

Does Overstock have plans to battle with Amazon on other products?

"We are already 9 percent cheaper than Amazon on other products," Byrne answered. "We have better customer service, and we're nicer people."

Them's fighting words.

In the battle for low prices, it's the customer who's coming out on top -- at least as long as they can afford to keep up the fight.

Updated at 12:29 p.m. PT with comments from Overstock CEO Patrick M. Byrne.