SAN JOSE — They haven’t been able to strike a truce yet in their worldwide patent war.

And as they make their cases to jurors in a closely watched rematch on damages, lawyers for Apple Inc. and Samsung Electronics Co. are $328 million apart on the question of how much the Korean smartphone maker must pay for patent infringement.

In his opening statement Wednesday, Apple lawyer Harold McElhinny of Morrison & Foerster told the jury that Samsung should fork over nearly $380 million for 13 infringing devices. Tacked onto what Samsung already owes, that would leave Apple with slightly less than the $1.05 billion award it was granted by a jury last year.

But when it was his turn to address the jury, Samsung lawyer William Price shot for a much steeper discount.

“What Samsung should pay is $52 million­—not a trivial sum at all,” said Price, who is a partner at Quinn Emanuel Urquhart & Sullivan. “Apple is simply asking for much more money than it is entitled to.”

In August 2012, a jury upheld Apple’s patents and found Samsung liable for infringement, imposing one of the largest patent verdicts in history. Now a new crop of jurors must revise its math. In March U.S. District Judge Lucy Koh slashed more than $400 million from Apple’s original award, finding that calculations for some Samsung devices were based on an improper notice date. She ordered a damages retrial to determine how much Samsung must pay for infringing five Apple patents.

Reprising themes that played well at the first trial, McElhinny asked jurors to remember where they were in 2007 when Apple debuted the iPhone to great success in the market. Competitors have since gained ground, eating into Apple’s market share. But the Cupertino company began a revolution, McElhinny said.

“The iPhone literally changed the way that people in this country and around the world communicate,” McElhinny said.

Apple called four witnesses Wednesday. Two computer scientists attested to the value of Apple’s patents, which cover features including the iPhone’s “pinch and zoom” technique. McElhinny said the strength of the innovations is their intuitiveness. He told jurors that his granddaughter spoke her first word, “more,” when his daughter took an iPad away from her.

To draw up a new bill for Samsung, jurors will evaluate the company’s sales of infringing phones and assign Apple one of three types of compensation: the profits Apple lost, the profits Samsung made, or a reasonable royalty that the companies would have reached if they negotiated a licensing deal.

To win the most lucrative prize, lost profits, Apple must show that it would have won sales that went to Samsung if not for the infringement. Jurors will consider how strong demand was for Apple’s products and whether or not the Silicon Valley stalwart’s sales would still have been undercut by sales of noninfringing devices.

As Apple tries—yet again—to demonstrate how badly consumers wanted the iPhone, Samsung will be its “star witness,” McElhinny said. Apple lawyers plan to use internal documents that illustrate Samsung’s desperate bid to imitate the iPhone, McElhinny said. But he warned jurors that Samsung will strike a very different tune in trial this week.

“When you hear Samsung’s lawyers describe our inventions as trivial or unimportant, I hope that when you’re listening to that evidence you will be asking yourselves, ‘Really? Then why did you copy?’” McElhinny said.

A soft-spoken Price conceded more than once that Samsung infringed Apple’s patents—a determination from the first trial that cannot be undone. He insisted, however, that the retrial’s purpose should not be “about punishing” but about determining a fair price.

Price challenged Apple’s assertion that Samsung customers would have switched camps if the infringing products had not been available. He insisted that consumers choose Samsung’s devices over Apple’s for many reasons, including the products’ lower price point, larger screens and removable batteries.

“I know a lot of you folks love Apple, and they make a great product,” Price said. “There are a lot of people who are diehard Samsung fans.”

He also fought to pare down the dollar figure for Samsung profits that could be handed back to Apple. Apple’s damages expert, Julie Davis, inflated profits because she did not subtract operating costs, Price argued. And Price scoffed at the $24 royalty that Apple claimed Samsung would have agreed to pay for each device. He showed a slide that displayed two similar Samsung phones­—one that infringed Apple’s patents and one that did not. With ample options that did not step on Apple’s patents, Price imagined how Samsung would have responded to Apple’s request in licensing negotiations.

“Are you willing to pay $24 per phone to use this?” he said. “The response would be, ‘No. I’m going to use this one on the right because it’s free.’”

The retrial is expected to last about a week.

Contact the reporter at jlove@alm.com.