How much does Samsung Electronics owe Apple for copying key features of the iPhone and iPad - which it yesterday admitted in a San Jose court? Apple says - precisely - $379.8m. Samsung counters with a much smaller amount: $52m.

But it's going to be up to a jury, which is in a San Jose courtroom hearing a new damages session from last year's patent trial between the two electronics giants, to decide.

And this is only the warmup for a much bigger trial next March - when Apple will be asking that Samsung be barred from selling some of its current devices in the US, and more money will be at stake as well.

The latest session follows the verdict by another jury in August 2012, which awarded $1.05bn in damages in Apple's favour against Samsung after deciding that 28 Samsung products had infringed six Apple patents, covering both the devices' function and design. But Judge Lucy Koh later decided that that jury had miscalculated $400m of that damages assessment, covering 13 products, and ordered a new trial - which is strictly limited to determining the correct amount due.

Judge Koh has made it clear that Samsung cannot argue against the original jury's determination of infringement, which still leaves it facing $639m of damages which are not disputed.

And Samsung's lawyer did not deny infringement. "This is a case not where we're disputing that the 13 phones contain some elements of Apple's property," Bill Price, Samsung's attorney said. "That doesn't mean Apple gets to come in here and ask for a windfall ... for more than it is entitled."

Copying concession

In the first day of testimony on Wednesday, the jury heard Apple's attorney Harold McIlhenny argue that the combination of Apple's lost profits, Samsung's profits on the infringing devices, and the royalties effectively owed to Apple, amounted to just under $380m. "Apple lost sales because Samsung was selling infringing products," McIlhenny argued. "In a fair fight, in a fair competition, the money [Samsung] got would have and should have gone to Apple."

Price countered during his own opening statements that consumers preferred Samsung's devices, which use Google's Android system, because of the many differences rather than the similarities they have with Apple's products. Price put the amount Samsung owes Apple at $52 million. "Apple is simply asking for much more money than it's entitled to," he said.

Price readily conceded that Samsung was guilty of copying Apple's features, but downplayed the significance of the technology in devices that are built with hundreds of patents each.

Apple called three expert witnesses and a company executive to discuss Apple's patents Wednesday before court ended for the day. The trial is expected to last into the middle of next week.

The new hearing on damages continues a long drawn-out series of courtroom battles between the two companies, which are the two largest smartphone and tablet makers in the world - Samsung leading handily in the smartphone market, and Apple similarly in the smaller tablet market.

Apple opened hostilities in 2010, accusing Samsung of copying key elements of the appearance of its early models of iPhone and iPad and infringing patents covering functionality such as scrolling and "bounce back" when trying to scroll past the end of a list. Samsung hit back with a number of lawsuits in the US and other countries, accusing Apple of infringing functionality patents, and some patents essential to 3G connectivity.

Few of the products now at issue in the current trial are available for sale in the US.

According to Mark McKenna, professor of law at Notre Dame Law School, who has observed the case since its hearing last year, Samsung has benefited from a combination of the original jury's error, and a separate decision in December 2012 by Judge Koh not to grant Apple a sales ban on the infringing Samsung devices.

Lowered risk for Samsung

Koh explained her decision by saying that Apple had not proven that the infringed patents were the "causal nexus" for people to buy Samsung devices.

“Most cases with these enormous stakes would have settled by now – particularly once the court ordered a new trial on damages, which could substantially increase or decrease the damage award," McKenna said by email. "But once the court took off the table the possibility of an injunction (which would have taken Samsung products off the market), the risk to Samsung was significantly lower, reducing its incentive to settle. And Apple wants something significant to show for its efforts. So I expect this case to be litigated through, and we could well see several more appeals. Who wins, ultimately, here? Lawyers.”

Last year McKenna told the Guardian that the amount of work involved in calculating the damages - which involved a 20-page document totalling hundreds of individual decisions - "isn't hugely out of step with patent cases generally. There are lots of cases that involve many patent claims and many products, some more than this case - but this case is on the higher end."

Samsung's lawyers argued that the original jury's calculation for $400m of damages did not make arithmetical sense, and moved for a mistrial. Koh declined that, but ordered the new session to calculate the damages.

No matter the outcome, McKenna and other experts expect the loser to appeal.

Samsung meanwhile is being investigated in Europe and the US for attempting to force sales bans against Apple over its use of other Samsung patents - known as "standards essential patents" (SEPs), which it is obliged to license to companies prepared to pay for them. Apple has said that it was willing to license the patents, but Samsung sought sales bans. In Europe it is believed that it tried to make licensing of the SEPs dependent on Apple licensing its non-essential design and function patents to it. However, companies are not obliged to license non-essential patents.

If the European Commission determines that Samsung has infringed its rules on abuse of monopoly - as SEPs essentially are, because they are needed to make a device conform to a standard - then it could fine it as much as 10% of its worldwide revenue.

• The Samsung devices at issue in the trial are: Captivate, Continuum, Droid Charge, Epic 4G, Exhibit 4G, Galaxy Prevail, Galaxy Tab, Gem, Indulge, Infuse 4G, Nexus S 4G, Replenish, and Transform.

• The patents blogger Florian Müller has written a Q+A explaining the reasoning, importance and issues in the new trial session.