Since assuming office in January, Trump has become versed in the school of hard knocks - the courts said 'no' to his immigration and refugee crackdown and Congress said 'no' to his 'repeal and replace' of Obamacare. This week he advanced to foreign policy, with a horrendous gas attack in Syria and yet another North Korean missile test serving as timely lessons on the impotence of rhetoric in the face of seemingly intractable global crises.

Trump might surprise his critics, but head scratching and questions abound.

Viewed as a sports encounter, how might Trump win? Can he make it a 'win-win' for himself and the Chinese leader? What if Xi gets the better of him, and walks off with the trophy? What if Trump walks off the field, in a fit of pique?

Just as importantly, who is Trump playing for? The rank and file Trumpists for whom his anti-China rants during last year's election campaign were a blood sport, or the US foreign policy establishment which has a more nuanced grasp of the three-dimensional interconnectedness of global issues?

"It's very hard for anyone to say what are the definitive answers to any of these questions," IMF veteran and Wilson Centre policy expert Meg Lundsager told Fairfax Media.

She's at a loss too, to understand why the administration wanted this meeting so early in Trump's presidency.

And in a phone interview, China scholar Robert Daly fretted about Trump's homework: "I'm of the school that Xi comes to this meeting better prepared - he knows what he wants and we're flailing. We haven't done a policy review; Trump doesn't even have a China specialist on his staff."

As they size each other up, each leader will appreciate the domestic standing of the other. Xi's authority is unchallenged, though he needs to look good ahead of a vital, upcoming party conference.

Trump's natural habitat is in a quagmire - can't shake off the Russia investigations; frustrated by congress and the courts; approval ratings in the toilet.

They come from such different worlds - Trump runs America by tweet; the Chinese are denied access to Twitter. Trump shoots from the hip with the last advice he heard - even a Fox News headline will do; Xi comes over as stitched-up - very formal, meticulously scripted.

American allies - Japan, South Korea and Australia among them - will be looking for assurances and certainty. But US administration officials send mixed signals on what to expect of their meeting.

Far from it all being the "difficult" confrontation envisioned in Trump's fore-play, they suggest variously - a cordial, informal getting-to-know-you session, after which officials will go away to do the heavy-lifting; a nitty-gritty "results-based" encounter - "sort of level the playing field on trade, talk about global challenges, how we can work together, but, basically, how we can bring home results for the American people out of the US-China relationship;" and even expansive, over-the- horizon stuff - "setting a new course for US-China relations for the next 40 to 50 years."

Trump's capacity to hurl himself from the frying pan into the fire, is undiminished.

But if he gets into his claims that China still manipulates its currency - in the past yes, but today, no; or if he whacks Xi with his bellicose tariff talk, the Chinese leader reportedly is ready with his own bag of nasties - a cocktail of threat to halt China's hugely valuable purchases of US grain, aircraft and microchips and cell phones.

Last week, Trump seemed ready for a bit of biffo, tweeting: "The meeting next week with China will be a very difficult one, in that we can no longer have massive trade deficits and job losses. American companies must be prepared to look at other alternatives."

And days later he told The Financial Times: "When you talk about currency manipulation, when you talk about devaluations, [the Chinese] are world champions. And our country hasn't had a clue, they haven't had a clue. The past administration ???I don't want to say only Obama; this has gone on for many years ??? They haven't had a clue. But I do."

Yet this week, administration officials have been attempting to row back expectations of Trump unleashing the virulent, anti-China persona that became a feature of last year's campaign.

Matt Pottinger, the senior director for Asia at the National Security Council, hosed down reporters who asked if Trump would resurrect his threat to use Taiwan as a stick to hit Beijing, as he did earlier this year, after which he pledged Washington to the long-standing One China Policy.

And Pottinger soothed them on Trump's oft-threatened trade war and punitive tariffs on Chinese goods, promising a longish-term dialogue - "the spirit of this summit is for the two to develop a relationship, to really establish a relationship, and to lay out the key concerns that each side has about the relationship and to then begin moving toward some kind of a formal series of dialogues that will aim to address those issues."

So the potential fly in the ointment is North Korea, with Trump demanding that Xi apply sufficient economic pressure to the erratic Kim Jung-un, to make the North Korean dictator abandon his pursuit of a nuclear missile capable of striking the US mainland.

Lundsager: "Trump has to ask Xi - 'you are Kim's patron or benefactor, can't you stop this guy? Aren't you worried - depending on which way the wind is blowing, China could be hit with a radiation cloud from one of his missile tests?'

"In how Trump plays this one, and how Xi responds ??? it's hard to see a win-win, but you don't want a lose-lose, because neither side has an effective way of stopping Kim short of marching armies into North Korea - and no one wants to do that."

And that's the intractability of the North Korea crisis. Secretary of State Rex Tillerson declared during his recent visit to Seoul that "strategic patience [with Pyongyang] has run out;" and in his The Financial Times interview, Trump warned that Washington would take unspecified unilateral action if China doesn't "help us with North Korea," just as he threatened unilateral action against Syria's Bashar al-Assad on Wednesday.

These are the kind of threats that focus some minds on those interconnected elements of global crises - military strikes on North Korea would almost certainly see reprisal attacks by Pyongyang on South Korea, where thousands of US troops are stationed; China doesn't want a war-driven tidal wave of refugees over its border with North Korea; Kim would likely lash out at Japan, where thousands more US troops are stationed; China already is discomforted by the US deployment of THAAD anti-missile systems on its doorstep, in South Korea; and is horrified of being left abutting a unified Korean peninsula that, inevitably, would be tied to the US.

Resorting to a turn of phrase that was more diplomatic that Trump's tweets on the issue, Pottinger suggested that Beijing knows the deal: "Of course we'd like to see China working closely with the US to address the menace emanating from North Korea - their weapons programs, the provocations that we're seeing every week; missile launches, including one that we just had not too many hours ago.

"There is an opportunity for this to be an area of cooperation and to grow that. I think it's in Beijing's interest. I think that North Korea long ago ceased to be a strategic asset for China. It is now quite clearly a strategic liability, and it is one that is having an impact on the region."

Acknowledging the sheer American power that Trump represents, Lundsager concludes nonetheless, that Xi tries to position himself more as a global leader - "Trump is inward looking; Xi is more the globallist, more statesmanlike and more sensitive to global institutions."

She's troubled too by a "kind of American silence" in the Asian region, particularly since Trump walked away from the Trans-Pacific Partnership trade deal, to which Australia was to be a signatory - but not China.

"Countries in the region worry about Chinese dominance, but Washington is not really reaching out. If the US walked away from the TPP, can it be relied on? And if the US is seen to be uninterested in the region, some countries will seek to protect their interests by leaning towards China."

The China scholar Daly will be placated if Trump and Xi remain in the realm of getting to know each other, "but if they get into deal-making it will be dangerous and premature - and because of all his rhetoric, Trump is under pressure to get a deal.

"If he plays to the DC crowd, he won't go for deliverables and deals; instead, he'll start trying to reconcile his contradictory positions on China, and begin the critical work of managing a difficult relationship."

On the Syria and healthcare-like complexities of North Korea, Daly tells Fairfax Media that the stage has been set as though Trump and Xi need a strategic break from each other. But in the absence of sound policy and deft diplomacy, there's a wild card possibility that relationship will be managed by crisis - "and that'll put distrust at an all-time high."

Daly invokes a Chinese saying -'throwing aside a watermelon to pick up sesame seeds' - to lay out a dynamic he fears could take hold at Mar-a- Lago. In the absence of a clearly thought-out American China policy, Xi will offer deals on secondary matters that are important to Trump, in the hope that China can gull the US into an indefinite postponement of the development of a seriously considered strategic response to China's rise.

For Xi, the watermelon is global influence. Trump's sesame seeds could be new Chinese factories to create jobs in the US, a commitment to a bilateral investment treaty, or a crackdown on Chinese corporations doing business with Pyongyang, all of which Xi reportedly will put on the table.

Daly explains: "Xi is ready for the summit. Trump can't possibly be. There are no Asia experts in his inner circle, he has not done completed a review of China policy, and he hasn't made appointments to the departments of State and DefenCe that are vital to effective management of the relationship.

"Most importantly??? and like Barack Obama before him???he has not conducted an audit of America's ability to uphold its commitments in Asia in light of China's economic and military rise and the of US strategic distractions, it's costly domestic agenda, and its looming structural budget crisis.

"Without that audit, bluffing Xi is out of the question. If Washington won't do its math, Beijing will."

In the absence of American understanding and judgment based on a considered China policy, Daly worries that Xi will run rings around Trump - China has moved beyond its reliance on Washington for economic and institutional advancement, and now simply wanted to be left alone, to get on with the less-catchy Chinese iteration of "make America great again" - "the great revitalisation of the Chinese nation."

Xi's offering of a few deals to Trump would focus American minds on gradual progress instead of on hard, long-term strategic questions - questions like US security if China dominates the Asia-Pacific, and the cost to Washington of preventing that dominance.

"If Trump thinks that America's greatness depends on its alliances and its leadership of a liberal global order, Xi may have to recalibrate his push into the Western Pacific and Eurasia," Daly writes in an article expanding his analysis.

"But if Trump views America only as a mechanism for the aggrandisement of its citizens, Xi will conclude that China's 'period of strategic opportunity' may last longer than previously thought and pursue his international agenda more aggressively.

"The danger in Trump's approach to China is not that he will push too hard at Mar-a-Lago, offend Xi, or make bad deals. It is that, despite his campaign rhetoric, China may be the thing Trump never quite gets around to. Immigration, health care, tax reform, a controversial budget, ISIS, and the Russia scandal are all higher up on his to-do list."

The China test for the US, as Daly sees it, is that the Chinese Communist Party, its propaganda organs, multinational corporations, military, universities, and a good many ordinary Chinese believe the country is destined to recover its rightful status as the greatest nation on Earth - and that requires weakened US influence in Asia.

"The China challenge, while broadly understood, is historic, not immediate; it seems remote in time and space and is so damnably difficult that Americans and their government are unlikely give it the attention it requires unless there is a threat of war," he writes.

All this is heady stuff for the Palm Beach set - in their Tommy Bahama shirts and flip-flops at week's end.

The choice of venue, the informality of a Trump resort over the formality of the White House, has raised eyebrows. But administration officials say "relaxed" is the way to go as these leaders get to know each other.

And there's always golf as an ice-breaker - yes?

Um, no. Japanese Prime Minister Shinzo Abe might have gifted Trump a $US3755, gold-plated golf club while visiting Mar-a-Lago in February, but Chinese officials who have played what Mao Zedong vilified as a "sport for millionaires," have ended up in jail.

"It's possible they'll walk around a bit as the mood strikes, but nothing formal and nothing involving golf clubs," a US official assured a press briefing this week, when asked how informal the schmoozing might get at Mar-a-Lago.

But was there a risk that Trump might follow his own advice, tweeted to the world after a "logistical flap" that some read as a calculated Chinese snub of Obama on his arrival in China last year, upon which Trump urged his predecessor to turn around and come home? Could an angered Trump stage a walkout?

Not going to happen, the Asia adviser Pottinger assured Wednesday's briefing: "President Trump is an extremely gracious host."

Fairfax Media