Donald Trump. Drew Angerer/Getty Images We should not take Rex Tillerson too seriously when he threatened last week that America would deny China access to its bases in the South China Sea, plainly implying a willingness to use force to do so if necessary.

He was not speaking from a prepared text, and his remarks were so ill-informed and foolish that he probably just didn’t know what he was talking about.

So this was a gaffe, not a statement of policy.

But that doesn’t mean his ill-considered words don’t have serious consequences. They have certainly damaged his credibility.

He might have been a very effective businessman, but it is hard to take seriously someone who, as the new administration’s nominee for secretary of state, presents himself to the Senate confirmation hearing so poorly prepared to discuss the most sensitive issue in the most important and difficult bilateral relationship that America has today.

And by damaging his own credibility, his effectiveness in that office, if he is confirmed, will also be undermined.

The damage goes further, too. Tillerson’s gaffe amplifies the damage already done to the incoming administration’s credibility in managing relations with China by Donald Trump’s threat, repeated late last week, that America might abandon the “one China” policy that governs relations with Taiwan, if it does not get concessions from Beijing on other issues. That, too, should not be taken very seriously, because it is also most unlikely to become US policy.

So there is a real problem here, and not just for Washington. The foolish threats made by Trump and Tillerson will make it much harder for them to handle relations with China. They make it harder to strike the right balance between firmness and accommodation, which will be needed if America is to constrain China’s growing power and ambition without risking a disastrous conflict.

They increase the danger that, over the coming years, America will find itself facing an impossible choice between going to war with China or abandoning any serious strategic role in Asia. It is easy to assume from the tough tone of Trump’s and Tillerson’s threats that, faced with such a choice, they would opt for war.

But, in fact, they are far more likely to back off in the face of a real risk of war with China, thus weakening America’s position in Asia, and strengthening China’s.

Rex Tillerson Kevin Lamarque/Reuters

Either way, the consequences of these rookie blunders are very serious indeed for all of us in Asia, as well as for America.

To understand those wider consequences, it helps to explore more closely why Trump’s comments on Taiwan, and Tillerson’s comments about the South China Sea, were so ill-advised. Let’s start with Tillerson.

There is a legal question as to whether blocking Chinese ships operating in international waters would break the international law that America seeks to uphold. However, in terms of power politics, threatening to use force to deny China access to its bases in the Spratlys could look like a smart move if you believe that China would be so intimidated by US military power that it would back off and abandon the bases. That would deliver a cheap and decisive win for America and a costly loss to China in their contest over strategic primacy in Asia. And this was probably what Tillerson did assume that China would do when he issued his threat.

But the assumption is almost certainly wrong. In making it, Tillerson commits the simplest and most serious mistake in strategic policy – underestimating your ­adversary.

To see this, imagine what happens next. Anytime it chooses, China can put Tillerson’s threat to the test by ostentatiously deploying ships or aircraft to its island bases. How then would Tillerson and his president react?

Their military advisers would soon tell them, as they told Barack Obama, that America no longer has the military superiority to guarantee a swift, cheap victory over China in the Western Pacific. Any clash would be long, costly and indecisive, with a real risk of escalation into a wider regional war. That means aircraft carriers sunk, regional bases destroyed, devastating economic dislocation, and the modest but real risk of a nuclear exchange. Then they’d have to decide whether the issues at stake in the South China Sea were really worth that kind of conflict.

President-elect Donald Trump stands with Vice President-elect Mike Pence at a news conference at Trump Tower on January 11, 2017 in New York City. Spencer Platt/Getty Images

If they decided they were worth it, Asia would be heading for catastrophe. But Trump’s slogan is “America First”, so he’d most likely back off. Tillerson’s threat would be revealed as mere bluff, and his bluff would have been called. Far from strengthening US leadership in Asia, he would have undermined it, making America look weak, and China look strong. It’s a gift to Beijing.

The same is true of Trump’s threat to abandon the “one China” principle. It looks smart if China were to take the threat to heart and make big concessions on issues like trade to avert it. But two can play that game. What if China countered by threatening key US economic interests unless Washington ceased all arms sales to Taiwan, for example? How much economic pain would Trump be willing to bear for Taiwan? Who looks smart then?

Both men have made the same basic mistake. They overestimate US power and underestimate China’s. And even more importantly, they underestimate China’s resolve. Both Taiwan and the South China Sea are vital symbols for China of its restoration as a great power in Asia.

This is an absolutely first-order priority for Beijing, and for the vast majority of Chinese people. It is something for which they are prepared to pay big costs and run real risks – much more so than America. After all, they see themselves as a great power comparable to America, and this is their backyard, not America’s, so they care more about it.

To be fair, Trump and Tillerson are not the first people in Washington to make this mistake. President Obama’s “pivot to Asia” assumed that America need do no more than assert its intention to remain the dominant power in Asia for China to pull back and abandon its challenge to US regional leadership. That’s why the pivot was so short on substance to back up its rhetoric, and why it has failed so badly. As Obama leaves office, American leadership in Asia is weaker, and China’s influence much stronger as a result.

Now it seems the Trump administration is going to make the same mistake, only much worse. They must be smiling in Beijing.