Early on January 12th American and British warplanes bombed dozens of targets in Yemen. More allied strikes could take place. President Joe Biden said: “I will not hesitate to direct further measures.” The strikes followed almost two months of Houthi attacks on commercial shipping in the Red Sea. The group says these are a show of solidarity with Palestinians in Gaza, and that it is only targeting ships with links to Israel (it has also fired missiles at southern Israel). In practice, though, the attacks have been random, seeming to target any vessel that happens to be within range, including American and British warships. Most of the world’s leading container-shipping companies are now avoiding the Red Sea.

Last month America stood up a multinational coalition to secure the waterway, and on January 3rd the coalition gave the Houthis a “final warning”. They responded hours later by detonating a naval drone a few miles away from commercial vessels and American warships, following that up a week later with a barrage against an American carrier group and a British destroyer.

The coalition had valid reason to strike the Houthis: freedom of navigation is a core tenet of international law. To do nothing would be to tolerate the blockade of a waterway that handles perhaps 30% of global container traffic. Hapag-Lloyd, a German container firm, welcomed the action: “The strikes were needed to guarantee the freedom of navigation through a vital sea route.” Whether the strikes will be effective is another matter: the Houthis have proved resilient before.

Once the instigators of a local Shia rebellion in northern Yemen, the Houthis swept south in 2014 amid the chaos that followed the overthrow of Ali Abdullah Saleh, Yemen’s longtime dictator, and seized most of the country’s big population centres. A Saudi-led coalition invaded in March 2015 to remove them from power and restore the internationally recognised government. At the time, Saudi officials thought they could wrap up the war in six weeks. It turned into a proxy war against Iran, and almost nine years later they are still trying to extract themselves from a quagmire.

The kingdom fought mostly from above, and air strikes proved ineffective at dislodging the Houthis. It left the ground fighting to inept local partners. The United Arab Emirates had more success: it sent thousands of ground troops and trained militias. But it fought primarily in southern Yemen, where the Houthis never enjoyed much support to begin with.

The Houthis for their part showed little concern for the cost of war. Yemen has often been described as the world’s worst humanitarian crisis. The UN estimates that 223,000 people have died from hunger and lack of medical care since the war began. 80% of the population now lives in poverty. None of this bothered the Houthis, who stole food aid, imposed a raft of taxes to raise funds and relied on Iran for military support. They have maintained a long siege on the south-western city of Taiz, barring civilians from bringing in food and medicine—exactly as they accuse Israel of doing in Gaza.

A group that emerged stronger from a nine-year war that killed thousands of its fighters and immiserated its country is unlikely to be deterred by a few targeted coalition raids. To be fair, America and its allies have narrower aims: they do not want to overthrow the Houthis, merely stop their attacks on shipping.

America says that it struck more than 60 targets across 16 locations, using more than 100 precision-guided bombs. The targets included command and control nodes, munitions depots, launching systems, production facilities and air-defence radar. Four British warplanes also hit two airfields used for launching drones and missiles. The Houthis said that there had been 73 strikes in total, killing five soldiers and injuring another six. These are likely to have degraded but not eliminated the Houthi arsenal.

Over the last decade Iran has supplied the group with a diverse stockpile of anti-ship missiles, including the 800km-range Paveh. The Houthis now operate up to six different types of anti-ship cruise missiles and another six variants of anti-ship ballistic missiles, according to a study by Fabian Hinz of the International Institute for Strategic Studies, a think-tank, though many of the latter are unproven. In addition to the missiles, the Houthis have also experimented with uncrewed surface vessels, or drone boats.

It is unclear how much of this arsenal has survived the barrage. Western warnings and leaks in the press gave the Houthis weeks to disperse and conceal their weapons, many of which are relatively small and mobile. If a significant proportion were nonetheless destroyed, the Houthis may be forced to ration missile strikes, allowing a greater proportion to be intercepted by Western warships in the area and creating a safer environment for commercial shipping to get through.

“The detailed results of the strikes are being assessed,” said the British Ministry of Defence in a statement, “but early indications are that the Houthis’ ability to threaten merchant shipping has taken a blow.” The fact that the Behshad, an Iranian spy ship which was probably helping the Houthis with intelligence, left the Red Sea on January 10th, perhaps for fear of being targeted, will also be a setback to the group.

On the other hand, if the arsenal remains largely intact, the Houthis will be able to continue as before—or to make good on their promise to expand the campaign. In the long-term, says Mr Hinz, the group will be able to replenish its stockpile by smuggling in new disassembled systems—anti-ship missiles can be taken apart relatively easily, unlike larger solid-fuelled ballistic missiles—and by refitting land-attack ballistic missiles for anti-ship use using local facilities and Iranian-supplied guidance kits.

Iran will no doubt be happy to send more. Its long relationship with the Houthis has deepened since 2015: arming and training the group was an easy way for Iran to bloody arch-rival Saudi Arabia and gain a foothold on the Arabian peninsula. The past few months seem to validate that strategy. Iran could already harass shipping through the Strait of Hormuz, off its southern coast. Now, through the Houthis, it can paralyse another vital waterway. “The Red Sea is even more useful to them, because they don’t have to do it directly,” says a diplomat from the Gulf. The Houthis have proven their worth to Iran, which will probably ensure more Iranian support.

Conflict with the West could have other benefits for them. Their supposed blockade of Israel has already won them new admiration across the Arab world, tapping into pro-Palestinian sentiment at a time when Arab states are feckless bystanders to the war in Gaza. Being targeted by America, while anti-Americanism is running high because of Mr Biden’s support for Israel, will add to their popularity.

It could also strengthen their hand in peace talks with Saudi Arabia. A few years ago the Saudis might have cheered Western strikes on the Houthis. Today they are in the awkward position of calling for calm, lest the group decide to expand its campaign by targeting Gulf states with missiles or drones (as they have done hundreds of times in the past). The events of the past two months will reinforce to the Saudis why they want to cut a deal and end their war—even if it leaves the Houthis as the dominant force in Yemen.

America does not want to be dragged into another long Middle Eastern conflict. The Houthis have no such qualms. They outlasted Mr Saleh, who fought a series of brutal counter-insurgency campaigns against them. They exhausted the Saudi-led coalition. And now they are no doubt pleased to have drawn America into its own open-ended operation.