Foreign states that go to war in Yemen usually come to regret it. The Saudi-led military intervention so far involves only air strikes, but a ground assault may follow. The code name for the action is Operation Decisive Storm, which is probably an indication of what Saudi Arabia and its allies would like to happen in Yemen, rather than what will actually occur.

In practice, a decisive outcome is the least likely prospect for Yemen, just as it has long been in Iraq and Afghanistan. A political feature common to all three countries is that power is divided between so many players it is impossible to defeat or placate them all for very long. Saudi Arabia is backing President Abd-Rabbu Mansour Hadi but the humiliating speed of his defeat shows his lack of organised support.

Shia militiamen have reportedly withdrawn from the city Tikrit but they haven't gone far (EPA)

The threat of further intervention by Saudi Arabia and the Gulf Cooperation Council may be intended to redress the balance of power in Yemen and prevent the Houthis winning a total victory. But Saudi actions and those of the Sunni coalition will be self-fulfilling if the Houthis – never previously full proxies of Iran – find themselves fighting a war in which they are dependent on Iranian financial, political and military backing.

Likewise, the Houthis, as members of the Zaidi sect, were not always seen by Shia in other countries as part of their religious community. But by leading a Sunni coalition Saudi Arabia will internationalise the Yemen conflict and emphasise its sectarian Sunni-Shia dimension.

The US position becomes even more convoluted. Washington had sought to portray its campaign in Yemen against al-Qaeda in the Arabian Peninsula (AQAP) as a success. Drone attacks were supposedly wiping out important AQAP operatives, but the humiliating end result of America’s covert war in Yemen came last week when US Special Operations personnel blew up their heavy equipment and fled the country for the US base at Djibouti. AQAP is becoming a stronger force as the shock troops of the Sunni.

In pictures: Fight for Tikrit Show all 16 1 /16 In pictures: Fight for Tikrit In pictures: Fight for Tikrit Fight for Tikrit Shiite fighters pose in front of a mural depicting the emblem of the Islamic State group outside one of the presidential palaces in Tikrit, on April 1, 2015 Getty Images In pictures: Fight for Tikrit Fight for Tikrit Iraqi Prime Minister Haider al-Abadi tours the city of Tikrit after it was retaken by the security forces in Baghdad, Iraq, on April 1 2015 AP In pictures: Fight for Tikrit Fight for Tikrit An Iraqi flag waves over the Tigris River om April 1 2015 AP In pictures: Fight for Tikrit Fight for Tikrit Iraqi security forces playing football in Tikrit after their country declared a 'magnificent victory' over the Islamic State group in the city on April 1 2015 Reuters In pictures: Fight for Tikrit Fight for Tikrit A member of the security forces holds Iraq’s national flag in front of a painted Isis emblem Getty Images In pictures: Fight for Tikrit Fight for Tikrit Iraqi security forces arrest a member of the Islamic State in Tikrit on April 1, 2015 Reuters In pictures: Fight for Tikrit Fight for Tikrit A member from the Iraqi security forces beats an Isis insurgent, who was captured in Tikrit Reuters In pictures: Fight for Tikrit Fight for Tikrit Shiite fighters from the Popular Mobilisation units celebrate in front of the the provincial council building inside the northern Iraqi city of Tikrit on March 31, 2015 Getty Images In pictures: Fight for Tikrit Fight for Tikrit Iraqi soldiers stand on a damaged tank during fighting against IS militants near Tikrit Corbis In pictures: Fight for Tikrit Fight for Tikrit Fighters of Iraqi Shiite militias who volunteered to support the Iraqi forces make their way towards Daquq town near Tikrit Corbis In pictures: Fight for Tikrit Fight for Tikrit Iraqi security forces and Shia fighters chant slogans as they gather at Udhaim dam, north of Baghdad, where they have been massing in preparation for an attack on Isis along the Tigris River Reuters In pictures: Fight for Tikrit Fight for Tikrit Pro-government volunteer Shia fighters in Awaynat near Tikrit AFP/Getty In pictures: Fight for Tikrit Fight for Tikrit Iraqi government forces and allied militias firing weaponry from a position in the northern part of Diyala AFP In pictures: Fight for Tikrit Fight for Tikrit A volunteer in the Iraqi Shiite Badr Army militia taking up position outside Tikrit Corbis In pictures: Fight for Tikrit Fight for Tikrit Volunteers of the Iraqi Shiite Badr Army militia patrol an area at eastern Tikrit city Corbis In pictures: Fight for Tikrit Fight for Tikrit Members of the Iraqi security forces coming from the city of Samarra drive towards al-Dawr south of Tikrit to launch an assault against the Islamic State AFP/Getty

US policy across the Middle East looks contradictory. It is supporting Sunni powers and opposing Iranian allies in Yemen but doing the reverse in Iraq. On Thursday US aircraft for the first time started pounding Islamic State (Isis) positions in Tikrit, 87 miles north of Baghdad. The city has been under assault for four weeks, with 20,000 Shia militia and 3,000 Iraqi soldiers pitted against a few hundred Isis fighters. The Shia militiamen are now reported to have withdrawn but they do not appear to have gone far. Effectively, the battle for Tikrit is being waged by Iranian-directed Shia militia backed by US air power, even if the two sides are rivals as well as allies.

Ultimately, the US may not have much choice. If it refuses to back anti-Islamic State combatants for whatever reason it will be to the benefit of Isis. The numbers tell the story: there are between 100,000 and 120,000 Shia militiamen in Iraq compared with only 12 brigades in the Iraqi army capable of fighting, about 48,000 soldiers, although this total may be inflated. Isis has been conscripting young men across its self-declared caliphate since last October and may have over 100,000 fighters. If the US relies on Iraqi government and Kurdish Peshmerga ground forces alone to put Isis out of business, it will be difficult.

Why did the US finally use its air power at Tikrit, formerly a city of 200,000? First, it was the only help the Baghdad government formally asked for this week. The US may have concluded, as it did with the 134-day siege of the town of Kobani last year, that it could not allow Isis to succeed in Tikrit. Second, if the city did fall, Washington did not want Iran and the Shia militia to get all the credit.

A further motive is that both the US and Iran want to restore some credibility to the Iraqi government and army after their crushing defeats by Isis forces last year. So far the Iraqi army has not recaptured a single city or substantial town from Isis since the fall of Fallujah, 40 miles west of Baghdad in January 2014. Such limited military successes as there have been were won by the militias in the provinces neighbouring Baghdad.

The US-led international coalition opposing Isis also needs to do something to bolster its own credibility. Despite some 2,500 coalition air strike launched against it since last August, the Islamic State has lost little territory. Isis may be battered but it shows no signs of being anywhere near to defeat.

Tikrit has been under assault for four weeks, with 20,000 Shia militia and 3,000 Iraqi soldiers pitted against a few hundred IS fighters (AP)

The Independent conducted a series of interviews in February and March with people who had recently left Isis and, while none were sympathetic to it, there was nobody who believed it was going to be destroyed by mounting internal discontent or external military pressure. A prime reason for this is that the Sunni Arab communities in Iraq and Syria are not being offered an acceptable alternative to Isis rule. They are all terrified of becoming the victims of a pogrom that does not distinguish between Isis supporters and ordinary Sunni.

A further feature of life in the Isis caliphate that emerged from these interviews is that it is well organised: it taxes salaries and sales, it conscripts young men of military age, controls education and mercilessly strikes down any opponents. Its stability might be shaken if it suffered a string of military defeats but so far this has not happened.

Air strikes have made it revert to semi-guerrilla tactics, not holding ground against superior forces backed by airpower but counter-attacking briskly when they have moved on or their lines of communication have become longer and more vulnerable. Given the difficulty in capturing Tikrit, it does not look as if an assault on Mosul will be possible for a long time. There seems to be no enthusiasm on the government side retake Fallujah, although it is so much closer to the capital.

Whatever happens in Iraq and Yemen, the political temperature of the region is getting hotter by the day. Looked at from a Saudi and Gulf monarchy point of view, Iran and the Shia are on the advance, becoming either the dominant or the most powerful influence in four Arab capitals: Baghdad, Damascus, Beirut and Sanaa. The Sunni Arabs in Iraq and Syria have linked their futures inextricably and fatally to Isis and other al-Qaeda type organisations. These have military strength, but they make many powerful enemies.