Picture the scene: in November, as polls close across the United States, an anxious Osama bin Laden awaits the first predictions of the result. If President Bush loses, will the world’s most famous terrorist claim victory? No. He will more likely be despondent. Bin Laden sees his struggle with the US in apocalyptic terms.

The US is the supporter of the House of Saud, the Saudi royal family, which Bin Laden and his al-Qa’ida followers regard as both politically and religiously corrupt.

It is hard to work out whether Bin Laden either grossly overestimates his own strength or is cannily playing his limited hand as part of some grand scheme. After so many setbacks, much of his strength is the continuing perception that he is a Lenin-like figure, seeing only progress in chaos.

The world vision of John Kerry, Bush’s challenger, as much as it can be discerned, does not involve the apocalypse. If international diplomacy in 2005 switches to trying to understand militant Islam, Bin Laden will have to work harder to find new recruits. Kerry’s world will still be anathema to al-Qa’ida but the global nature of the problem may appear to diminish for a while. By this analysis there is a curious coincidence between what is good for Bin Laden and what is good for George Bush. The President’s strategists probably consider another attack on the US as beneficial to his chances. Equally, capturing or killing Bin Laden might be perceived as ending the “War on Terror” and allowing for a change in domestic political preferences.

To President Bush’s credit, he probably doesn’t think like this. His world is more good versus bad; black and white. Hence his comments late on Friday after learning of the beheading of the American hostage, Paul Johnson: “We must pursue these people and bring them to justice.” Bold words, good for the American electorate, but potentially embarrassing for the Saudi authorities that even in better times preferred American support to be low-key.

Diplomatically, the Americans are in a quandary. Relations with the Saudis are already poor. Yet the House of Saud cannot just be ignored. The kingdom has a quarter of the world’s oil reserves and accounts for 11 per cent of world oil production. If the Saudis are no longer able or willing to produce oil at current levels, the consequences are almost too scary to imagine: world energy crisis leading to world economic crisis, leading to calls for military intervention.

Washington’s challenge is made worse because the senior princes appear to be disconnected from reality. While thousands of police searched Riyadh in a desperate search to find Johnson before the hostage-takers’ deadline expired, Crown Prince Abdullah, the de facto ruler, was in Jeddah to watch football.

Saudi Arabia’s security appears to be in the hands of Abdullah’s younger half-brother, Prince Nayef, the interior minister. He guards his control of the police and security forces jealously. His reputation for toughness is matched only by his apparent tolerance of inefficiency, incompetence and even treachery in his own ranks.

Nayef’s motives are assumed to be twisted by his determination that the ailing King Fahd is not succeeded by Abdullah but rather by Prince Sultan, the defence minister and a full brother of Nayef. Fahd, Sultan and Nayef are all members of the so-called Sudairi Seven, the most important sub-group of many sons of the kingdom’s founder, Ibn Saud, who seem to think the crown belongs them alone.

Poor old Fahd, who suffered the first of a series of debilitating strokes in 1995, is widely assumed to owe his continued life to the determination of the Sudairis that he should be kept alive. Sultan’s recent 18-day hospital stay, reportedly for the removal of a stomach polyp, would not worry Nayef so much. Diplomats widely assume he is number four in the line of succession, although chanceries across the world prefer another, but younger, brother, Salman, the governor of Riyadh province.

Washington wants tough police action to continue. With the reported death of Abdul-Aziz al-Muqrin, the leader of the al-Qa’ida cell that murdered Johnson, the immediate problem might be over. Prince Turki al-Faisal, the Saudi ambassador in London, said last week that only one cell was still operating in the kingdom. Saudi police are also blaming al-Muqrin for the attack on the BBC crew that left cameraman Simon Cumber dead and correspondent Frank Gardner seriously injured.

But journalists trying to cover the kingdom and expatriates living there are learning the hard way that the initial Saudi version of an event often turns out to be far from the truth. After the terrorist incident in al-Khobar at the end of May, in which 22 died, the initial version was that helicopter-borne commandos had ended the siege, SAS-style. It later turned out that the terrorists had been allowed to walk free hours earlier in a deal “to avoid further casualties”. A wounded terrorist, left behind, was nearly sprung from his hospital bed a few days earlier in another attack that was not opposed.

The Saudi royals appear to be hoping that, apart from an occasional shoot-out, the threat from al-Qa’ida can be overcome using Saudi traditional methods of defusing crises – the involvement of the militants’ own families and tribes.

The House of Saud is also seeking to delegitimise the Islamic credentials of the terrorists. The Saudi religious leadership keeps issuing fatwas (religious rulings) against them. The Saudi princes calls them “deviants” or, eye-poppingly in an international context, “Zionists”.

The key to predicting the future may well be in gauging sympathy for al-Qa’ida and Bin Laden in the kingdom. The Saudi authorities say the terrorists have little support; anecdotal evidence suggests the contrary.

Al-Qa’ida can tap into a deep xenophobic seam in Saudi society, especially towards non-Muslims. The conservative nature of the average Saudi also suggests that government proposals for “reform” are either misplaced or merely insincere gestures towards local liberals. Proposed changes have so far turned out to be musings rather than promises.

If recent Saudi history is anything to go by, crises slip by rather than develop. The socio-economic indicators – high-birth rate, few employment opportunities – remain gloomy in the long term. But the crucial tests will be an absence of al-Qa’ida attacks for a while and the return of expatriates after vacations in the cooler climes of Europe.

Like Iraq, President Bush does not want Saudi Arabia to be an issue in the November polls. Better to campaign on the notion that the world is potentially a dangerous place than a really dangerous place. Bush needs to force more effective, albeit low-key, security co-operation on the Saudis, preferably securing Nayef’s replacement. And keep going after Osama bin Laden so that his dying thought might be that he miscalculated American determination.

Simon Henderson is a London-based associate of the Washington Institute for Near East Policy and author of ‘After King Fahd – Succession in Saudi Arabia’