The succession beyond King Abdullah - the fifth of Ibn Saud's sons to reign and who is, at 89, recovering from major surgery - is a sensitive subject among the al-Saud dynasty's hundreds of princes; but it will determine the path of the world's top oil exporter and main Arab ally of the United States as it navigates domestic change and regional turmoil.
"In the next 10 years, there will be great changes in terms of the royal family," said Khaled al-Maeena, editor-in-chief of the local English-language newspaper the Saudi Gazette. "The younger generation will play a role."
Abdullah, not seen in public since an 11-hour back operation last Saturday, has pursued cautious economic and social reforms aimed at reconciling an ultra-conservative Islamic kingdom with the demands of a modern economy and youthful population. Doctors have said his surgery in Riyadh was successful.
The immediate line of succession is to the crown prince, Prince Salman, born in 1936 and another son of the kingdom's founding monarch, King Abdulaziz, known as Ibn Saud, who died in 1953. But beyond Salman, there is much less clarity.
In October last year, there had appeared still to be a formidable line-up of half-brothers standing beside King Abdullah as heirs to the conservative Islamic state founded by their father in 1932 after decades of tribal warfare.
Yet 13 months later, the deaths of princes Sultan and Nayef, both of whom had been in turn the designated successor as crown prince, as well as the departures of princes Ahmed and Muqrin from senior posts, have left no obvious heir-apparent after Crown Prince Salman, who was promoted after Nayef died in June.
There is debate as to whether Prince Ahmed might remain the principal contender, but some Saudi analysts and foreign diplomats now think it a possibility that after the death of Abdullah the next crown prince will be a grandson of Ibn Saud.
"I think there is no other alternative to the next crown prince being a grandson of King Abdulaziz," said Saudi political scientist Khalid al-Dakhil.
In a system built on the idea that consensus ensures stability, and which prizes both seniority and competence, the sprawling al-Saud clan will have to weigh the balance between the family's many different branches.
Saudi analysts see the al-Saud as adept at managing the succession process, something a former Western ambassador to Riyadh said they would be especially anxious to do now at a time of democratic ferment, which has felled republican Arab autocrats and pressured some neighbouring monarchs.
"You can bet with the Arab Spring in the background they'll want to take a decision they can all live with and support," he said, speaking on condition of anonymity.
However, the generational leap may prove fraught because Ibn Saud's grandsons - of whom there are hundreds - may fear that if they or their brothers are passed over in favour of cousins, the line of succession will set off down a different branch of the growing family tree, excluding them and their offspring forever.
"It's very difficult to make the jump to the next generation," said Madawi al-Rasheed, a London-based critic of the al-Saud and author of "A History of Saudi Arabia". "But if there are enough government positions to go around, they can keep them all happy," Rasheed added.
The family might still chose to postpone the generational shift by elevating to the position of official successor Prince Ahmed, who resigned abruptly in November as interior minister after less than five months in the position.
"It doesn't rule Prince Ahmed out of the equation. He's still there," said a Saudi analyst who spoke anonymously. "He's still a choice to become crown prince when Salman becomes king."
Another of Ibn Saud's sons, Prince Muqrin, lost his job as intelligence chief in July and seems less favoured, as do other surviving sons of Ibn Saud's several wives and concubines.
Unlike typical European monarchies, there is no automatic succession from father to eldest son. Instead the kingdom's tribal traditions dictate that a new king and senior family members select the heir they consider fittest to lead. The practice of polygamy means they can have a wide choice of sons.
For all the difficulties, little is likely to be heard in public. Any dissent among princes over the succession would only happen in private, said Saudi commentator Jamal Khashoggi.
There may be arguments behind closed doors. But, Khashoggi said: "Then it would be 'Long live the King!' and 'Long live the Crown Prince!'."
King Abdullah set up a family "Allegiance Commission" in 2006 which ensures representation for different branches of Ibn Saud's descendants and must approve or reject a new king's choice of heir, if necessary selecting its own candidate.
The commission only comes into effect after Abdullah's death, but analysts said it in some ways only formalised an existing process of seeking consensus on naming a crown prince.
Even if the al-Saud do elect to move down a generation at the next opportunity there is no guarantee that if Salman's heir were to be one of his nephews, he would be a much younger man.
Mecca Governor Prince Khaled al-Faisal, one of the leading candidates among the next-generation princes and viewed as a comparative liberal, was born in 1941, making him older than either of his uncles Prince Ahmed or Prince Muqrin.
The grandson with the biggest job, however, is Prince Mohammed bin Nayef, who replaced Ahmed as interior minister this month. The post not only brings control of the kingdom's formidable security apparatus but formal command over the regional governors, who are all themselves royal princes.
Prince Mohammed was Saudi security chief before becoming minister and earned the plaudits of foreign diplomats and King Abdullah for crushing a domestic al Qaeda wing in recent years. He is seen by local analysts as an astute politician.
At 59, he is roughly a contemporary of his cousins Prince Mohammed bin Fahd, governor of Eastern Province, and Saudi Arabian National Guard commander Prince Miteb bin Abdullah, both also seen as possible future kings.
Other prominent grandsons include Deputy Defence Minister Prince Khaled bin Sultan and Tourism Minister Prince Sultan bin Salman, son of the crown prince and the first Arab in space. As the ruling dynasty prepares to enter uncharted territory in the years to come, Saudi Arabia's 28 million people will be following closely the health of their rulers and any further shuffling in the responsibilities of Ibn Saud's many heirs.