I've just devised a mathematical formula that you're unlikely to encounter in a text book: Take a small country, add a large and accessible royal family, combine with a relatively low number of tourists and the probability of visitors encountering the King and Queen - or at least a Queen Mother or two - is relatively high.
Okay, I've only tested this less-than-scientific calculation in Bhutan, but after about 10 years of implementation, it has been holding up to scrutiny rather well.
Bhutan, which in 2008 crowned its fifth king, His Majesty Druk Gyalpo Jigme Khesar Namgyel Wangchuk, put its first king on the throne in 1907.
It was in the 1950s, that the third king, Jigme Dorji Wangchuk, began cautiously to edge his Himalayan kingdom into the modern era. He abolished slavery, instigated work on the country's first road to connect west with east, established a cabinet and sought and got Bhutanese membership of the United Nations.
When he died in 1972, his son (and father of the present king) took over and change in Bhutan accelerated - although it was closely monitored.
During the reign of the fourth king, Jigme Singye Wangchuck, television and the internet were introduced and tourist numbers increased (the first tourists only entered the kingdom in the 1970s).
It is the fourth king's family life that perhaps intrigues visitors the most, and has led to the statistically high chance of a royal encounter for visitors.
He has four wives, all sisters, who between them have 10 children. The fifth king is the oldest of the princes and the son of the third queen. Polygamy is not common in Bhutan; the fourth king's marriage of the sisters is connected with a prophesy linking the Wangchuck family with that of the queens' as a way to improve the longevity of the kings.
The four queens, now officially known as the Queen Mothers, each have a villa set on the hills overlooking Bhutan's capital Thimpu.
The fourth king lives in a separate, very simple, wooden house nearby.
One of my earlier encounters with royalty came on the roads near the palaces when we rounded a corner in the tour bus and straight across the intersection was the fourth king at the wheel of his land cruiser.
Even if there wasn't a small retinue of vehicles with flashing lights it would have been easy to spot, as there are special licence plates for the royals; the king's is simply BHUTAN. Other members of the family have vehicles bearing the numbers Bhutan2, Bhutan3 etc.
The one trap for visitors is that the country's chief abbot, the Je Khenpo (who is held in almost equal rank with the king) travels in a vehicle labelled Bhutan 1. However, this most senior monk doesn't drive and is normally swamped in prayer scarves given to him by locals during his travels.
The Queen Mothers have always been extremely active in their country's development, whether it be education and vocational opportunities for girls, preserving and furthering the country's superb textiles tradition or working to reduce HIV/Aids.
This means they too are often out and about. Because there is only the one main road that links the country from the capital in the west to the far east, encounters en route are not uncommon.
Now in their late 40s-early 50s the Queen Mothers are all strikingly beautiful and always dressed in the most superb examples of khira, the traditional dress for women that features Bhutanese silk-on-silk weaving.
The fourth king abdicated at age 50 to make way for his Oxford-educated son, and as a step towards the move from an absolute monarchy to a constitutional democracy (which took place in 2008).
Last year, the fifth king to wear the Raven Crown was married. This was a cause of much celebration in Bhutan, although it equally broke rather a lot of young women's hearts - the fifth king being exceptionally handsome. (On an official visit to Thailand some years back he caused scenes among Thai young women akin to those that once surrounded an unmarried Prince William.)
The king, who is 31, married 21-year-old student and commoner Jetsun Pema Wanghuck, whose father was a pilot with Bhutan's national airline, Druk. The ceremony took place in the Punakha dzong one of Bhutan's most stunning buildings, and a uniquely Bhutanese combination of religious and administrative offices.
Following the ceremony, the king and his new bride took more than 10 hours to travel back to the capital, stopping continuously along the way to meet their subjects.
The Bhutanese revere their royal family. They believe they have every reason to do so. Not only did their fourth king voluntarily give up his power as a absolute monarch but the dynasty has also managed to steer Bhutan along a relatively peaceful path, sandwiched as it is between China and India.
The population is also justifiably proud of its kings being instrumental in Bhutan's being renowned as the only country in the world where Gross National Happiness is regarded as more important than Gross National Product. Policies to conserve and nurture Bhutan's forests, wildlife, culture and spiritual heritage are also regarded as being very much spearheaded by the royal family.
One of the few really serious gaffes a visitor can make is to criticise or make jokes about the royal family. The closest to any levity surround the royals is that the present king is sometimes referred to as K5 and his father as K4.
While I was in Bhutan recently, in the central Bhutanese valley of Jakar, the young royal couple had also been in town. It was impossible not to get caught up in the hype as everyone wanted to see their new king and queen on what was an informal walkabout of the town centre.
We'd already seen the king earlier that day enjoying a little time out. A keen mountainbiker, he had been cycling up towards the 2900-metre-high Kiki La (Kiki Pass) - two companions riding just slightly behind him, Jeeps with flashing lights in front and behind. Apparently he cycles in the hills around Thimpu most days, often followed by a bevy of other cyclists. His interest is doing wonders both for fitness levels in the capital and the promotion of cycling as a sport.
Jakar had suffered two catastrophic fires in recent times which had destroyed much of the central business area and the king and queen's walkabout gave them a chance to visit shopkeepers who were now back in action.
We were standing on a street corner along with a gaggle of giggling school kids and under the relaxed but still watchful gaze of the royal bodyguard and local police, when the couple emerged from a general store.
The king was holding his bride's hand. Physical displays of affection are not common in Bhutan so this gesture is significant, and, say some locals, has started a whole new trend.
The king, as befitting his position was not only in traditional dress, complete with magnificent handmade knee-high boots, but had a golden yellow kabne (a large ceremonial shawl) draped over one shoulder.
The queen was in a multi-coloured khira and high heels. They walked towards us, pausing as they came alongside.
"It is very nice to see you in Bhutan; thank you for coming," said the king.
We'd been carefully schooled not to take photos or otherwise make spectacles of ourselves, so possibly their highnesses' lasting impression, should they have one, would have been of a group of rather scruffy tourists (we'd been out walking that day) grinning inanely at them.
The rest of the retinue swept past, including varies local dignitaries with silver swords strapped to their sides. There was one photographer.
Our last sight of the king (the supreme protector of the people; the great elected one; the upholder of the law) and his queen, was them popping into another shop, while a policeman shooed away the ubiquitous stray dogs that had been sleeping nearby.