Double treble: What's the chance of having three sets of twins?

Last month Karen Rodger, 41, from Renfrewshire in the UK, gave birth to a third set of non-identical twins. Doctors said the chance was 500,000 to one - but how accurate is this estimate?

Twinning rates vary around the world, but in the UK there is a 112-to-one chance of a pregnancy resulting in non-identical twins.

That's if we don't include babies conceived through in-vitro fertilisation (IVF), where twin births occur much more frequently.

So in theory the odds of having two sets would be 112 multiplied by 112, which is around 12,500 to one and the odds of having three sets would be 112 cubed, or 1.4 million to one.

But it's not quite that simple, because non-identical twins come in clusters.

Rolling a six on a dice doesn't suggest that another six is on the way, but having non-identical twins makes more twins much more likely next time.

"Family studies have shown that a woman who has had DZ (non-identical) twins is more about four times more likely to have more" in a subsequent pregnancy, than a woman who has not, says Jane Denton, Director of the Multiple Births Foundation.

So for a woman who has had one set of non-identical twins, the chance of another set is not 112 to one, but just 28 to one.

Rowan and Isla Rodger - the third of three sets of twins

Therefore, the probability of having three sets of non-identical twins is not one in 500,000, but one in 112 x 28 x 28... which is about 88,000.

Identical twins are much less common. In the UK, they turn up once in 227 pregnancies on average - again, excluding IVF conceptions - and they do not come in clusters.

So the chance of three sets of identical twins is 11.7 million to one against.

These figures for the UK, however, do not apply to the rest of the world. Twinning rates vary enormously from one country to the next.

In Vietnam, on average, there are 6.2 twins per 1,000 births, while in the US there are five times as many - 33.2 per 1,000 births.

It's not known why this is but it appears that body composition can influence the chance of having twins.

Several studies have shown that for tall women (164cm and over), the relative chance of having twins is between 1.5 and two times higher than for short women (under 155cm).

Mothers of twins also have a higher body mass index (BMI) compared to mothers of single children - a BMI of less than 20 is associated with a lower probability of twinning while a BMI of 30 or more is associated with a higher likelihood.

There is also evidence that the chance of having twins increases the later a mother gives birth.

Experts think this happens because of a change in hormonal signals sent between pituitary gland and the ovary.

In the UK, the odds of having any kind of twins at any age is one in 63 but these odds reduce to one in 46 once a woman is older than 35, and one in 18 if a woman conceives after the age of 45.

A number of studies have shown that in several countries seasonal variation influences non-identical twinning. There are higher rates of conception during the summer and autumn.

One theory put forward is that day length may influence hormonal concentrations driving ovarian activity and influence fertility and multiple ovulation.

A study by Johan Fellman and Aldur Eriksson at the Folkhalsan Institute of Genetics in Helsinki also suggests that changes in food supply during different seasons may also contribute.

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