In many sports a particular tactical conundrum arises. The team captain has to choose the best order in which to use a group of players or set-plays in the face of unknown counter choices by the opposition. Do you want to field the strongest players first to raise morale or play them last to produce a late run for victory? John D. Barrow shows that randomness holds the answer.

By cleverly cross-referencing different databases it can be possible for evil adversaries to reveal intimate information about individuals. Given that it's hard these days to keep your details off these databases, what can be done to protect privacy? We talk to Cynthia Dwork from Microsoft, whose talk at the ICM showcases some mathematical tools to keep our details safe.

Researchers from the University of Maryland have devised a new kind of random number generator that is cryptographically secure, inherently private and — most importantly — certified random by the laws of physics. Randomness is important, particularly in the age of the Internet, because it guarantees security. Valuable data and messages can be encrypted using long strings of random numbers to act as "keys", which encode and decode the information. Randomness implies unpredictability, so if the key is truly random, it's next to impossible for an outsider to guess it.

David Spiegelhalter explains that waiting for an infinite number of monkeys to produce the complete works of Shakespeare is not just a probabilistic certainty, it also gives us an insight into how long we can expect to wait for a rare event to happen.

How to win with quantum uncertainty

How much evidence would you need before buying into a get rich quick scheme? Do high ice cream sales cause shark attacks? And just how likely was it that you were ever born? Andrew Stickland finds out that, when it comes to probability, our instincts can lead us seriously astray.

There are many different types of lottery around the world, but they all share a common aim: to make money. John Haigh explains why lotteries are the way they are.

In the early days of the UK National Lottery, it was quite common to see newspaper articles that looked back on what numbers had recently been drawn, and attempted to identify certain numbers as "due" or "hot". Few such articles appear now, and John Haigh thinks that perhaps the publicity surrounding the lottery has enhanced the nation's numeracy.

You might think that if you collected together a list of naturally-occurring numbers, then as many of them would start with a 1 as with any other digit, but you'd be quite wrong. Jon Walthoe explains why Benford's Law says otherwise, and why tax inspectors are taking an interest.

Coincidences are familiar to us all but what are the so-called laws of chance? From coin tossing to freak weather events, Geoffrey Grimmett explains how probability is at the heart of it all.