Game shows offer ordinary people the chance to be on TV and maybe even win some money, but when the studio lights are blazing and the presenter is waiting for your answer, you might wish you’d just stayed watching at home! Probability and statistics can help out when the pressure is on, so take a look at these TV tips.

### What’s in the box?

It sounds simple. Just you and 22 boxes, each of which contains between 1p and £250,000. One of them is yours, it’s value unknown, so to work it out you’ve got to eliminate the other boxes and hopefully end up with the grand prize. Things get more complicated when the mysterious Banker steps in. After a few boxes have been eliminated, contestants receive a call from a hidden person offering them a cash payment if they agree to stop playing. But how do you know whether to say Deal or No Deal?

Contestants normally have all kinds of strategies to help them beat the Banker, but the only one that really works is the mathematical concept of expected value. Imagine playing a simplified version of the game, with just three boxes. One box contains £1, another £2, and the third £3. You get to pick one at random and take home the prize. To find the expected value, you multiply the amount in each box by the probability of picking it, then add all these values together. In this case, the probability of picking any box is 1/3, so the expected value is 1/3 + 2/3 + 3/3 = 2. In other words, on average you’ll win £2 playing this simplified version of the game.

There are more boxes in the real game of course, but you work out the expected value in the same way. At the start of the game, with all 22 boxes in play, the expected value is exactly £25,712.12. This number will move up or down as the game progresses, depending on which boxes are eliminated. Knocking out the top prize of £250,000 in the first round drops the expected value to £15031.74, but getting rid of the 1p box only boosts you up to £26936.50, so some boxes change the expected value more than others.

Knowing the expected value helps you understand the Banker’s deals. He’ll normally begin by offering contestants a sum below the expected value – not much of a deal at all. If they hold on for a few rounds, the Banker’s offer gets nearer to the expected value, and sometimes even above it. At this point, contestants need to decide whether its worth the risk to continue. An offer above the expected value is definitely a good deal, but people are often tempted to gamble and risk joining the infamous 1p club! It all depends what kind of person you are, but the maths says to play it safe and take the deal.