Transcript

MARCUS DU SAUTOY

If you’ve ever played a dice-based game such as Snakes and Ladders, Ludo, Monopoly or Backgammon, you may have wondered whether dice rolls can be predicted. This question was explored in 2012 by a team of mathematicians in Poland, who used a high-speed camera to capture the trajectory of a die roll at a rate of 1500 frames a second. They found that in addition to knowing the initial position and the velocity of the die, that the most important factors are the friction and bounciness of the landing surface. Air resistance, on the other hand, can be disregarded.

On a high-friction rigid surface, dice tend to bounce around a lot more than on a low-friction or soft surface. The more a die bounces, the harder it is to predict the outcome. Energy is dissipated each time the die hits the surface, and at some point there’s little energy left, and the die comes to rest. If the amount of energy dissipated on impact with a surface is quite high – so, not many bounces – and the initial conditions can be established with sufficient accuracy, then the outcome of the throw can be pretty predictable. Furthermore, this predictability implies that the die lands on the surface that was lowest when the die was rolled. But if less energy is dissipated on impact with a surface – which means we’re going to get more bounces – then the outcome is more chaotic.

So, what do you think: do we use baize-covered tables for games because they look nice, or to increase the number of bounces, which therefore increases their chaotic behaviour and makes it much harder to predict the outcome?