As Storm Kyle hit the UK last week many of us found ourselves back inside (thankfully in much better circumstances) but once again looking for indoor activities to stay entertained. Board games were dug out, bringing with them the inevitable discussions (more likely arguments) of luck versus skill, with the winner insisting that intricate tactics and decision making is the sole cause of their victory. This element of ‘skill’ for most games boils down to the ability to make a decision based on a quick mental estimate for the probability of the various outcomes of a given situation, which for the maths enthusiast is all part of the fun.
Take for example a game of the popular board game Risk, where each player controls an army and battles with others using dice to conquer territories. Sometimes a battle will involve a single dice versus another with the higher number winning (the defence winning at a draw) and in these occasions it is clear, and can be determined mentally, that of the 36 outcomes for the two dice, 15 will indicate a win for the attacker and 21 for the defender.
If however the battle involved 2 attacking dice and 2 defensive ones then suddenly the time taken to mentally compute the likelihood of the attacker losing 2 armies could take a few hours, at which point the game may get quite boring. The method to do so however is a straightforward counting problem and so, after finishing a game, why not refresh your matlab skills by calculating the probabilities exactly? For example – take the below loop to calculate the probabilities of the above scenario in Risk.
The remaining task is to consider the conditional probabilities of each of the outcomes that will follow a decision, and then given the actions of each of the other players constantly access the likelihoods in order to give yourself the best chance of victory. Fortunately Storm Kyle is expected to pass within the week, so there’s unlikely to be time to quantify these decisions in such detail... maybe it is best just to leave it to chance.
Maths in the media…
‘The numbers have no way of speaking for themselves. We speak for them, we imbue them with meaning.’ - Making sense of the vast quantity of coronavirus statistics:
On a lighter note, a new model for dog years using the natural logarithm:
age_(human )= 16ln(age_dog)〖 + 31〗_.
Sticking with animals, discover the mathematics of penguins:
A fun challenge for mathematicians of all ages: