Games, whether video games, board games, physical games or something else entirely, make up a good chunk of the population’s hobbies. Math, on the other hand, doesn’t. However, if you stop and take a closer look at some of your favourite games then you might be surprised to see just how much math is involved.
Whether it’s mathematical strategy that you have to implement, or math used by the developers of the games, understanding the games you love gets a whole lot easier when you understand math. Let’s take a look at some of the games that heavily feature math; we’ll even give you some tips on how to use your new math knowledge to your advantage.
Roulette – American or European?
Like many casino games, there’s a whole lot of numerical strategy involved in roulette. In this game, it all boils down to probability, which is easy to calculate if you know how. One of the most interesting pieces of probability in this game surrounds whether you choose to play American or European roulette. In American roulette you get 38 slots in the wheel – numbers 1-36, a single zero, and a double zero. In European it’s different. Here you get 37 slots on the wheel (numbers 1-36 and a single zero). In both games, the players bet on where they think a ball will land – so what does this extra slot in American roulette do to the probability? Well…
In European roulette, the probability of the ball landing on any one ‘slot’ is 1/37; in American roulette, it’s 1/38. This translates to 2.7% and 2.63% respectively. Where it gets really interesting is when you factor in the zero squares. In European roulette, that single zero is the only one players can’t bet on; in American roulette, there are two of ’em. This means that if the ball lands on a zero, the players aren’t paid out and the house always keeps the money. In European roulette you’ve got a 1/37 (2.7%) chance of that happening. In American roulette it’s 2/38 (5.26%). See why math is so important? Your house edge is nearly double on an American roulette wheel!
Blackjack Is a Game of Probability
Another classic casino game, blackjack might seem simple – you’ve just got to be able to add up to 21, right? But, actually, mastering maths can hugely improve your chances of winning. Many casino games are almost entirely about luck, but blackjack has a definitive strategy. A group of mathematicians literally worked it out. The core of this strategy is understanding the odds of drawing certain cards, ensuring you’re able to beat the dealer, without scoring higher than 21.
You can think about this as the “expected value” of the different decisions you could make. For instance, you have a hand totaling 16, and the dealer shows a 10. Uh oh. You must decide whether to hit (take another card) or stand (keep your current hand). The probability of busting if you hit is high (really high) since 16 is a weak hand. There are loads of cards (10s, face cards, basically anything over a 5) that could push your total over 21. In math terms, there are 20 cards out of 52 that would cause you to bust. This is just a 38.5% chance of success – if you hit.
So what’s the other option? Standing. If you stand, you’re relying on the dealer to bust, which happens about 23% of the time when the dealer has a 10. Comparing these probabilities helps you make the optimal decision: typically, standing on 16 against a dealer’s 10 is statistically better. If you want to take things a step further, you can try to keep count of the ratio of low to high cards remaining in the deck. This is called card counting and is super helpful, but only if you’re good at it!
The Role of Math in Modern Games
Modern games take things a step further still. Just imagine the math that goes into those involving virtual reality (VR) or augmented reality (AR). These games are math heavy. Developers use complex algorithms to create realistic environments and ensure fair play. VR games often use geometry and trigonometry (remember saying you’d never need those in school?) to create immersive 3D worlds. AR games often rely on mathematical models to overlay digital objects onto the real world – like in Pokémon Go.
Even escape rooms, which are becoming increasingly popular (both physical and virtual), use math. You’ll often find puzzles and challenges that require mathematical thinking to get to the bottom of them. The design of these puzzles often involves logic, pattern recognition, and sometimes pure arithmetic, providing a brain-teasing challenge that is as educational as it is entertaining.
