There’s a certain characteristic that’s common to the world’s most successful gamblers – they understand the mathematics of the games they play. More specifically they understand probability theory which is normally fairly simple to implement because most games of chance can be determined by a finite sample space.
This limited sample space and the randomness of events make most games of chance perfect for implementing a mathematical approach. Anything from drawing cards, spinning wheels or rolling dice allow us to build a simple probability model something like the basic blackjack strategy you can see here. The idea is that this will contain all the numerical probabilities of the events possible in the game.
Building a model like this supposes a finite probability field which contains the events and that the probability function of these events aligns with the classic definition of probability. Using this method you can add any events no mater how complicated into this field breaking them down into simpler events if required.
Then using this field you can work out the probability of any single or compound event by applying the laws of probability and doing some calculations. This approach works brilliantly for many casino games for example like cards and roulette. Working out the probabilities for roulette is probably the easiest as they are all one dimensional events based on a single spin of the wheel and the numbers. Most of the dice games are a little more complicated to work out the probability as you are dealing with combinations of events (and numbers).
Card games are harder still and indeed working out the probabilities for something like Blackjack is possible but a little trickier although to be fair it’s not hard to find out a basic template which can be adjusted to any specific configuration – alternate rules, house limits and number of decks for instance.
If you’re going to start applying mathematics to a game of chance then roulette is where to start. Indeed it’s possible to follow these events with even a minimal mathematical background. The only time it will become slightly more complicated is if you’re dealing with repeated events and analysing something like the Martingale System. You can see a couple of useful documentaries about people using maths to combat the casinos, including some entertaining ones on Netflix. Unfortunately they only seem to be available on the US version of the media site so you might have to change Netflix country if you’re based somewhere else.