The intent of this blog is to do some really basic discussion on probability, and how that can inform thinking about your games, and a bit of thinking about how we can model outcomes.
First then, what this blog is. I will aim to keep this relatively straightforwards in terms of what I am describing, and I will aim to not use excessive amounts of jargon or technical terms. Although I intend to focus on Age of Sigmar most of the logic is applicable to any dice rolling game and I would like to do some looking at Underworlds as well.
What this blog is not. Full disclosure I am not a mathematician. I have been playing Games Workshop games for about 25 years, I am post graduate qualified in accounting, and I do a lot of work with numbers, but I do not hold a tertiary mathematics degree. Therefore it is very much focused on real world probability and application rather than academic level discussion.
For this first blog then, let's look at a really basic concept that helps to put some context around mathhammer (by this I mean the discussion around the 'hard' aspect of the game being the numbers versus the 'soft' aspects such as the social contract, positioning, decision making etc.) and how it is useful or is not.
Discussion of probability within games must be considered using 2 different lenses: theoretical probability versus experimental probability. Theoretical probability is the probability that is produced through pure calculation. As an example, the probability of rolling a 6 on 1 dice is 1/6 (~16.6%) so if we roll 6 dice theoretical probability indicates 1 of these dice will be a 6. Experimental probability is the result of actually doing the thing we are discussing. So to contrast the example above, for the experimental probability of rolling a 6 on 6 dice, we would roll 6 dice, count the number of 6's and that would give us the percentage of 6's rolled.
The importance of this is probably obvious; intuitively we know that 6 dice 'should' include a 6, but from personal experience I know this is all too often not the case. Thus, when we talk about probability and what 'should' happen always keep in mind that we are discussing theoretical probability, and that experimental probability is quite significantly different.
The other thing to consider is the concept of independent versus dependent probabilities. Independent probabilities are probabilities that are in no way influenced by another probability. I.e. if you roll a dice the chance of getting a six is 1/6. If you roll a six, then the next roll has a chance of rolling a six of... 1/6. Dependent probabilities are where probabilities change. As an example the chance of pulling any given card (let's say Great Strength) from your deck in Underworlds is 1/20. After you draw your first card, the chance of the next card being Great Strength is 1/19.
Why is this important? If a thing is an independent probability then a player has no control over the outcome (you rolls your dice and you takes your chances). If a thing is a dependent probability you have a degree of control - if you draw and discard cards then in order to increase your chances of drawing a specific card you need to draw more cards as each card drawn increases the odds of drawing the card you want.
Next blog post will be basic mathematics of working out the possibility of something happening.