This is a idea that I've been thinking about for quite some time, but I'm not good enough at statistics to work out how to do it. Sorry in advance. I don't plan to implement this, but feel free to correct anything I've written about the game that is wrong.
What is TF2 and what are crits and crithack?
Team fortress 2 (TF2 for short) is a game where you shoot people. Occasionally on your escapades the game randomly grants you "critical hits" (crits) which means that your attack will deal triple its usual damage if it hits. Given that this is quite the advantage, people inevitably found ways to fake the dice roll that determine crits and can fully control when they happen.
Problem statement
The probability of a crit varies, but is always known for that attack. Lets say that the $n$th attack has a crit probability of $P_{crit}(n)$. If the dice roll succeeds game will perform additional checks, which may or may not prevent crits from happening. These conditions are fairly complicated, but means that cheaters at most are able to crit at the same rate as a normal player. Let's assume weather a specific crit validates or not is known and move on.
The way a cheater would see these conditions is as a "crit bucket" which fills up with possible crit attacks as they deal non-crit damage with that specific weapon. This means that a cheater will first intentionally prevent crits to fill this bucket before using them when needed.
So from this I would like to know
- Some way of representing the probability of the player cheating.
- If possible, how to get the specificity and sensitivity for a player cheating.
- How easy it would be to cheat while avoiding detection. (i.e. if its possible to detect all cheaters with confidence after enough data)
Sorry if this question is bad, I haven't managed to get particularly far myself. It would be easy to calculate the cumulative probabilities of a specific run of attacks happening with or without crits, but I have no idea how to combine them.
