I see a lot of people calculate averages for hits evades and damage etc, but i dont find that a useful way of looking at it. I think it is much more useful to look at the probability of each event ie 0, 1, 2 etc of damage in a given situation. I even went as far as to make a Monte Carlo simulation* of attack vs defence with all the different options (focus, evade etc) this allows you too see the spread as well as the likely outcomes that just looking at an average doesnt show. Ie 2 actions might have a similair average but the chance of a high output might be better than another similair average situation.

I was wondering what others think of this and how they use this.

* A monte carlo simulation is something where you run a model using known probabilities and count the results by running it multiple times, so in the terms of this game rolling dice and calculating outcomes based on what was rolled. I made mine in excel, all it takes a little bit of excel fu.

I feel like using averages is fine if you're just trying to compare the effectiveness of different actions and upgrades. I can't see when I would need to know the actual probabilities, but I'm not really an expert on this kind of thing so I could be completely wrong.

Many situations in X-wing actually have distributions that can be determined analytically. You really only need simulation methods for very complex situations or for trying to average something across the metagame.

Overall, though, you're right. Averages are a convenient shorthand, but particularly in a game with as much variance and (speaking relatively) as few rolls as we have, it's important to consider the entire distribution.

Sometimes, yeah, you just really need that last hit to make Han/Phantom/whatever _dead_. In that case, averages be darned, unload on the bugger, and hope.

But knowing what sorts of things are more likely to let me win- knowing why a couple Z-95s are good, but that 8 of them are not as good as 8 Ties... That's important knowledge. And Mathwing lets us understand that in a way that intuition might not.

I feel like using averages is fine if you're just trying to compare the effectiveness of different actions and upgrades. I can't see when I would need to know the actual probabilities, but I'm not really an expert on this kind of thing so I could be completely wrong.

Lets consider the following simplified situation:

You have three attack dice, and on average you will score 1.5 hits. As you cant score 0.5 hits in this game, what are the single outcomes? You either score 0, 1, 2 or 3 hits. When each of this four situations have the same probability, you will get on average 1.5 hits.

Now lets assume by some action/upgrade/whatever, there are only the following outcomes: You either score 1 or 2 hits, each with the same probability. Then you have again the average of 1.5 hits, but you know that you cant score three hits, which you may need to kill a ship, and you know you score at least one hit compared to the zero hits in the first example. Depending on the situation, it might be better to take the action which gives you a guaranteed hit, or to take the other, where you can do more damage when you get the three hits.

The above is just an example, and the values/probabilities are not taken from the game. But I think for the advanced targeting computer from the Advanced fix, you really should not only take a look at the average outcomes when you spend the target lock to reroll, or add the critical hit, but also what are the single outcomes with their probabilities.

The exact probability density function for how much damage gets through after both offense and defense are rolled is the most useful. But you don't need (or want) to use a Monte Carlo simulation; you can get the exact answer faster using the binomial distribution, as Vorpal mentioned.

I make a lot of calculations involving multiple attackers and one defender, specifically for a build where I need to protect a ship for as long as possible. I calculate % of survivability for different scenarios, based on those I make an attack plan ("I need a range 3 engagement/ I want to get straight into range 1 if possible/ I want the Talas to not have a shot but Dash can have a shot").

I make the decision based on that percentage, for instance 20% of dying is slightly too much and doesn't make me feel safe, however everything under 10% is good. I can *almost* count on that. If the ship dies, c'est la vie, I'll try to work from there, but generally I assume it will survive if I have 10% of dying.