Simulating War, Casino-Style

One of the biggest challenges for me in game design is getting enough playtesting done. I get to playtesting meetups with other designers from time to time, and have a couple of groups of great people who help me out when they can, but I just can't get as much playtest time as I would like.  So I need to make the most of the playtesters I do have.

Methods to increase the effectiveness of playtesting include solo testing before involving other players, having several games on the go so there is more likely to be a game that can make use of whatever playtesters I have available, getting cleverer at observing tests and questioning players, and using maths or computer simulations to analyse the games and focus aspects of games from a statistical point of view.

Most of the games I have worked on to date haven't really lent themselves to maths and simulation, but my wargame, currently codenamed Craghold, absolutely does.  And, more to the point, early playtests have revealed a question that I need answered.  Combat in the game involves each player rolling a bunch of six-sided dice depending on the situation of their unit in the engagement, and counting the number of dice that roll at least a set target number.  Assuming the general mechanism is OK, then what is the best target number to use to get the sort of combat results I want to see?

A chart of some of my results. I'll explain a bit...

I'm not a great mathematician, so I don't feel confident about doing an analysis of the game by manipulating the various probabilities. I'm not a great computer programmer either, but I know enough to be able to code up a quick simulation of any given battle: the number of dice used by each of two players, and the target number they are rolling against.  I could then, in a matter of seconds, choose the relative unit strengths and run a thousand simulations for each possible target number. I'm not considering a target of 1, because in that case the more powerful force always wins.  A little bit of coding to produce numbers which I fed into a spreadsheet meant that I quickly had charts representing the outcomes of several different situations.

The resolution of an engagement is basically to find the difference between the number of "hits" scored by each side: whoever has the most wins, and the loser is penalised according to the size of the difference (being driven back, "shaken", or destroyed).  On the charts, the bars of each colour indicate the number of times a result occurred for the target number matching that colour. Positive numbers on the horizontal axis mean that player A wins, while negative numbers mean player B is victorious.

Fewer dice in the combat tightens the results up.

Armed with these charts I was able to use an entirely unscientific method of deciding which set of bars looked most like what I wanted the results to be.  For instance, with a target number of 2, the results went overwhelmingly in favour of the stronger force, and with more dice the results would end in absolute carnage.  This is actually probably a good choice for a game like this, rewarding the player who can bring large masses of force to bear where it counts, but I want the game to be a bit looser and lighter than a true strategy game.  On the other hand, a target of 6 makes engagements extremely unpredictable, but generally only marginal outcomes occur, which seems both boring and frustrating.

I'm planning on going with a target number of 3 as it gives the sort of profile I was looking for.  We shall see how this works out in actual playtesting when I next get a chance...