Granularity

D6 or D10, that is the question? Whether it is nobler of the mind to suffer the slings and arrows of outrageous fortune…

With due apologies to Mr Shakespeare, I would like to consider dice this time.
We use dice in wargaming because battles are unpredictable. Battles are complex affairs with plenty of contingent activity, and nothing can be predictable in such circumstances. So we use dice to model these contingencies, chances and probabilities.

Now, this gives rise to two effects. The first is a granularity in our wargames. Real life is a continuum. Groups of soldiers do not go from a ‘let’s get on with it’ to a ‘let’s run away’ frame of mind directly. There is a period of time, great or small, when they lose confidence, coherence and so on, and then the rout starts slowly, before the panic spreads. We cannot model this continuum, partly because it is so poorly understood, and secondly because qua wargame the troops need to be is a definite state, standing firm or running, not somewhere ill-defined in between.

So dice impose a degree of order on the wargame table, a controlling of the chances, but at the cost of losing the continuum of real life. Of course, the more dice you use, the less granular you can make the game. Role playing games, for example, often use D20 or D100. The effects of being able to roll from 01 – 99 are to wash out many of the effects of the granularity of the dice roll, although there is still a real distinction between a hit and a miss. For some, a near miss could be as demoralising as a light hit, but somewhere the complexity has to be cut off.

To spill the beans a little more on the early days of Polemous, the original was based on using a D10. We wanted a more finely grained set of results. However, the first battle with the rules showed us the error of our ways. The results were fairly wild. Using a difference system and a D10 a side gave a huge range of results, and as the body count mounted we decided that switching back to a D6 system made more sense. Variety is the spice of life, but too much just gets silly.

The choice of dice thus makes a significant contribution to the nature of the game. I’m sure we could have found some means of tackling the wildness of the D10 game. At least, by increasing the factors for the troops we could have reduced the effects of the difference between rolling a 0 and a 9, and by adjusting the tactical factors we could have made them balance the dice fluctuations. I think the reason we didn’t do this was that D6 systems are more familiar and thus intuitive, and we would have had to have worked much harder to balance the system with D10’s.

The second effect is a bit more subtle. Initially, I’d like to make a distinction between chance and probability. Chance is the randomising effect of unknown factors. For example, three arrows shot by the same person consecutively under the same conditions will land in slightly different places. This is due to factors like wind fluctuations, material differences and so on. Probability is the ability to predict the likelihood of some event happening. By this I mean that there is, say, a 10% chance of 15 hits from a volley of 100 muskets hitting a battalion sized target at 100 paces.

Now, the probability may be a cumulation of all the chances affecting each individual discharge of each musket, and the factors affecting each might be different, depending on the individual’s consumption of alcohol before the battle, whether they’ve just shot their ramrod at the enemy and that sort of thing. But the overall effect is one of probability.

How does this affect a wargame? I think the issue is the confluence of chance and probability. Suppose our volley at 100 paces is at the enemy general at the head of his guards battalion. We have a global probability of hits, but does the general get wounded, incapacitated or does he laugh in the face of danger as his invincible guards mow down the enemy? This is surely the province of chance.

But here is the rub: we use the same system to resolve both of these events. Roll globally to determine the overall number of hurts. Then roll again to determine the damage to the general.

Does this matter? Probably not much, but sometimes I do wonder. As a species we are not good at doing probability. The gambler’s fallacy is alive and well and living on a wargames table near you. Million to one chances do not come up fifty-fifty. As for wargaming, of course, probabilities do get complex, and a wargame is a diversion, a hobby, not an extension of applied mathematics. But there are issues.

How many squares were charged in the Napoleonic era? How many of those were broken? Now, suppose we could document all of them. So far as I know only a few squares were broken, and I’d imagine well over 2000 squares were charged. So, to make the numbers easy, let’s say 2 broken squares and 2000 charges, giving a 1:1000 chance of breaking a square. Now, 1/6 to the fourth power is 0.00077, which is just under 0.001. So on this basis the chances of breaking a square are the same as rolling a 6 four times.

Now here comes the problem: we charge squares in wargames many more times than was done in real life, so we see squares broken in wargames many more times than we do in real life. In fact, from real life, we have no idea how often squares were broken, so we land up with meaningless probabilities which we translate to the wargames table. The numbers above look reasonable but were in fact plucked from thin air.

How do we deal with this?

It seems to me that the only way forward is to ignore real life and make the best guesses we can. But if we do that, how can we stay in even slight contact with historical reality? Are we all just playing fantasy games, regardless of whether we have the right coloured piping on the Imperial Guard’s uniform or not?