Saturday, 18 March 2017

How far?

"Only those who will risk going too far can possibly find out how far one can go." - T.S. Eliot

It's been a while since this blog interested itself in the higher mathematics. Those who recall the offset square line-of-sight debacle will know why. However, having done some, with hindsight, bogus calculations the other day regarding likely movement distances in Blitzkrieg Commander I have developed a bit of a taste for it and have had a short (actually very short) play with the numbers again, this time on a spreadsheet rather than in my head. This is a bit of a 'spherical chicken in a vacuum' exercise because what I calculated has nothing to do with reality, but then again we're wargamers so we should be used to that. And before I start let me apologise for sloppily referring in the previous post to averages when I really meant expected values.

So, if we assume that the Germans are trying to move an armoured formation as far as they can in a straight line across open terrain without firing or being fired at, without encountering anything in their way, without the units changing their relative position to each other, and making the assumption that only the first command roll each turn doesn't suffer a distance penalty, then the expected value of the distance they would move before failing their command roll is 21", or at least it would be if the commanders were not restricted to moving 24". Rather counter intuitively, the fact that they are so restricted means that the expected value averaged across several turns would be reduced somewhat further even though they can actually move more than the expected movement of the units under their command. However, to calculate the effect of that with greater precision is more complicated than even I can be bothered to do. On the same basis the British can expect to move 16", which would be similarly reduced by the command unit move restriction. The difference is entirely due to the Germans having a CV of 9 and the British 8. Possibly the most interesting point of all of this is just how much of a difference that lower CV makes.

Clearly we use inches rather than the centimetres of the original rules - embarrassing but true - and (mostly) convert them by multiplying by 60%, meaning tank units move at 12" per segment. The fact that neither expected value is a multiple of 12" gives a good indication of the abstract nature of all this. Anyway, apart from providing a tangible example of the importance of not unnecessarily reducing the target one is making a command roll against if one can avoid it, there were actually some concrete results from my self-indulgence. On re-reading the rules I think I've found two that we are playing wrongly:
  • Distance from commanders does not affect command rolls in respect of infantry guns (page 12, note 2)
  • The German flexible tactical doctrine means that HQ command units can issue orders without any penalty on their command roll (page 43)
So, not a complete waste of time then.

 "In mathematics the art of proposing a question must be held of higher value than solving it." 
- Georg Cantor

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