Firstly the resource. AnyDice is an online dice calculator which is best described in the words of its creator:
“Role-playing games [and wargames] are filled with dice. At some point, you might want to know what your odds really are. Perhaps you're a player, perhaps you're writing a game yourself. In any case, you'll find there's a lot of math[s] involved behind the scenes.Version 1 of the calculator is no longer being actively developed but it does a awful lot of interesting things such as distributions like (4+d6)-(4+d6):
I created AnyDice because I grew tired calculating probabilities in my head all the time.”
As I tried the calculator I realised that it is very handy for calculating the probabilities of DBMM combats. When exported the results can also be used to work out the effects of gradings on the raw results. So far I’ve been unable to work out the percentage of doubling but I’ll have another go later. Highly recommended.
The second part of this post is about the psychology of wargamers and how this effects the estimation of success or failure. My regular DBMM opponent is frequently disappointed when losing combats he believes are even contests. This happens so often that it has become a regular feature of our post-game discussions over a pint or two. We found out he applies the DBMM grading factors to the base combat factors before assessing the chances of winning the dice roll.
We both know this isn’t correct because in DBMM the grading factors don’t apply in every circumstance and are applied depending on the raw (factors + dice) scores not the factors. I have pointed out that the two routes produce different distributions but to no avail.
Having found the AnyDice calculator I thought I’d use it to check out the numbers and sure enough the root cause of his frequent disappointment is immediately clear:
|Effect of ± 1|
Adding the grading factors to the factors correctly estimates the chance of success but significantly under estimates of the chance of losing. It’s interesting how player psychology dominates. In this case it’s optimism: “my superior troops will get a bonus if they win, or draw, so I’ll assume they do and estimate the probabilities accordingly”. If only it were so simple.