Tag Archives: Probability

Wargaming and the Law of Averages – Never the Twain Shall Meet

The United Kingdom, over which the 6 Inch Move floating citadel err… floats… had another public holiday yesterday. So, once again, following the pattern that has been established for this year we abandoned wives, mothers, girlfriends etc… and met together to push our collections of over-priced metal and plastic army men across make-believe battlefields. And it was GOOD!

The day saw a lot of interesting armies, from my slightly reworked Ogre Kingdoms and Gribblin’s Zombiedragon led Vampire counts, to Servitob using a proper almost tournament level Space Marine list. Carabus fielding 1500pts of Grey Knights (that’s a box of five Terminators to you and me) and Gribblin with an experimental Eldar army list that was so experimental it seemed to experience quantum effects similar to chucking a moggy into a box.

However, my purpose today (I assume you read the title?) is not to regale you all with massively detailed battle reports of the day’s frivolities (somehow I managed to table the Vampires bottom of turn 6) but really to explore a great phenomenon that I think pretty much all gamers are privy too.

At the heart of wargaming is a heck of a lot of maths. No matter whether you are using the traditional dice based systems or some of those new-fangled decks of cards you are normally trying to achieve a number in order to perform an action or do some damage. Therefore the laws of probability are something that are familiar to all gamers. Most of you will probably be aware of the concept of Theoryhammer, the pure maths of average probability that used to work out what units are capable of doing. It is this Theoryhammer that means you are (supposedly) better off taking Striking Scorpions against Space Marines rather than Banshees as the S4 offsets the power weapons of the Banshees. Knowing that the average result of a single die is 3.5 meaning 2D6 is a 7 is of use when calculating if you want to do something. You can use it to work out how many wounds you are likely to do against a certain unit using one of your own. Theoryhammer shows that Wyches are best taken in units of 6-8, should be enough to do some casualties and stay in combat during your opponents turn, allowing you to finish them off and avoid getting shot up (Incidentally my Wyches are finding it hard to even get to combat at the moment).

However, there is one problem with Theoryhammer in general and that is that the law of averages does not exist in wargaming. Now, it could be argued that this is just a product of perspective, in that you are far more likely to remember poor dice than when things go more normally, but I don’t think this is the case. For instance, more often than not I will fail leadership tests, this is a disease I appear to have caught from Gribblin who has been plagued with the same thing for years, hence why he plays Undead and Lizardmen, his Wood Elves are massively prone to this, especially Treemen. I have consistently rolled above 10 for leadership tests and then rerolled the same or higher when applicable. Even when I am using armies with above average Leadership Is struggle to pass the test, in the last 40k game I played my Mandrakes failed their Ld8 panic test from shooting casualties, and then failed to rally in the next turn. We already established that the average score of two dice rolled together is 7 so I should be passing these more often than not.

Another awesome example of this playing out was in that same game. I have 14 Lance weapons in my current Dark Eldar list, not a lot by many standards but certainly enough to not struggle against a mechanised army, which is pretty much what 40k is these days. I faced off against Servitob who is always a great opponent and is using a much tougher version of Space Marines now with his Salamanders. He took a Land Raider and three Razorbacks, I have three Ravagers, 3 Raiders and a unit of 6 Reaver Jetbikes with 2 Blasters in them, plenty enough to dent that Land Raider. However, that Land Raider was still rolling around virtually unharmed in turn 5, even after I had (perhaps unwisely) spent most of my heavy shooting trying to pop it, the number of 1s I rolled on the Vehicle Damage Chart after penetrating the armour was ridiculous and had a profound effect on the game. With my flimsy armour there is no way I can let a tank like that have free rein through my troops. Half the shots missed and when I did hit and penetrate all I could do was shake it multiple times but then the Power of the Machine Spirit still allows it to fire (how I hate Space Marines and their “we can get around the rules” abilities).

Ok, now you can just roll that to bad luck which is of course really just another way of saying you cannot count on the law of averages. While Theoryhammer can be all well and good, when you roll those dice you have just as much chance of getting that annoying 1 than the exhilaration of a 6. While we like to factor in what things should do there are those times when the dice do seem to abandon you and you are fighting an uphill battle regardless of whether you have actually played well.

The second solo battle where I’ve played with my Dark Eldar has certainly been another schooling, we didn’t have any LOS blocking terrain which wasn’t ideal as pretty much all my stuff could be shot, we did have enough terrain overall though. I think I need to learn to be more patient with my Commoragh Elite. Sure they die to a stiff breeze but I think I am starting to understand the way to play them, sure they are horrifically offensive in terms of their power output but you need to tread softly and cautiously before committing them. You really do get punished hard when things go wrong or when things are used badly.

So then Interwebs, are there any particular instance where you seem to be able to defy the laws of probability? Or accounts of universe ending bad luck you’d like to share?


By the way, the Land Raider did die in the end… to my Archon with a well placed Haywire grenade! 150pts of HQ did over two turns what 700pts of Lances could not do over five turns!