It’s a Game of Sixes by Stuart Andrew

15 Nov

In this series of blog posts, I hope to provide readers with to ability to utilise mathematics to improve both their game and their army selection. In doing so,there shall be slight diversions into some basic probability. All anybody will need to understand this, and more importantly utilise it, is the ability to multiply fractions, and a calculator at a stretch.

This week then we shall be examining the issue of re-rolls. There are many thingsin this game we play that grant re-rolls. Twin-linked weapons, preferred enemy, numerouspsychic powers. People are aware of them being a good thing, but just how good.

To illustrate we shall use a scenario I encountered not long ago.

In the Dark Eldar Codex, Duke Siliscus allows the controlling player to make tworolls on the combat drugs chart, and choose their preferred result (He does also confer other advantages, so this is not the only reason one might include him). One result allows oneto re-roll to would, and another grants +1 strength. Thus if confronted with both these optionswhat should one choose. To analyse this properly we need a quick introduction to probability.

 

In probability, what one is interested in doing is assigning a probability value to an event. An event that would be relevant to the 40k universe would be what is the probability of making a single 4+ save. I would hope that most would be able to say 50\%. To get to this, one sees that in rolling a single D6 there are 6 possible outcomes, 3 of which represent the event we want to occur. Thus 3 divided by 6 times 100 and we arrive at our percentage. This example was of course very simple. Let us now try computing the probability that a twin linked weapon, whose firer has BS4, hits its target. To do this one needs to know one of the basic tricks of probability.

 

when considering any event, it remains true that something will always happen. That is, the probability that the event you want to occur does + the probability that is does not, is 100\%. This instead of computing directly the probability of what you want to happen happening, one can compute the probability that it does not. Then one simply takes the latter probability, subtracts it from 100\%, and we get the number we want. Lets apply this to the above situation. The odds that I miss with a BS4 twin-linked weapon is 1/3*1/3 (I miss with the first try needing 3+, and then do so again on my second attempt) times 100 which gives approximately 11\%. Thus the chance if hitting is 89\%. For BS3 twin-linked the odds of hitting are 75\% and one can rinse and repeat for other values of the BS.

 

So armed we can now return to our original conundrum. Let us assume that the combat drugs are on a unit of wyches. With their weapons they are a basic strength 3 in combat. Against toughness 3, with re-rolls they have a 75\% chance to wound per hit. With +1 strength they have a 66\% chance. Against toughness 4, they have a 55\% chance to wound. With +1 strength its 50\%. Using the the above procedure one can how that against toughness 5 (this is notable outside the MEQ (marine equivalent) meta)  the +1 strength has only got a less than 3\% better chance at wounding than a re-roll. In a really absurd turn of events one can show that against toughness 6, the re-roll provides nearly double the chance to wound per hit than the +1. Thus the only real reason to take the +1 strength is if you imagine you will be fighting toughness 7models, which strength 3 cannot harm. This is quite rare, and two of the few examples are the Dark eldar monstrous creatures. Alternatively one may want the additional strength to engage light vehicles. However, considering that wyches can be armed with haywire grenades, which are substantially more dependable than strength 4 attacks (that one may not even roll up),  then that issue becomes moot.

 

On balance one would conclude that re-rolls are defiantly the option one would take. I would recommend to all player to take every opportunity to get re-rolls in their list somehow. The above calculations show that it really does substantially boost either the survivability (In the case of the psychic  power fortune). Indeed the new triarch stalker in the necron codex allows all weapons fired at a unit to become twin-linked. Combine this with the Deathmarks ability to nominate a unit to be wounded on a 2+ and you can very dependable hammer key units in the opposite army.

 

Next week I shall attempt to explain why the current meta is to do with “weight of fire”, a term used often on the podcast, using Mathematics.

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3 Responses to “It’s a Game of Sixes by Stuart Andrew”

  1. Gaz1858 November 15, 2011 at 05:18 #

    Sorry guys but this is the worst grammatically written blog. Someone needs to go back through this and edit the mistakes!

  2. Andy Ovel November 15, 2011 at 14:19 #

    Slightly harsh I feel; sometimes we can make the odd msiatke in the excitement to get something down. I followed this piece, and found it enjoyable. I’m looking forward to reading more about applying maths to my 40k tactics. 🙂

    It’s a good blog Stuart 🙂

  3. Stuart Andrew November 15, 2011 at 15:17 #

    I do apologise about the number of mistakes present. This serves as an excellent example
    why you should remember to proof read something, especially after you transfer it from a pdf writer (thus the reason for the formatting \% appearing consistently), to office. The next posting, however, should be somewhat more of an easier read.

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