Making a charge in 40K is arguably one of the riskiest parts of the game – and not just because your unit might get blown apart by overwatch. Fail a charge roll and not only do you lose out on movement and the chance to smash something in glorious melee, but you are left standing around for your opponent to shoot and/or charge as they please.
Now that the psychic phase has been retired, the charge phase may be the only place where two dice will regularly have a huge impact on your games.* When you’re rolling lots of dice you should
A recent example of this is in the World Team Championships – Team England’s Mike Porte failed a 4” charge with a reroll against Team USA’s Anthony Vanella. A roll which may have turned the draw into a win for Team England if it had gone differently.
A 4” charge with a reroll is generally considered to be safe, but as with any charge requiring more than a 2 on the dice there is a risk of failure. The key question is: what amount of risk are you comfortable with? To determine that, and just how unlucky Mike was, let’s crunch some numbers.
*Alright, unless you’re brave enough to be regularly using gambits.
Basic charging probabilities
A charge roll is usually a simple 2d6 roll – roll two 6 sided dice and add them together and that’s how far you could charge. Unlike rolling a single dice, not all outcomes are equally likely. There is only one way to roll a 12 but there are 6 ways you can roll a 7.
So what does this mean for charging probabilities? To succeed on a charge roll you need to get at least a certain charge distance, so to get the chance of success you add up the probabilities of all rolls that are greater than or equal to that distance. Let’s take a look at what this means for your chances to make that all important charge:
Note: 12” charge not included in this table as you must be within 12” to declare a charge
One important thing to note is that As 7 is the most likely result, the difference between an 8” charge and a 7” charge is greater than the difference between a 9” and an 8” charge, or between a 6” and 5” charge.
When is the risk worth the reward?
The above table shows that Mike Porter was almost certainly justified in taking the risk of a 4” charge with a reroll – unfortunately for Mike, he hit the 1 out of 144 times that this goes wrong, during one of the most competitive events in the world.
However somewhere between the 4” charge with a reroll and the 11” charge without there is a turning point, where the risk outweighs the reward (unless a 11” charge is the difference between winning and losing your game – in that case roll the dice and say your prayers to the Emperor). Where this turning point is will depend on the reward.
Let’s take an example where not charging will gain you 2 points on an action secondary. If you make the charge however it will deny your opponent 5 primary points. At what distance does the charge become worth doing? This question can be answered by looking for when the expected value of the charge option gives greater than 2 points. Writing this as an equation:
Probability of charge x 5 > 2
Probability of charge > 2/5 = 40%
So if we’re willing to commit a reroll, a charge of 9” or less gives a greater expected number of points. If you don’t want to or can’t reroll, only a charge of 8” or less would be worth it.
Of course in reality 40K is rarely so clear cut. If you make the charge does that put your unit in a position to easily be taken out in your opponent’s turn? Will you kill one of your opponents key units? Are you already in a winning position and the charge failing could put you in a losing position? Questions like these need to be factored in when weighing up the risk vs reward, and ultimately it may be your gut that needs to make the decision.
Unfortunately maths can’t provide all the answers, but if you want to learn more about how special charge rules and advance and charge affect the probabilities, look out for part two of this article coming soon.