In Hammer of Math, we look at statistics and math-related problems in Warhammer 40k, talking about how they affect games and how you can use them to your advantage. Today we’re talking about rituals in the new Codex: Thousand Sons.
Codex: Thousand Sons introduces a new way for the faction to do Rituals, giving them four different options for buffs and mortal wounds. In case you missed our review of the book, you can find it here. Each of these Rituals gives a specific effect, and has a way to improve the effect if you roll high enough.
Before we dive in I’d like to give a special thanks to TJ Lanigan for requesting this topic, and for doing much of the stats work behind the scenes.
Cabal of Sorcerers
The Thousand Sons army rule that lets you perform rituals is Cabal of Sorcerers. Here’s how it works:
At the start of the Shooting phase,
- You pick a Psyker to do the Ritual and then roll 2D6.
- Then if you want to try for a higher value, you can attempt to Channel the Warp. When you do this, you roll an additional D6.
- Then if there are any doubles or triples, the model’s unit suffers D3 mortal wounds.
- If the model wasn’t destroyed, now you take the combined total of all the dice rolled to generate your Psychic Test result.
If that total meets or exceeds the Warp Charge value of the Ritual being attempted, then that model manifests the Ritual and you resolve its effects.
There are four Rituals you can manifest:
- Destiny’s Ruin (WC 5) – Pick a visible enemy unit within 24” of the manifesting model. Until the end of the phase, Thousand Sons units in your army re-roll hit rolls of 1 against that unit.
Added effect (10+) – Re-roll all hit rolls against that target instead. - Temporal Surge (WC 6) – Pick a friendly Thousand Sons unit not within Engagement Range of an enemy unit and within 24” of and visible to the manifesting model. They can make a Normal Move of up to D6”. That unit is not eligible to charge until the end of the turn.
Added Effect (10+) – they can move up to 6” instead.
- Doombolt (WC 7) – Pick a visible enemy unit within 24” (excluding units with Lone Op outside of 12”). They take D3 mortal wounds.
Added Effect (11+) they take D3+3 mortal wounds instead.
- Twist of Fate (WC 9) – Pick a visible enemy unit within 24”. Until the end of the Shooting phase, when Thousand Sons units shoot that unit, improve their AP by 1.
Added Effect (12+), improve their AP by 2.
That’s a lot of effects to look at, and on top of all of this, there are a few ways to get additional bonuses to your Psychic Tests:
- Magnus the Red gets an inherent +2 to his Psychic Tests
- Ahriman gets an inherent +1 to his Psychic Tests
- The Mutalith Vortex Beast has an aura that gives psykers within 6″ +1 to their Psychic Tests
This gives us a lot to work with, so let’s go through this in steps, starting with the odds of manifesting a Ritual.
Manifesting Ritual Odds
There are three things we want to look at here:
- Your odds of manifesting each ritual on 2D6
- Your odds of manifesting if you rolled an additional D6
- Your odds of rolling doubles or triples
Let’s start with the basic 2D6 odds. When you roll 2D6, your odds aren’t uniformly distributed; instead, they have a curve distribution – there are more combinations of results which add up to 7 than any other result, and the further you go from 7 the fewer combinations you get, and the less likely you’ll roll that result. You’ll find a similar distribution for results on 3D6, though centered around 10.5 – the average result on 3D6.
If we put our different buffs together, here’s the chart we get:
That’s a solid chart, and shows off a few things. First, we can see that hitting those higher manifestation totals is typically going to require pushing our psykers to get those 3D6 odds, where our chances of 7+ jump up to 91% and even pulling a 10+ is fairly likely.
But this also shows off just how powerful the Mutalith Vortex Beast is as an asset, and where Magnus can really strut his stuff – if you want to be able to reliably hit those 12+ Twist of Fate casts, you need to have Magnus supported by a Mutalith for the +3 bonus. Or just to get the big Doombolts. This is also an area where if you’re bringing the Incandeum Enhancement from the Grand Coven Detachment you’ll want to make sure you have a Mutalith nearby for your second Doombolt Cast to help ensure you can get those 95% odds.
But Wait, There’s More
There’s one more interesting aspect to this, and that’s conditional probability. While your baseline odds of success on 3D6 are always the same, whether you opt to roll that third die to manifest will likely be based on your roll on 2D6, where the most common result is 7, and your odds of rolling 7+ with those first two dice are 58%. You will always know the results of your first two dice before rolling the third, and so if you roll a 7, you’ll know immediately that your odds of getting a 10+ with a third die are 4/6, or about 67%.
So when you are making your decisions about what Rituals to attempt and where, it’s good to keep in mind the initial odds of getting what you want, and understand how likely success is after pushing a third die once you’ve rolled the first two.
Perils of the Warp
Let’s talk about those doubles and triples odds. Your odds of rolling doubles on 2D6 are 1 in 6, or about 17%. Your odds of rolling doubles on 3D6 are 44%. That said, you get a little knowledge before you decide to roll that third die. As with manifesting, this doesn’t change your overall odds at all (die rolls are independent statistical events), but it does break the process up into two smaller steps – if you roll doubles on your first two dice, your third result just won’t matter since your odds of taking mortal wounds have solidified at 100%. That said, if you didn’t roll doubles on the first 2d6, your odds of rolling doubles when you roll the third die jump to 1 in 3, or about 33%. The good news is you dodged the initial 17% odds of rolling doubles.
Finally, if you do roll doubles or triples, you’re going to take 2 mortal wounds on average. Enough to kill a Rubric, and one third of the time you’ll take a third one and potentially lose a whole Scarab.
The Rituals
Let’s finish off with a few notes on the Rituals themselves:
- Destiny’s Ruin. Re-rolling 1s to hit is pretty good, especially when you have a large number of units that can hit on a 2+, such as Magnus, Daemon Princes, and anything tagged by a Sorcerer in Terminator Armour. That said, Re-rolling all hits is basically just Oath of Moment, an ability so powerful it’s just the faction ability for Space Marines.
- Temporal Surge. On average, you’ll move 3-4 inches with this if you’re rolling for the distance moved.
- Doombolt. Your expected result on a D3 is 2, so you should expect to do 2 mortal wounds with the basic version of this and 5 with the beefed-up version.
- Twist of Fate. This one’s harder to talk about mathematically. Dropping the save on a target will just make everything shooting it better. If you think about saves as an increase in wounds, where a 5+ is roughly the same as having 50% more wounds, then you can start to see how dropping a target from a 4+ to a 5+ can be a big help.
Final Thoughts
Rituals offer a powerful set of effects for the Thousand Sons, and it’s kind of bonkers that “Oath of Moment on a target 24″ away” is just the easiest one to cast. While they may not quite have the same raw power some of the Index ones had, you’re more likely to actually cast four in a turn now and you can notably keep attempting to manifest rituals if you keep failing them, just trying with new psykers. That said, be wary of those doubles – you should expect to lose a few models per game to this, as 44% of triple cast attempts will end up with doubles or triples.
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