Dice are a core mechanic for 40k affecting all phases. Standard dice in use are 6 Sided (D6) though some abilities use 3 Side Dice (D3) usually by halving the result of a D6.
All modifiers (if any) to a dice roll are cumulative; you must apply all division modifiers before applying all multiplication modifiers, and before applying all addition and then all subtraction modifiers. Round any fractions up after applying all modifiers. [Core PDF Page 5]
Dice modifiers have a set order of operations, and they are similar to the usual mathematical order (often called PEMDAS or BODMAS);
It’s common practice with a simple modifier to just think of them as changing the successful result, so a when firing a BS3+ model with +1 to hit, any dice showing 2+ are successful as they will become 3+. This also means that if an ability is triggered on the roll of a 1 (not unmodified 1s) then with a +1 to the roll it will never trigger, as all the 1s become 2s once the modeifiers are applied.
Some older abilities also have wording such as “re-roll failed hits”. Re-rolls are processed before modifiers, so if you have a -1 to hit and BS3+ then whilst you need 4+ to hit, the 3s do not count as failures for the purpose of these abilities, because they have not failed yet.
Some rules allow you to re-roll a dice roll, which means you get to roll some or all of the dice again. If a rule allows you to re-roll a dice roll that was made by adding several dice together (2D6, 3D6 etc.) then, unless otherwise stated, you must re-roll all of those dice again. If a rule allows you to re-roll specific dice results, only those dice can be re-rolled. If a rule allows you to re-roll a specific dice result, but the result is obtained by halving a D6 (such as when rolling a D3), you use the value of the halved roll to determine if it can be re-rolled, not the value of the original D6. For example, if a rule states to re-roll results of 1, and you roll a D3, you would re-roll if the D6 rolled a 1 or a 2 (which is then halved to get a D3 value of a 1).
You can never re-roll a dice more than once, and re-rolls happen before modifiers (if any) are applied. Rules that refer to the value of an ‘unmodified’ dice roll are referring to the dice result after any re-rolls, but before any modifiers are applied. [Core PDF Page 5]
There are many abilities that allow one or more dice to be re-rolled, such as the Command Re-roll Stratagem, available to all armies from the Core Rule book. A dice can only be re-rolled once, so the face value shown after a re-roll is final, after which any modifiers are applied.
Many rules modify the characteristics of models and weapons. All modifiers to a characteristic are cumulative; you must apply division modifiers before applying multiplication modifiers, and before applying addition and then subtraction modifiers. Round any fractions up after applying all modifiers. If a rule instructs you to replace one characteristic with a specified value, change the relevant characteristic to the new value before applying any modifiers that apply from other rules (if any) to the new value. Regardless of the source, the Strength, Toughness, Attacks and Leadership characteristics of a model can never be modified below 1.
You may encounter a characteristic that is a random value instead of a number. For example, a Move characteristic might be 2D6″, or an Attacks value might be D6. When a unit with a random Move characteristic is selected to move, determine the entire unit’s move distance by rolling the indicated number of dice. For all other characteristics, roll to determine the value on an individual – per-model or per-weapon – basis each time that characteristic is required.
Characteristics of ‘-’ can never be modified. If a model has a Strength or Leadership characteristic of ‘-’ and that characteristic is required to resolve a rule, then substitute the model’s Toughness characteristic for that characteristic for the purposes of resolving that rule (note that the substituted characteristic still cannot be modified).
Similarly to Dice Rolls, Modifying Characteristics now follows the same order as dice rolls with one extra step:
- Rules that Set A Characteristic to a Value
These rules also clear up how to determine random characteristics for a unit. When a random movement stat if required should be determined for the entire unit once (so that it can stay together) but all of the other characteristics are determined per model or per weapon.
In addition, modifiers from equipment are processed alongside those from other abilities, so following that order a +1 to Strength from a weapon comes after any doubling or halving effects on a model, while weapons that double your strength are applied before any +/- effects coming from other abilities. This is explicitly different to how it worked in 8th Edition, where weapon multipliers/modifiers were always processed last.
See Ruleshammer Q&A
Games Workshop FAQ
Regarding Ignore AP Abilities
This question came from many different users so rather than quote any one of them I’m going to summarise the question and issue. Basically GW have really mucked up some of these abilities and how they interact with the new Modifying Characteristics rules (well actually, these new rules are from FAQs that 8th had so the issue is older than this but un-noticed).
Some abilities to ignore AP are worded like this;
Reactive Countermeasures: BATTLESUIT model with airbursting fragmentation projector only. Ranged weapons with an Armour Penetration characteristic of -1 or -2 are treated as having an Armour Penetration characteristic of 0 when resolving attacks against a model with this Weapon System.
The key thing to notice here is that this wording has you “treat” the attack as having AP 0, it does not set the AP of those attacks to 0. Why does that matter? It matters because of the order in which these abilities are applied. Here’s the relevant part from the Modifying Characteristics rules;
If a rule instructs you to replace one characteristic with a specified value, change the relevant characteristic to the new value before applying any modifiers that apply from other rules (if any) to the new value. Regardless of the source, the Strength, Toughness, Attacks and Leadership characteristics of a model can never be modified below 1. [Core Rules PDF Pg8]
Okay so the first AP ignore ability doesn’t trigger this, so why am I mentioning it? Take a look at this one.
Tarsus Buckler: When resolving an attack made with a weapon that has an Armour Penetration characteristic of -1 against a model equipped with a tarsus buckler, that weapon has an Armour Penetration characteristic of 0 for that attack.
This is different, not “treated as”, it literally sets the AP Characteristic of the weapon to 0. As such this happens before ANY OTHER modifiers. So if you used this against Space Marines for instance and they has a Doctrine buff to use the against the buckler an AP-1 weapon would become AP0, then be modified again to AP-1. Against the Countermeasures it would be improved to AP-2 and then treated as AP0 when being resolved.
This is obviously a bit pedantic and a very intricate example of RAW, and the presence of the treats as wording definitely in my opinion implies intent. This really gets compounded by the Sisters of Battle convictions.
Stoic Endurance: When a model with this conviction would lose a wound, roll one D6; on a 6 that wound is not lost. In addition, when resolving an attack made with a weapon with an Armour Penetration characteristic of -1 against a unit with this conviction, that weapon has an Armour Penetration characteristic of 0 for that attack. Whilst a unit with this conviction is under the effect of an imagifier’s Tale of the Stoicability, weapons with an Armour Penetration characteristic of -2 are also treated as having an Armour Penetration characteristic of 0 when resolving attacks against that unit.
This ability has both the “has an” and “treated as” wording for different sections, however notice that the AP-2 part says “also treated as” as if it’s intended that the first section be taken in the same way. Needless to say this gets super confusing very quickly. It could be explained away as an issue of 8th’s rules writing being incompatible with 9th but actually this is how set characteristic rules have been for a while, they were just more obscure as it was only in an FAQ.
Q: If an ability instructs me to resolve an attack with a different characteristic (e.g. a Culexus Assassin’s Etherium ability) does this happen before or after any other modifiers that also apply to that characteristic (e.g. the Drukhari Serpentin Combat Drug)?
A: When resolving such an attack, change the relevant characteristic to the new value before applying any modifiers to that new value. – 8th Edition FAQ
This issue was revisited in the September Feedback Review, see below.
However the FAQ above has been removed and upon further inspection it contradicts one of my points. It did establish that setting characteristics happens before other modifiers however the ability mentioned is Etherium.
Etherium: When resolving an attack that targets this model, the attacking model is treated as having a Weapon Skill and Ballistic Skill characteristic of 6+.
Interestingly this ability’s wording changed during 8th, and from “as if they had a Weapon Skill…” to the new “treated as having”. However that doesn’t actually change much for Etherium as very few abilities alter an enemy’s actual WS and BS, so this would still apply before any abilities that cause a + or – to the hit roll itself but the passing value would now be 6+.
However it doesn’t end there. As that FAQ was not carried forward into 9th so it no longer applies at all. There are however some other AP ability related FAQs though.
Q: If the Dour Duty Stratagem is used on a unit that is within 6″ of a model with the Bastion Warlord Trait, will enemy attacks with an Armour Penetration characteristic of -2 that are made against that unit be treated as AP -1 or AP 0?
A:The attacks will be treated as AP 0. The Dour Duty Stratagem turns any attacks with AP -2 that are made against that unit into AP -1, at which point the Bastion Warlord Trait will cause them to be treated as AP 0. – Faith & Fury FAQ
And for clarity here’s the wording for the stratagem and for that Warlord Trait.
Dour Duty: Use this Stratagem in your opponent’s Shooting phase or your Charge phase, when an IRON WARRIORS unit from your army is chosen as the target for an attack. Until the end of that phase, when resolving an attack made with a ranged weapon against that unit, worsen the Armour Penetration characteristic of that weapon by 1 for that attack (e.g. AP -1 becomes AP 0).
Bastion: When resolving an attack made with a weapon that has an Armour Penetration characteristic of -1 against a friendly IRON WARRIORS unit that is within 6″ of this Warlord and receiving the benefit of cover, that weapon is treated as having an Armour Penetration characteristic of 0
So putting all these pieces together then;
- Unit is shot at with AP-2 weapon and the Iron Warriors player using Dour Duty.
- This reduces the AP-2 to AP-1
- They are in range of their Warlord with the Bastion Warlord Trait so that AP-1 is treated as AP0.
This sequence supports that the fix I’ve suggested is actually accurate for 9th edition which has tweaked AP ignore rules to play as everyone has been using them.
Because in 9th it’s made specifically clear that modifiers are cumulative, you should resolve all rules that affect a characteristic together. This example suggests that AP ignoring abilities, especially those using the “treat as” language do not actually change the AP and should use the AP value after other modifiers as their trigger.
Worsening AP0 – What does it become?
What does Dour Duty do to AP0? Does it make it AP+1? At the minute, I don’t think this is covered explicitly. It’s not a characteristic with a rules enforced limit like Strength, Toughness, Attacks or Leadership. However there’s a good argument that AP0 is the worst AP in the game, so there’s nothing to “worsen” it to. In addition to that if it did create AP+1 then the stratagem would be functionally equivalent to giving the unit +1 to their saving throws, as this is an effect quite commonly found in other rules I think reducing AP is meant to be distinct from it. I’m hoping a future FAQ will make this clear though as there’s a lot of supposition in all of that reasoning.