Game Design #117: Pre- and post- dice math

Something I've been thinking about lately. I tend to be pretty free with swapping in/out mechanics in my homebrew rules, as long as they achieves the result (probabilities) I desire. 

However, when playing with my kids I've found doing modifiers and math before you roll the dice to be better/clearer. Hmm. That sounded clear as mud. 

Guess I'd better define what I'm trying to articulate:

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Pre-Roll Math (Modifying the Target Number)

Any math (adding/subtracting modifiers etc) occurs BEFORE you roll dice.  You already know the results you are looking for. It usually involves modifying the initial stat or target number.

 
Example: A archer is shooting at a target in cover. It is a tricky shot that needs to be penalised.

You need to roll a 4+ on a d6 to hit. (target/stat)

There is a +2 modifier to this 4+ target number, making it 6.  (modifier+math)

You roll, knowing you need 6s and can ignore the rest. (roll) 

There is a single piece of math - modifying the target number. The individual dice can be quickly be counted or discarded. Masses of dice are no problem - you're just looking for 6s - no mental effort required.

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Post-Roll Math (Modifying the Dice Roll)

Math (adding/subtracting modifiers etc) occurs AFTER you roll the dice.  You are adding and subtracting numbers individually to the already-rolled dice. It involves modifying the results on the dice.

Example: A archer is shooting at a target in cover. It is a tricky shot that needs to be penalised.

You need to roll a 4+ on a d6 to hit. (target/stat)

There is a -2 to the dice rolls. (modifier)

You then roll your dice (roll)

You then deduct 2 from each dice rolled (math)

You are performing a math operation (albeit as simple as -2) from each and every dice rolled, which is then compared to the 4+ target number.

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Geez - this seems like hair splitting!  Isn't this just wording?

Obviously the math above is very simple. Most people, even when the rulebook uses post-dice math wording, will just mentally look at the above situation and go "ah I need a 6" - kinda converting it into pre-dice math on their own.

However as someone who has to grade kids work, the second way is kinda "trickier" question - there's an extra step and more busywork involved.  And we're trying to make dice rolls and rules quicker and more clear.

So - we should just re-word rules so it uses pre-roll math aka target numbers? 

There are other considerations though.

Pre-dice math (modifying the target result) has a disadvantage in that the results (and stats) tend to be more strictly limited to what is on the dice.  

What is "on the dice?" If you use target numbers on a d6, you are limited to stats of 1-6. Or probably 2-5 if you want a chance to succeed/fail i.e. if  a stat/target number is ever 1+ you will always succeed on a d6, on a target/stat of 7+ you will always fail.

I do think modifying target numbers dice tends to work better with bigger dice (my current craze is d12 - gives plenty of stat/modifier variation without the extreme feel of 'swing' of d20). You need 'room' to modify target numbers. I.e. on a d12 you could have stats of 4,5,6,7,8 and leave plenty of room for 1/-2/+1/+2 modifiers etc without hitting the "ends" of the dice.

An example of a limitation of the target number method is by changing the target number it's harder to make crits more or less likely.

Post-dice math tends (in my experience) to be more associated with shenanigans for crits i.e. "you exceeded the 4+ by 2" and exploding dice. These are not a hard and fast rules of course; but more how I see it used in practice.  

I think what I'm trying to say here is there are still advantages and disadvantages for each method, despite "pre-roll math" aka target numbers being more "clean" or streamlined. It's not automatically "best" every time.

The Dice is Right

Regardless of your method, using the right size dice is important, whether you plan to modify the target number or the dice themselves.

D6 are very limited. Most modern games use them in handfuls, adding or subtracting the the dice themselves rather than modifying the dice result or target number:

Example: instead of rolling a 4+ on a d6 and -2, you might roll 4 d6s with 4+ succeeding, then remove 2 dice so you roll less dice, but the target/dice required (4+) remains the same.

This gives the pleasing sensation of chugging handfuls of dice (well, my kids enjoy it) while avoiding the limited scope of d6s. Target number/pre-roll math is closest to this modern method, which you could call "add/remove dice" + "fixed target number" method. Newer GW games like Kill Team and Warcry kinda lean in this direction. You're not changing the number to roll, but the amount of dice you roll.

But why limit things to d6?  d20s, d12s, d10s, d8s, d4s - these are all available in normal department stores or videogame shops like EB Games - it's not the 70s, they are mainstream now (no one thinks you are using them in D&D to summon eldritch forces into the real world) and available for a few dollars. Nerd stuff is mainstream!

My rule of thumb is "if the results/modifiers are regularly going "off the dice" then it's time to upsize your dice. E.g. in my tankmunda game, I've used d6s as I didn't think I "needed" d10s etc - and it felt 'neat' to throw 3 different coloured d6 together which scored to-hit, penetration and location at the same time. But.... if I've got 3+, 4+ and 5+ to hit stats and I have modifiers for cover, range and crew damage, then quite a lot of times I'm going to need a number higher than 6...

Otherwise we end up with GW nonsense where you have to roll a 6 then another number i.e. a target of 7 is a 6 then a 4+, a target of 8 is a 6 then a 6+, etc. An uneccessarily complex two-stage process to deal with a problem that no longer exists.