Tag: study

Because I’m a geek for the Warhammer 40000 universe fiction, I sometimes come across the Warhammer 40K tabletop game.

Now, this is a game of dice. Lots of dice. More dice than an Ork Nob can shake a bashin’-stick at.

And lots of dice-altering stats, too:

In the battles that take hours, dozens of dice are brought to bear. Me, a nerd, thought of only one thing:

What can we do to streamline the game?

Here’s what I found:

The Game Right Now

Stats

Warhammer 40K is a game of tiny model soldiers and monsters. A group of models is a “unit”, which is what acts on the battlefield.

A unit has these stats:

• Name – easily distinguishes what you’re talking about.
• Power – the level of the unit. Counts towards how large an army comprised of units may be.
• Movement (M) – how far a unit may move on the board in a normal turn.
• Weapon Skill (WS) – chance of hitting a target in melee combat. (Really, “Melee Skill”.)
• Ballistic Skill (BS) – chance of hitting a target by shooting at it.
• Strength (S) – how hard a unit hits in melee.
• Toughness (T) – how difficult it is for an attack to do damage to the unit.
• Wounds – health points per model; 0 is the death of the model.
• Attacks (A) – how many melee attacks the model may make.
• Leadership (Ld) – how likely a unit is going to keep fighting after taking losses. (Losing models in a unit can cause the rest of the models to ‘flee’, AKA die.)
• Save (Sv) – what a player must roll to not have their models die when attacked.

Units also have special abilities and weapons. While weapons have Range, Armor Piercing (makes it harder for a target to Save), Strength (in melee, use this or the unit’s Strength, whichever is higher), Damage, and a special effects, these are self-evident in what they might do.

Turns

A single player turn is defined by phases:

• Movement – if a unit can move, it may do so.
• Psychic – special to only certain units in the game. Like shooting, but with your mind.
• Shooting – ranged units fire.
• Charge – units can move again. If they do, they get shot at.
• Fight – all units close enough to enemy units use their melee weapons.
• Morale – for any unit that lost models in the turn, they roll against their Leadership. Failure here can collapse the rest of the unit. (Heard you liked taking losses, so here are some losses for your losses.)

Shooting and Fight are the dice-heavy portions of the game and will be our focus here.

How It Works

Let’s look at the similarities of the Shooting and Fight in how they make models die.

Both phases start by using Ballistic and Weapon Skill (respectively) multiplied by the number of Attacks that can be made in the form of numbers of dice. A success here is when set A of dice roll equal to or greater than the Skill, becoming subset B.

Next, an attacking player must check the Strength of their attacks against the Toughness of the target. What subset B needs to be or greater to changes when Strength is the same or different to the Toughness. Subset B will become subset C.

Finally, the player owning the target units will roll for their Save. The number of dice in subset C is how many dice must be rolled, their face value needing to be equal to or greater than the Save of the target. The number of dice that fall below this value are the number of models to apply the Damage of the attack to the model’s Wound (or “taking a Wound”).

TLDR; An attacker must see if they hit, then see if they harm a target. The target gets a chance to save themselves. If not, models take Wounds.

Clear so far?

My Turn

Looks like we have some formulas to crunch, starting with combining the attacking player’s “did I hit” and “did I harm” rolls.

The Attacker

We’ll ignore the differences between Shooting and Fight phases, instead focusing on only the hit/harm cycle.

For that, the hit roll is determined by the chance of Skill passing a value roll times the number of Attacks.

To Hit = chance Skill * Attack

Easy.

To harm, it gets tricky. We ought to compare the Strength stat of the attacker to the Toughness of the target.

To Harm = (Variable, given Strength compared to Toughness)

This marriage of stats means we can’t have one nice roll for the attacker as it changes every time they pick a different target.

Let’s get a divorce.

If we only consider the Strength of the attacker, the Strength ought to also be considered as a chance roll. Say, for a five Strength, it’s two (five or greater, six) divided by six (six-sided die D6), or 33%.

We’ll need to do something with chance Strength. How about combining it to Skill and Attack?

For that, we can put the passing chance of Skill and Strength together, forming a percentage. This percentage will be low because we’re multiplying percentages, so take 100% minus the low chance we got, thereby betting   Let Attack be the number of dice to roll:

To Hit and Harm = 100% – (chance Skill * chance Strength), per #D6, # from Attack

We’re forgetting the Armor Piercing stat of some weapons. Originally, this would apply to the Save roll of the target. Since we’re trying to divorce the stats of two different units as much as possible, Armor Piercing should apply to the hit-and-harm combination roll:

Single Hit and Harm Roll = ((100% – (chance Skill * chance Strength)) * 6) + Armor Piercing

If a unit can roll dice greater than or equal to the value from the formula above, the attacker has successfully struck.

How does this work? Take an Intercessor Squad, armed with a Bolt Rifle, as example:

One model in the unit is going to fire at a target. Thus, it’s chance of success for a single die (ignoring that it could make multiple attacks) is:

Success >= (6/6 – (4/6 * 3/6) * 6) – 1

>= (1 – (.333)) * 6) – 1

>= (.667 * 6) – 1

>= 4 – 1 >= 3

This example shows we have a 67% chance to succeed on any roll. People like succeeding, so this high chance is perfect for an attacker’s immersion when they get to keep dice on the table. No problem there!

We see how what would normally be multiple rolls of dice distills into a single roll per attack for either ranged or melee combat. Time savings, huzzah!

The Target

We have to keep our target from dying. From the previous section, Toughness is on its lonesome. We also took care of the Save vs. Armor Piercing. Thus, pairing Toughness with Save, we get something like:

Get to Live >= (100% – (chance Toughness * chance Save)) * 6, per successful attacker die

Any failure here will cost Wounds from the Damage of the attack.

Using the Intercessor Squad above and for a single successful die, we get:

Get to Live >= (6/6 – (3/6 * 4/6)) * 6

= (1 – (.333)) * 6

>= .667 * 6 >= 4

If we don’t get a four on our dice, our own Intercessors will die. Sad day 😥

Still a good day, though, since we can provide a base stat to our unit on what it must roll to survive being attacked!

So we’re looking at a 3+ to attack and a 4+ to live. The numbers boil down to a 33% chance of Wounding a model (66.7% chance of a successful attack roll multiplied by a 50% chance to fail a saving roll).

But again, only two rolls are needed to determine an outcome from end to end, compared to three previously, and with a lot less mental math of comparing attackers to targets.

So Where Do We Go From Here?

I have a confession…

I didn’t playtest this system.

It’s a shame, I know. You know. Playtesting would be the next step. This could be done with Excel simulations, seeing what the typical outcome of this system is compared to the actual game.

There’s a concern already that we aren’t removing enough models, the chance of Wounding being a little low. That, and how can we leverage the Power of a unit? Can it be added to rolls or the difference between attacker and target be applied? I don’t know yet. Merely, it wouldn’t make a lot of sense for a tiny bug (yes, these are in the game) to survive being stomped on by a giant robot.

Doing research for this post, I also found fun numbers and percentages when using a D20 (20-sided dice). The result made calculating roll value requirements a lot easier when different weapons were applied to different units. An article here could be forthcoming with a proper investigation.

Finally, consolidating the stats of a few units is in order. That’d allow for a few examples of simpler, streamlined play.

That’s it! What have you done to improve games in your life? I hope this mod is an inspiration to look at things through a lens of “how can this be made into something new, maybe better?” Cheers for now!