Dungeon Crawler dice system and odds

So my recent Dungeon Crawler game (as of yet unnamed, but probably something with Crystals – EDIT: named it Glowquest) has this for a combat dice system:

Well wait, I should talk more about the game a bit first. The idea is to strip away all the RPG elements that a lot of combat focused games have (D&D 4th edition was the worst offender, but really D&D in general is pretty light/unsupportive on non-combat actions). You choose a Race and Class and various equipment to make a “build” that interests you. That might scare about people who like narrative games, but hey that’s what Fickle RPG is for, this dungeon crawler is about kicking doors and taking names, Icewind Dale CRPG style (or the hundreds of modern run-based roguelikes).

I also wanted to use the Advanced Heroquest tiles…because they are beautiful and fun and bring back a flood of memories for me. Anyway this post isn’t about my childhood, it’s about the dice system.

Roll 3D6. The two highest results become the to-hit roll and the lowest result is the number of Surges available. This means you will have between 1 and 8 Surges.

If there is a tie for lowest result, add +1 Surge for each tie. For example rolling 5, 3, 3 would make a to-hit roll of 8 (5+3) and gives you 4 Surges (3+1). Another example would be rolling 5, 5, 5 which gives a to-hit roll of 10 (5+5) and 7 Surges (5+1+1).

If the total to-hit roll is greater than or equal to the target’s Grit, the attack was successful, otherwise the attack missed. Some Activators can modify the to-hit roll to turn a miss into a success.

Grit is basically Defense, except one of the class roles is called Defense. Not sold on the name, might do Agility, Resilience, Endurance, Evasion, or Dodge instead or something.

I’m happy with this dice system concept. Before I was trying D12 or 2D12 (so you get 2 attacks all the time) to hit and D4 or D4+2 for Surges, but yeah, that might seem fine on paper but felt awful to roll. I hate D4s. I imagine using a D12 numbered 1-4 three times (like this) would feel better. But yeah, once I thought up the 3D6-use-lowest system I got super excited and really dove back into the dungeon crawler game idea, which has been rattling around my head for the past 3-4 months.

Odds and Statistics
As I was starting to hash out Activators that you can spend Surges on, I wanted to take a look at the odds of everything. So far I’m considering having Activators cost 1-5. But I needed to know how likely 5 was. What about how likely the max 8 Surges is? And so on. I also wanted to compare 3D6 drop lowest to a flat 2D6 in terms of the to-hit chances. I knew it’d be higher than the average of 2D6, but how much higher?

Here’s a bunch of math results:

SURGES:
Surge 1: 16257 (32.51%)
Surge 2: 14823 (29.65%)
Surge 3: 9426 (18.85%)
Surge 4: 5403 (10.81%)
Surge 5: 2521 (5.04%)
Surge 6: 1142 (2.28%)
Surge 7: 213 (0.43%)
Surge 8: 215 (0.43%)

SURGES where lowest ties add +2 instead of +1
Surge 1: 16318 (32.64%)
Surge 2: 10121 (20.24%)
Surge 3: 10208 (20.42%)
Surge 4: 5933 (11.87%)
Surge 5: 3548 (7.10%)
Surge 6: 2041 (4.08%)
Surge 7: 1123 (2.25%)
Surge 8: 232 (0.46%)
Surge 9: 235 (0.47%)
Surge 10: 241 (0.48%)

HITS (3D6 drop lowest):
Hit 2: 227 (0.45%)
Hit 3: 650 (1.30%)
Hit 4: 1627 (3.25%)
Hit 5: 2809 (5.62%)
Hit 6: 4423 (8.85%)
Hit 7: 6327 (12.65%)
Hit 8: 7879 (15.76%)
Hit 9: 8474 (16.95%)
Hit 10: 7734 (15.47%)
Hit 11: 6188 (12.38%)
Hit 12: 3662 (7.32%)

Standard 2D6 odds:
2 2.78
3 5.56
4 8.33
5 11.11
6 13.89
7 16.67
8 13.89
9 11.11
10 8.33
11 5.56
12 2.78

What does this all mean? Well, many interesting things. Getting 5 Surges is equivalent to getting a “standard” D&D style critical hit of 20 on D20. So rare. Perhaps too rare. If I try the approach of lowest ties (such as rolling 5, 3, 3) adding +2 bonus Surges instead of +1, this improves from 5% to 7%, but also makes the maximum 10 Surges, which is quite a few (and also extremely rare – anything over 7 or 8 is).

The game has an idea of “Fate Points” (again name likely to change) which are a limited resource each hero has that can basically be spent during an expedition as extra Surges. So tweaking those numbers might affect what dice system I use (whether ties are +1 or +2) and how I scale the Activators.

But what I’ve done first is taken a step back and thought: what do I want the players to do each turn. How do I want the game to feel? Basically I want them to be able to fairly reliably hit, and do 2-3 cool things a turn.

The +1 bonus Surge on ties seems a lot more intuitive: you have 1 tie, so you get 1 bonus, compared to +2. I also like the narrow 1-8 Surge range instead of 1-10. How it boils down is for +1 on ties you have a 62% chance to get 1-2 Surges, and 81% chance to get 1-3 Surges, so only 19% chance to get 4+, 8% chance to get 5+. When put that way, a 1/5 chance to get 4+ Surges, that doesn’t actually seem that bad, and 8% for 5+ is higher than a standard D&D crit of 1/20.

As for hitting, the odds are a lot better with 3D6-drop-lowest compared to flat 2D6. Basically the average goes to 9 from 7. Which means base Grit/Defense will have to be bumped up a lot, because getting a 7+ on 3D6-drop-lowest is literally an 80% chance. Drops to 68% for 8+, and 50/50 (well, 52%) for 9+. Then 10+ = 35%, 11+ = 20%, 12+ = 7%. That’s before any Activators as well. Which means it’s really, really easy to hit, and half the spectrum of Grit is more or less an auto-hit. Seems like base Grit should be 8, easy to hit/squishy guys are 7, and Defense roles are 9

And that’s okay! I like hitting a lot in games. There are many defensive layers and damage reduction/absorption that players can stack on. Damage itself is a flat value based on the weapon (and potentially boosted by Activators), so it’s fairly easy to calculate how soon you’ll die.

All in all a useful exercise to model out.

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