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Dice mechanic. Need math help and opinions.

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Anonymous

Hi people.

I'm working on a tile laying solo dungeon crawl. It has RPG elements, as the characters will increase in skill and what not. I'm an artist and designer, but not a mathematician. (As will become quickly apparent)

I desperately need opinions about the mechanic I'm using for attribute and skill checks. I need to know if it's going to provide variable enough results to represent both high skill and low skill characters. I'm using six sided dice. Here's how it goes:

Skill checks:
Each skill has a value from 1-5, which corresponds to a d6. 1 is no skill, and 5 is rather great.

Your skill level tells you how many dice to roll. From these dice, you pick the die with the highest value. Every 6 rolled after the first nets you an additional +1 to your final total.

You then add the associated attribute value to the result for a final score.

I.E.: The skill is climbing, and has a value of 3d6. The associated attribute is REFLEX. You roll 3d6, and pick the highest. Let's say the roll was

2, 4, 3.

You pick the 4, and then add the value for REFLEX which is 3. The final total is 7.

If the roll had been 3, 6, 6, then you would pick the 6, add 1 for the additional 6, and then add the REFLEX of 3 for a grand total of 10.

Here's the stickler - all skill, attribute, and combat rolls are opposed. What I mean is that you'll be competing against a similar roll to represent your opponent. Combat works just like the roll I described above. Dice for your opponent are rolled in the same fashion. You subtract the lower total, from the higher total. The "loser" takes the difference in wounds. Armor subtracts from the total difference in the rolls, after it is determined who "won" the round.

EXAMPLE of COMBAT

Hero:
Skill 3, Reflex 3, leather armor (Takes 1 hit)

Giant Rat:
Skill 1, Reflex 3, no armor.

Round 1

Hero rolls:

2,3,1. Uses the "3", adds a Reflex of 3 for a total of "6"

Rat rolls:
1. Uses the "1", add a Reflex of 3 for a total of "4".

Rat takes 2 wounds.

On the second round, the rat wins somehow, and beats the Hero's roll total by 2. 1 is subtracted for the Hero's leather armor, so the Hero only takes 1 wound of damage.

I'm using d6 here, because I *like* using d6. I wondering however if I should move to d10, to provide a greater variation in the results. With a d6, I may find that the results are too predictable. I'm wondering if that rat is not going to have any chance at all of hitting the hero once the hero gets up to the higher skill level. (Unless he surpises him) A d10 may allow that rat to get lucky. If I moved to d10, I could say that a result of "10" nets an additional +1 to the total, or perhaps even an additional die altogether. if I go with a d10, what would be a decent number of dice to assign to a character's skill for basic proficiency? 3 dice? 4 dice?

Anyway - sorry for being so chatty for a new guy. I'd be grateful for your opinions and suggestions.

Respectfully submitted
Falloutfan

larienna
larienna's picture
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Joined: 07/28/2008
Dice mechanic. Need math help and opinions.

First have you checked my probability tables:

http://www.bgdf.com/files/My_Uploads/Larienna/diceprob.pdf
http://www.bgdf.com/files/My_Uploads/Larienna/d10prob.pdf

It is not an exact solution but it can help you. "Heavy gear" was using a system which looked almost like this.

Now since you are using opposing rolls, it is a bit more complicated to calculate, but calculating probabilities is a bit less important.

For dungeon crawlers, there are some things to consider.

First, you must make sure that you offensive roll give generally higher results than defensive rolls. Else, the balance will 0 and there will be a lot of situations where there is no hit no damage.

Second, hindering the monsters strenght or probability to hit is also a good idea considering that few heroes are fighthing a lot of monsters. (this is why in hero quest, monsters defend on a black shield). Else, you should make sure the heroes together has about the same number of Hp than all the monsters in the dungeon to keep the balance between forces.

markmist
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Joined: 12/31/1969
Dice mechanic. Need math help and opinions.

I don't see your situation as a problem and I would stick with the D6. A Level 5 skill SHOULD wipe the floor against a Level 1 rat. You want some predictability or else it will not matter enough to get stronger and winning will come down to mostly luck.

To combat this, why not have the option of being attacked by more lower level creatures at once or just make the monsters tougher as the game progresses? Once you reach level 5 in a skill, you will be facing harder creatures and therefore the results will be less predictable.

D6 is a better choice because they are more readily available and are cheaper if you plan on publishing this game later on.

erael
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Joined: 12/31/1969
Dice mechanic. Need math help and opinions.

I think it sounds clever and will provide lots of variation, assuming that you always want the small guys to have at least a shot against the big guys (which I assume you do). 2 things I'd ask:

1. Do you really need to have attributes being added to everything? Couldn't you just add the attributes as dice?

2. Why not have each additional die at the highest number add +1? So if you roll 4,4,4 it's as good as 1,2,6?

I think some combination of (1) and (2) might make for slightly better distributions of outcomes (depending on what you're trying to acheive), but I don't think there's any problem with what you have.

Well--if you roll 3 dice and have a Reflex of 3, you're going to get a number between 7 and 9 some very large portion of the time your way. If you rolled 6 dice instead (with the +1 for each additional die at the highest level), you'd have something lower with more variability--probably could be between 4-7 with the same confidence interval. So it might introduce slightly more variation.

Anonymous
Dice mechanic. Need math help and opinions.

Larienna wrote:
First have you checked my probability tables:

http://www.bgdf.com/files/My_Uploads/Larienna/diceprob.pdf
http://www.bgdf.com/files/My_Uploads/Larienna/d10prob.pdf

It is not an exact solution but it can help you. "Heavy gear" was using a system which looked almost like this.

Now since you are using opposing rolls, it is a bit more complicated to calculate, but calculating probabilities is a bit less important.

Those are interesting. Thanks for providing the link. It's easier to check a table rather than roll 5d6 a hundred times.

Larienna wrote:

For dungeon crawlers, there are some things to consider.

First, you must make sure that you offensive roll give generally higher results than defensive rolls. Else, the balance will 0 and there will be a lot of situations where there is no hit no damage.

Good point, I'll bear that in mind while play testing. I think I'll extend the skill ranges a bit. I do want there to be SOME hits that cause no damage, as that would be useful for influences that don't need to penetrate armor. Too many hits like that however, will lead to boredom.

Sincerely,
Falloutfan

Anonymous
Dice mechanic. Need math help and opinions.

erael wrote:
I think it sounds clever and will provide lots of variation, assuming that you always want the small guys to have at least a shot against the big guys (which I assume you do). 2 things I'd ask:

1. Do you really need to have attributes being added to everything? Couldn't you just add the attributes as dice?.

My thought here was that being faster - (Having a higher reflex) would allow "fast" characters to shine. It makes the player choose between moving fast or having better protection. Metal armors will slow the character down by reducing reflex. This is especially interesting, I think, when initiative is computed. Initiative for a situation is SENSE # of dice, + REFLEX. This I hope will allow faster characters to duck out of combat before a heavier opponent can really get going. It's an advantage the first round of combat, where the faster and more alert character can get a first strike, but it diminishes directly afterwards when you have to go "toe-to-toe". The higher inititiative character attacks or withdraws first. If you choose to attack, then you pick the range you wish to use. From farthest to nearest, they are: Spell; Bow; Melee; scroll. You get a free attack, and then the round starts in earnest.

erael wrote:

2. Why not have each additional die at the highest number add +1? So if you roll 4,4,4 it's as good as 1,2,6?

That's intriguing...I hadn't thought of that. I'm going to kick that around a bit and see what I come up with.

erael wrote:

I think some combination of (1) and (2) might make for slightly better distributions of outcomes (depending on what you're trying to acheive), but I don't think there's any problem with what you have.

Well--if you roll 3 dice and have a Reflex of 3, you're going to get a number between 7 and 9 some very large portion of the time your way. If you rolled 6 dice instead (with the +1 for each additional die at the highest level), you'd have something lower with more variability--probably could be between 4-7 with the same confidence interval. So it might introduce slightly more variation.

I'm going to play around with those distributions a bit, to see what I come up with. Thanks for the tips.

Sincerely,
Falloutfan.

Anonymous
Dice mechanic. Need math help and opinions.

markmist wrote:
I don't see your situation as a problem and I would stick with the D6. A Level 5 skill SHOULD wipe the floor against a Level 1 rat. You want some predictability or else it will not matter enough to get stronger and winning will come down to mostly luck.

You make a good point here. I guess that what I wanted was for the rat to get a lucky hit once in a great while. It would only be a small nick, but it would still be something. But you're right, If I play with the numbers too much, it'll be just a "luck fest". Right now, the rat may get a little nibble in on an advanced character just occasionally. That's probably good enough.

markmist wrote:

To combat this, why not have the option of being attacked by more lower level creatures at once or just make the monsters tougher as the game progresses? Once you reach level 5 in a skill, you will be facing harder creatures and therefore the results will be less predictable.

D6 is a better choice because they are more readily available and are cheaper if you plan on publishing this game later on.

I think that in practice you're going to be right - smaller creatures will have to band together to have any chance of success. I was planning to have the smaller creatures appear in greater number later on. There are also some pretty tough creatures that come up later. Multiple attacks, high reflexes, immunities, and what not. I think Ill stick with the d6 as you suggested.

Thank you for your suggestions.

Sincerely,
Falloutfan

Schmendrick
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Joined: 12/31/1969
Dice mechanic. Need math help and opinions.

Using "+1 for each matching highest die" yields average rolls of:

3.5, 4.64, 5.29, 5.75, and 6.11
for 1, 2, 3, etc. dice.

It's notable that with that system, 2,1,1,1 is worse than 1,1,1,1.

The probability curve for "best of X dice" is rather sharp (probably what you want), but adding the "matching dice" element helps keep the squeeze "shut" the low end of the curve.

Schmendrick
Offline
Joined: 12/31/1969
Dice mechanic. Need math help and opinions.

falloutfan wrote:
I think that in practice you're going to be right - smaller creatures will have to band together to have any chance of success. I was planning to have the smaller creatures appear in greater number later on. There are also some pretty tough creatures that come up later. Multiple attacks, high reflexes, immunities, and what not. I think Ill stick with the d6 as you suggested.

You may also want to consider a +1 for each additional creature, or depending on how big mobs will be, +1 for each die that meets or exceeds the number of creatures (so every 1 counts as +1 for a "group" of 1, and every 1 OR 2 counts as +1 for a pair of creatures, etc.) That way each member of a group of X creatures gets a +X/6 bonus (per die) to its check.

Anonymous
Dice mechanic. Need math help and opinions.

Schmendrick wrote:
falloutfan wrote:
I think that in practice you're going to be right - smaller creatures will have to band together to have any chance of success. I was planning to have the smaller creatures appear in greater number later on. There are also some pretty tough creatures that come up later. Multiple attacks, high reflexes, immunities, and what not. I think Ill stick with the d6 as you suggested.

You may also want to consider a +1 for each additional creature, or depending on how big mobs will be, +1 for each die that meets or exceeds the number of creatures (so every 1 counts as +1 for a "group" of 1, and every 1 OR 2 counts as +1 for a pair of creatures, etc.) That way each member of a group of X creatures gets a +X/6 bonus (per die) to its check.

Great idea - I was thinking something like that myself. It creates a consideration for additional attackers, without needlessly complicating things. Also, when a creature dies, it's influence is easily subtracted. This addresses the whole multiple attackers thing without getting too unwieldy. I've always thought that multiple attackers should be handled without adding tons more dice rolling.

Multiple attackers are tough - even on a person who is very formidible one-on-one. I'll relate an example, albeit an lame one: My daughter was having a birthday party, and there were about 15 kids there between the ages of 8 and 10. At one point, they wanted to go outside, but I wouldn't let them. The little buggers swarmed me! (I'm a nice friendly, easy going guy) About 6 of them glommed onto my legs, and literally dragged me to the ground, the rest then proceeded to run off during the chaos. It was nuts. Anyway, the point I'm trying to make is that if those had been Goblins or some other little critter, I would have gotten a few of them but the rest would have had me for lunch. That was a very enlightening little melee there. It's probably one of the funniest things that has ever happened to me.

Respectfully

Falloutfan

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