# d6, d8, d12, d20 weighted mechanics

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releppes
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Joined: 09/17/2010

Take a d12 die and weight it as such:

{Human, Human, Human, Human, Human, Orc, Orc, Orc, Orc, Elf, Elf, Elf}

That's a 5/12 change of rolling Human, a 4/12 chance of rolling Orc, and a 3/12 chance of rolling Elf.

OK, I think you know where this is going.

Health stats are as follows:

Human = 12
Orc = 15
Elf = 20

In a PlayerA vs PlayerB battle, PlayerA rolls the weighted die and scores a hit if the result depicts PlayerA's race. Any result other than PlayerA's race is a miss. PlayerB takes damage by losing one health per hit.

Example:

PlayerA is Human (ie: health=12)
PlayerB is Elf (ie: health=20)

PlayerA has a higher chance to hit PlayerB, however PlayerB starts with more health.

I've not run this through a simulation yet, but the odds should match up where each race is equal.

releppes
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Joined: 09/17/2010
Alternative using d6

I suppose this Rock, Paper, Scissor example could have been played using a d6 as well. Weight the d6 as follows:

{Human, Human, Human, Orc, Orc, Elf}

And assign starting health as:

Human = 10
Orc = 15
Elf = 30

The rules apply as before. Player rolls die and scores a hit on the opponent if result is Player's race.

The d12 example is slightly nicer in that the starting health for all three races are closer in value.

Game progression may be slow when using a single die per turn. The probabilities of a hit are only 1/2, 1/3, and 1/6. My thinking is that the game should scale to using multiple dice per turn (ie: roll 3 dice to do damage 0-3).

releppes
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Joined: 09/17/2010
One more example using d20

I've still not tested the balance of the system, but heck, here's one more example using a d20. Weight the d20 as such:

1-6: Dwarf (probability = 6/20)
7-11: Human (probability = 5/20)
12-15: Orc (probability = 4/20)
16-18: Elf (probability = 3/20)
19-20: Ent (probability = 2/20)

Assign starting health as such:

Dwarf = 10
Human = 12
Orc = 15
Elf = 20
Ent = 30

Each Player rolls the dice. The Player scores a hit for every die showing their race. The opponent take the damage of one health per hit.

stubert
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Joined: 01/26/2009
R-P-S?

I may be misunderstanding, but where does the R-P-S mechanic fit in here?

Is it that Humans only hit Orcs, Orcs only hit Elves, and Elves only hit Humans?

releppes
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Joined: 09/17/2010
stubert wrote:I may be

stubert wrote:
I may be misunderstanding, but where does the R-P-S mechanic fit in here?

Is it that Humans only hit Orcs, Orcs only hit Elves, and Elves only hit Humans?

What I gave was examples of balanced battle mechanics. The RPS concept disappeared when I implied classes could attack each other.

The example of RPS you gave should suffice. I suppose one could say each class could attack anything but itself. Would that qualify for a RPS mechanic?

Because the d20 mechanic I gave has 5 unique races, I think it has the most promise for an interesting RPS design.

rcjames14
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Joined: 09/17/2010
Applications

What kind of overall game do you plan to apply this weighted die system into?

Off the top of my head, I can think of four game designs: a RPG where the players are the characters, a battle-miniatures RPG game, a customized deck RPG card game and a Euro style fantasy based board game. But, I'm sure there's more.

The genre will largely dictate whether you need 3 races, 5 races, 10 races or X number of races. However, in each of these genres, the best designs will use the weighted die results as a framework for resolving conflict between these races. Not as a deterministic R-P-S engine where one race always defeats another.

Instead, imagine a system similar to your previous post where there are melee, ranged, cavalry and magic attacks. And, merge that with the suggestion that I made about having different types of dice. Under those circumstances, humans may get a special human set of dice with an roughly even distribution of attacks. The orc dice may be weighted towards melee, the elf dice towards range and the centaurs towards cavalry. Magic attacks may be considered a special case with certain races capable of using magic results in different ways.

In this case, the conflict resolution occurs through attack types and the races are geared to favor certain ones over others... so all races can attack all races and you end up with a framework which can accommodate X different races.

releppes
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Joined: 09/17/2010
No plan

I didn't have any game plan for this weighted dice mechanic. At the moment, it's been an investigation into possibilities. I've been using game examples to help visualize the concept.

Here's another weight problem I'm working on. It's a combination of all three d6, d12, and d20 weight schemes. Consider this:

d20: {A,A,A,A,A,A,B,B,B,B,B,C,C,C,C,D,D,D,E,E}
d12: {B,B,B,B,B,C,C,C,C,D,D,D}
d6: {A,A,A,C,C,E}

Assign weights as such:

A(10), B(12), C(15), D(20), E(30)

As for how the weights are used, that depends on the game. If the weights are used in an attack, then rolling the d12 and d6 will produce the value of 5 on average for any particular weight. Meaning if you roll 3d12, you'll score an average of 15 for weights B, C or D. The d20 will produce the value of 3 for any particular weight. So 5d20 will give on average a value of 15 for A, B, C, D or E. Fascinating? Well, I thought it was interesting. The output for each die produces a nice distribution around the average.

Unfortunately, the weighted average does not necessarily mean each weight is equal. This I learned. However, if the weight is used as a defense buffer (ie: health), and attacks are counted as 1 point each, then I think the system really is balanced.

Consider the d6: 3 out of 6 times you'll get a hit with A. So 60d6 would on average produce 30 hits for A. Likewise, 60d6 would give on average 20 hits for C. If one wanted an even battle between A and C, give A=X health and C=X(3/2) health. Hence the weights provide an even balance.

What's interesting about the above weight scheme is that d20 relates to both d12 and d6. Also, d12 and d6 are related via the weight for C. If one wanted a slightly more interesting battle mechanic for attack vs defense, a player would choose the appropriate d12 or d6 die for attacking (ie: the one having the attacker's race), and the defender would roll the d20 in defense. The attacker counts hits for each d12/d6 die showing their class, and the defender gets a block for each d20 die showing the defender's class. As you may guess, the system easily scales for multiple d20, d12, and d6 dice. The attack vs defense is equal when it's 3d12 vs 5d20 or 3d6 vs 5d20. Note: If you're class is C, then it doesn't matter if you use d12 or d6 dice. The odds are the same.

Since the d20 has a weighted average of 3 and the d12 and d6 have a weighted average of 5, it's nice to pick multiple dice strategies that take advantage of that. I was thinking a system where one uses 4d20, 4d12, and 4d6. The attacker would use the d12 or d6 dice and the defender would use the d20 dice. In such a case, the attacker would have a 5/3 advantage over the defender and the hits would be in the range of 0-4.

Another idea I had was using the relationship of the d20 vs d12 vs d6 above to craft an R-P-C mechanic. Say one race used d20 dice and had five types of attack. The d12 and d6 races had fewer attacks, but they have a (5/3) advantage over d20. I do not think such a system is balanced. I thought it novel if each player was assigned unique dice, both in appearance and weight scheme, yet balanced in battle.

releppes
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Joined: 09/17/2010
A completely balanced system!

releppes wrote:
...Here's another weight problem I'm working on. It's a combination of all three d6, d12, and d20 weight schemes. Consider this:

d20: {A,A,A,A,A,A,B,B,B,B,B,C,C,C,C,D,D,D,E,E}
d12: {B,B,B,B,B,C,C,C,C,D,D,D}
d6: {A,A,A,C,C,E}

Assign weights as such:

A(10), B(12), C(15), D(20), E(30)

...

In addition to the d6, d12 and d20, consider these two d8 schemes:

d8: {B,B,B,B,B,D,D,D}
d8': {A,A,A,A,A,A,E,E}

With A, B, D and E having the respective weights 10, 12, 20 and 30. This too fits nicely into the multi-dice weight scheme. The weighted average for the d8 works out to be 7.5. Thus making all four weighted dice balanced on average if:

2d8 = 3d6 = 3d12 = 5d20

What does that mean? It means you stand equal chance to roll a B from 2d8 or from 3d12 or from 5d20.

Another interesting property is what happens when you roll one of each die? How does this affect the weighted average? It just so happens they balance out:

(avg=3.0) d20: A_B_C_D_E
(avg=5.0) d12: __B_C_D__
(avg=7.5) _d8: A_______E
(avg=7.5) _d8: __B___D__
(avg=5.0) _d6: A___C___E

NOTE: I use two separate d8 dice to represent the BD and AE weights.

Which means if we roll 15 dice (3d6 + 2d8 + 2d8 + 3d12 + 5d20) we'll score on average 45 for each weight A, B, C, D and E. However the distribution for each of the 5 weights are quite different:

http://anydice.com/program/356

So what eh?

Maybe it's just me, but I find it interesting that 5 completely different dice both in weight and probabilities (counting the d8 dice twice because they're unique) when used in combination can produce an identical average for 5 completely different weights.

I suppose this could be made into a game somehow. From a marketing perspective, I would think it novel that a CUSTOMIZED dice set include 3d6 + 2d8 + 2d8 + 3d12 + 5d20 dice (15 total) where 5 symbols across all dice in varying weight schemes. Yet when the dice are used together can produce an identical weighted average for all symbols.

releppes
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Joined: 09/17/2010
Battle mechanics

Well, I couldn't resist.

Since the d20 has all the weights, it's not really needed when computing the average. Taking it out will of the 3d6 + 4d8 + 3d12 + 5d20 equation will drop the average outcome from 45 to 30. And since the d20 will produce an average of 3 for each weight, 10d20 will also give an average outcome of 30.

Let the battle begin: http://anydice.com/program/357

As seen, the average result of each battle is always 0. But the distribution around 0 is slightly off. It tends to favor the the d6+d8+d12 combination. So getting back to an earlier comment on an attack vs defender scenario, it's nice to have a player choose a combination of d6+d8+d12 dice to attack, and have the defender roll a multiple of d20 dice to defend. For an even battle (based on average), the attacker is slightly favored to win. To give more bias to the attacker, all one needs to do is remove one or more d20 dice from the defender.

How does one use the weights?

I've been using the term weight in two different contexts. In one context, the weight is the value assigned to a particular symbol (ie: C=15). In the other context, weight refers to the probability of each symbol for a particular die (ie: d6 -> C=1:3). I should point out that the two contexts are NOT interchangeable. Getting a B on a d8 is 5:8, but getting an B on a d12 is 5:12. In both cases, B has the same value, but different weight in probability.

The symbol weights are the magic numbers 10, 12, 15, 20 and 30. It means that instead of pips on a die represent a sequential count, the 5 symbols produce outcomes in multiples of those magic numbers. If going for symbol A, you'll always get an output value in multiples of 10.

Of the magic numbers, 30 being the most difficult to get, also has the highest payout. On average it might be the same as 10, but 30 as a higher payout in the long run. For that reason, the weights, although equal in average, are not really equal in the long run. The higher the weight, the better payout in the long run (ie: after multiple rolls).

A different method of using the symbol weights is to give them all a payout of 1 (ie: count them like pips). That way, the only way the weights differ is in the probability of them occurring (ie: A will occur more frequently than E). In a simple combat system, if each player was to be represented by one of the symbols and their initial starting hit points was set to their respective symbol's weight (ie: A=10). Then a battle between all characters is evenly balanced. 'A' has low hit points but a high probability to hit against 'E' with high hit points and a low probability to hit. This battle "on average" is an even match. Even in the long run, 'E' does NOT stand a better chance to win. This also has the advantage of producing a normalized output:

http://anydice.com/program/358

In summary: This is a nice easy system to fine tune and tweak. It uses 5 different dice, both in geometry and weight and provides unique probability outcomes for 5 different types, and when used together provides a balanced system between all 5 types.