d6, d8, d12, d20 weighted mechanics

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.

My bad, I gave this thread a bad title.

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.

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.

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.