Weighted dice mechanics

You know, with this system, short of being at infinity rolls (which is exactly equal), magic is by far the better choice.

see: http://anydice.com/program/33c and look at the graph tab. As you can clearly see magic puts out more damage, more reliably. Sure there is the bigger chance of "whiffing" but the amount of damage put out per hit is far greater and makes up for it. This is over 100 rolls, but modify it for 10 or 5 and the pattern remains, magic is just better at doing damage.

The only time I wouldn't take magic was if what I was trying to kill had <6 health. other than that, it's strictly the better choice.

Sure, when the battle goes on it's similar in results...but it seems that in any game most battles wont be 12 dice rolls.

Let's break this down into a table, vertically is the number of rolls in the combat, and the table is the % chance to deal 12 damage

Rolls....... melee........pierce..........magic
..4.............0.............1.23............13.9
..8...........14.5...........25.9...........39.5
..12.........61.28........60.69.........61.87
..16.........89.49........83.41.........77.28

(sorry this is ugly)

And if you want to compare, try doing it with n damage and k rolls. As long as n>k, magic is better. The break even point on all 3 attacks is when the number of rolls in the combat is the same as the damage required to kill the monster (this goes back to damage per roll = 1). Since I imagine most combats with a 12 health monster will last less than 12 rolls (assuming this game isn't malicious), and most battles with a 6 health monster last less than 6 rolls, and most battles with a 500 health monster last less than 500 rolls, I will be rolling magic.

You are correct though, i figured it wasn't until infinity this was the case, the it is still at a fairly high number of rolls until melee catches up.

Alright, Figured out my errors, Please ignore my last post, it was woefully wrong. My results match up exactly with yours. The Mage is a clear favorite... (I also changed my terms to yours, archer makes sense).

Mage=magic; Archer=pierce; Knight=melee;

Knight vs. Mage
Over 100000 battles with 30 starting health:
44130/52815/3055
Percent Knight Wins: 44.13%
Percent Mage Wins: 52.815%
Percent Draw: 3.055%

Archer vs. Mage
Over 100000 battles with 30 starting health:
45345/51760/2895
Percent Archer Wins: 45.345%
Percent Mage Wins: 51.76%
Percent Draw: 2.895%

Archer vs. Knight
Over 100000 battles with 30 starting health:
49767/45912/4321
Percent Archer Wins: 49.767%
Percent Knight Wins: 45.912%
Percent Draw: 4.321%

I'm working a system where if all three fight each other who wins, just because I'm curious.

Again, really sorry about the above posts...gotta double check your work right :D

I figured out why and it makes sense. A lot of it has to do with the starting health. If it is a multiple of 6 it helps the mage (obviously). Try running your scenario with 30 as the goal and then run it was 32. The Knight gains some ground in the 31 scenario since that extra point of damage may as well be 6 to the mage.

That said, the reason is the the mage get's a benifit for finishing quickly. In the battle if it is tied at 6 health, all it takes is one hit by the mage and it's over, even though the knight is going to get to 0 at the same rate, once it's over it's over and the percentages go out the window. So even if over 6 rolls it's the same, if the game ends in 2 because the wizard hits a home run, it's over, even if the wizard would have missed every one of the last 4 rolls he already won.

That's why anydice was misleading, it was always giving the Knight his remaining rolls, when really once the wizard one hits him, he doesn't get the rest of the dice to "catch up" the wizards big hit potential.

That said, some really interesting things happen when you start having 3 and 2v1 fights (something I configured my app to run). For instance, since Mage vs Knight is so clearly biased towards the Mage I assumed a Mage vs Knight vs Knight fight, were each fighter attacks the other two each round until they are dead would have the mage winning by a huge amount as well but the knights actually fare better than the Mage here..

This was weird to me until I realized what is happening. Having two knights on the mage effectively doubles his per round damage compared to only have one knight against him. Whereas from the knights point of view, having the extra knight attack him is negligible compared to the mage in the first fight (a 33.33% increase from the first scenario).

I actually really like this system of combat. there are lots of nuances here and although strait up magic is more powerful. seeing how easy it is to combat by teaming up or applying small bonuses to the damage makes it a great system overall.

For instance, adding +1 damage to each attacker makes the knight 50% more effective and makes the mage only 16.67% better. So you can help close this gap with clever in game bonuses and the like.

If there are any scenarios you want to see the stats on let me know, i can test them quickly.

You have to stop looking at average damage per turn, it's irrelevant in an actual battle. This is why the mage always wins, and the archer is 2nd best. Instead of looking at average damage, Start with 6 health each and look at the % chance to end the fight round by round.

----------- Mage vs Knight
Round 1: 16.67% -- 0%
Round 2: 16.67% -- 0%
Round 3: 16.67% -- 12.5%
Round 4: 16.67% -- 31.25%
Round 5: 16.67% -- 50%

Sure in the long run the odds of the knight winning go way up because he's more consistant, the mage is basically rolling for the home run every round. But if the mage hits in the first 2 rounds, it's over. Even if the knight in the long run is more consistent; he has 0% chance of winning until the third round, and even in the third round, the mage is still more likely to have rolled a 6 by now than the knight is to have rolled a hit three times.

Does this help explain it?

::EDIT:: those numbers above are actually a little low for the mage, who has a better chance round by round of course, but the point stands, the mage has the ability to win the game in the first round rounds before the other fighter even has a chance to catch up, this is the mage's advantage.

There are a number of game designs which have implemented a weighted die rolling mechanic. Axis & Allies, Memoir44 and Cookie Fu are three games that immediately come to mind for adjusting the probabilities of success on a six sided die.

In the Axis&Allies board game, they utilized six sided dice pips and assign a different number to each type of unit for attack and defense. Whereas Memoir44 created customized dice similar to your melee, range, magic mechanic. Infantry appears twice, cavalry and artillery once, a grenade once and a blank side once. Cookie Fu introduced the idea of collectible dice, so each die in the set has a slightly different weighting of basic punch, throw and kick sides.

Axis&Allies and Memoir44 resolve success slightly differently. A&A requires that you match the strength of the actor. Memoir44 requires that your die result matches the target. But, they both make a one to one equivalence between success and damage. If you hit, the opponent removes one unit. Cookie Fu allows you to take your die results and perform 'maneuvers' with them which interact roughly on a rock-paper-scissors level. But, some dice may be combined for more powerful maneuvers and each maneuver inflicts a different level of damage.

Both A&A and Memoir44 were remarkable hits. Cookie Fu is an obscure game that flopped completely based primarily upon its very limited strategic nature. But, for a while, I have been contemplating a way to reinvent a Fantasy RPG with weighted dice rolling as its principle mechanic. So, Cookie Fu remains an interesting failure to learn from and your topic reminds me of this long-standing backburner project.

As I see it, there could be some very interesting room to design in the area of customizable weighted dice rolling. By combining elements of Memoir44 and Cookie Fu with a more robust resource and maneuver mechanic, I think there's promise in building a weighted RPG.

So, here are my thoughts (for a fantasy war game):
For production purposes, let's keep the six sided dice conceit and run with all the ways you can modify a weighted system.
Let's assume there are five different energy resources. A-B-C-D-E
The most basic die could have one of each type and a wild. A-B-C-D-E-W
But, you could have a whole range of different possibilities. A-A-A-A-A-W, B-B-B-C-C-C, D-D-E-E-W-W, you can imagine a very large number of combinations.
Let's assume there are units which perform three different types of actions. But, in order to perform each action it must 'use' the appropriate resource.
The most basic unit would have a 1 resource cost action, a 2 resource cost action and a 3 resource cost action. example: A: Move 1 space in any direction. A-A: Move 3 spaces in any direction. C-C-?: Inflict 6 damage to a unit in the adjacent space.
Before the game begins, you would be able to select which dice and which units you play with. But, the idea is that all dice and units would be balanced with each other so you build your armies based off of total number of dice and total number of units. So, you might have a limit of 10 dice and 20 units.
The game could be played on board and the objective could be TA or destroy a certain number of units or capture the flag... whatever.
Each turn you would roll all your dice and then players would take turns activating the powers on their units (by discarding their dice) until both players pass.
Units dealt more damage than their health would be removed from the board (or captured) and there could be a variety of different bonuses to armor, damage, etc... based upon both the terrain as well as the activated powers.
But, when each turn is over, players would have the opportunity to throw their dice again and continue the battle.

This same mechanic could be adapted to a fantasy RPG, by giving each player a set of dice. At the beginning of each round of a combat/conflict, each character would have a number of dice available based upon his class and level and then use them to perform the actions.
Ostensibly, each of the five resources types would correspond to a different type of attribute. So, things that take Strength to complete, would require more strength type dice to be rolled. But, each time a player 'levels up', he would be given the opportunity to gain one more die of his choosing based upon the 'class' he wants to take. So, each character would be identified by the type and number of classes they have acquired throughout the game.
Instead of rolling dice all at the beginning of each round... each player has a pool of dice each round and when he wishes to perform an action, he chooses to roll any number or type of dice from his pool. That way, if a player really wants to get one action performed, he can roll all his dice at once, but he would be drained for the rest of the turn (and defenseless). Defensive players may choose to roll a minimum number of dice at the beginning to wait until others are drained to counter-attack, etc...
But, essentially this, first choose your action then roll customized weight dice to see if you succeed mechanic, combined with a much larger pool of dice would give players a lot of discretion over how they hedge their risk. Specialists (players with a lot of dice of one or two energy types) could count on doing certain things more consistently and more powerful things, but they could also likely be unable to do things outside their field. So... as players level up, they need to choose their dice wisely.
In fact, in this mechanic, all actions could be known to all players. So, really what makes your character yours is the dice you own. You may tell the GM what you want to do and he may say that requires 1 strength and 1 dexterity die and you would then choose which of your dice you want to roll.
In combat situations, the dice available to you would be time sensitive so you do not get a chance to refresh your pool until everyone passes. But, the requirements for performing any action may be low (to allow for defensive responses). Whereas, in non-combat situations, you may be able to use all your dice at once and the die results needed may be much higher.

As a third possibility, this mechanic could be adapted into a Euro game. Each turn, players would roll all their dice and they would then have to dice how they want to allocate them amongst a number of different tasks, with different tasks requiring a different number/type of dice. However, the number and type of dice that players start with may be remarkably smaller than what they end up with, so a lot of the mechanic might revolve around collecting dice.
As a typical Euro, economic, engine, the players may use dice to acquire access to more dice... in which case the choice of what dice they acquire each turn will act as a form of strategic commitment over the game.
You could even layer another currency mechanism onto the game and use cards to roll different dice. So... there may be six to ten different dice and cards that allow you to roll D number of X,Y,Z dice. You would have to select at the beginning of each round which cards you want to play. Once everyone has selected their cards, they roll those dice and use them to perform other actions. Since cards can be discarded, they might be the fundamental currency and the limiting resource... So players have to decide when best to use what cards to do what they want to do.

But, essentially, each of these mechanics pushes the design possibilities of using a weighted die system with the possibility to customizing the results and controlling the number of dice you have access to.

d12 3/3/3/3/3/3/6/6/6/9/9/18 (though 4 types of damage)
or
d12 2/2/2/2/2/2/3/3/3/3/6/6 (3 types- just doubling the 6 really)

d3 1/1/2 (though 2 types)
d4 1/1/1/3 (2 types)
d5 2/2/2/3/3 (2 types)

etc. unless I am not understanding what makes the d6 and d10 "unique."

4/4/4/4/4/5/5/5/5/10/10/20
1/1/1/1/1/1/2/2/2/3/3/6