I came up with this after finding the Wikipedia page on non-transitive dice, though the "elemental magic" premise is admittedly fairly weak and just there to spark the imagination while playing. To start off with, you'll need either the following tables to compare your actual d6 rolls to, or to print and assemble paper or cardstock dice with the following sides, at least one of each for each player:
water: 1, 2, 16, 17, 18, 19
air: 3, 4, 5, 20, 21, 22
fire: 6, 7, 8, 9, 23, 24
earth: 10, 11, 12, 13, 14, 15
Examining the numbers involved will show that each element beats the preceding element on the list 2/3 of the time, but is even against the "traditionally opposed" element (fire vs. water or earth vs. air) and that fire has a slight overall advantage, but is rather inconsistent in any given roll.
Each player should roll all four (or one of each if hey have more than one each) to determine their primary element, which will be the highest single die of the roll. Dice of that element may always be rerolled once each turn. Descriptive narration of attacks and defenses is encouraged, such as "With Water, Air, and Fire I send a jet of high-pressure steam at B!" "I raise a wall of twice-hardened Earth to block A's attack and deflect the cloud of vapor." Of course, due to the reroll rule described above, even when they have access to multi-element attacks most players will stick to their primary to gain the best advantage, like the defender, B, above.
Two players then each pick one die and roll against each other, the winner of the roll subtracting the loser's result from his own and adding it to a tally of Victory Points. At 25, 50, 100, (and so on, doubling each time) VP the player gains the ability to roll another die for each attack or defense, in whatever combination suits their fancy - ala Zero no Tsukaima mages and their dot/line/triangle/square system, though in a long game even larger polygons are possible. In the example above, A has Fire for the primary element and rolls 17, 5, 8 (rerolled 7 so the original is kept) for a result of 30, B is Earth and gets 10 (reroll 13) & 14 (reroll 11 so the original is kept) for a total of 27 - so close, but A gets three VP. With three or more players, the attacker and defender positions should be rotated evenly, or else the loser becomes the next attacker and chooses their target from the players other than the previous attacker. Note that the latter method can lead to some players not having the opportunity to face as many contests and thereby fall behind in VP.
An unlucky player can be left far behind in the power stakes despite the widening intervals, so it is suggested to eliminate anyone who falls two dice per roll behind the lead. Play continues until only one player remains, a predetermined number of VP is reached, or all players get sick of rolling dice and keeping a tally. My own suggestion would be 300 VP divided by the number of players for a start. Possible further modifications involve the abiliy to bet extra VP on a roll before it's made, granting a bonus related to the number of VP involved, adding effects for specific element combinations/ratios, or taking the simple combat mechanic and turning it into the core for a basic RPG with persistent characters and so on, deducting VP lost from a pool of hit points and maybe adding some standard dice for non-magical attacks - I'd suggest 2d8 or 2d10 for each VP tier; given that elemental die results can range up to 24 this makes physical attackers a viable threat but still inferior to elementalists on average.
- CD, has played week-long games of Cosmic Wimpout to one million points before...
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"Anko, what you do in your free time is your own choice. Use it wisely. And if you do not use it wisely, make sure you thoroughly enjoy whatever unwise thing you are doing." - HymnOfRagnorok as Orochimaru at SpaceBattles
woot Med. Eng., verb, 1st & 3rd pers. prsnt. sg. know, knows
Wow... seriously, nothing? I thought I'd at least get a 'bwah?' Oh well... I guess no one's intersted if I work up the combinations, either.
- CD, frownie bunny
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"Anko, what you do in your free time is your own choice. Use it wisely. And if you do not use it wisely, make sure you thoroughly enjoy whatever unwise thing you are doing." - HymnOfRagnorok as Orochimaru at SpaceBattles
woot Med. Eng., verb, 1st & 3rd pers. prsnt. sg. know, knows
Sorry, I've been busy on another forum.
Bwah?
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Rob Kelk
"Governments have no right to question the loyalty of those who oppose
them. Adversaries remain citizens of the same state, common subjects of
the same sovereign, servants of the same law."
- Michael Ignatieff, addressing Stanford University in 2012
I've got nothing, aside the thought of just using a D20, D30 or D100 for it. Cos I find rolling 20D6 a pain.
I'm kind of confused. If you are water aspected, then you will roll either 1, 2, 16, 17, 18, or 19 dice? Or you just roll some number of dice and use the total, or something? How many dice? If you could explain this step by step, it would probably be easier to follow. ("Each player rolls all four (...) to determine..." All four what? Dice? Elements? I'm confused.)
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Stand between the Silver Crystal and the Golden Sea.
"Youngsters these days just have no appreciation for the magnificence of the legendary cucumber." --Krityan Elder, Tales of Vesperia.
The tables are the numbers on the faces of a d6 for that element - each element has a die with different markings. To start, everyone uses one die at a time, and yes, you are supposed to roll one die of all four elements and take the highest to determine your primary. Unless you're playing to ludicrous numbers of VP, you shouldn't ever have more than four or five dice at the very most for one roll, and even five would be 200+ VP as written above, which considering you subtract high roll from low roll and the high rolling player gets the result in VP is a pretty large number itself. Given that you could have all of the dice in your roll be of your primary element and possibly reroll all of them, that can get high at the upper end, but it's still not terrible if you've got four or five d6 to compare to the table, or have printed and folded up a bunch of each type.
To take it step by step like you asked:
I'm starting up a rousing game of non-Transitive Elemental Dice with my chums. Having accquired a glass of ginger-beer apeice and settled in the drawing room, we dump out the Big Bag O Dice on the gaming table and grab a few of each type. By some means, perhaps an amusing belching contest, we have determined an order of play, and skillful fellow that I am mine was the longest so I get to go first. Snapping up one of each type of die I give them a good shake and let fly! After retrieving the dice form the corner of the room and under the Chesterfield, I give them another good shake and release them more moderately. w18, a5, f23, e12 Huzzah! I've lucked out and gotten a Fire affinity! From now on, any time I roll a Fire die, I can reroll and use the better result one time per die. My chums repeat the procedure, though happily without the bit where their first attempt goes bouncing off like Br'er Rabbit into a hedgerow.
Now it's time the first round of contests, so I turn to Tuppy - capital chap, that Tuppy! - and challenge him with a bolt of Fire, while he, having an Air nature, judges it better to use Earth, less favorable to him but strong against my own burning spirit, to defend. f8 e13 Botheration! Fortunately, as I am a Fire user, I can reroll to try to fix that pesky score, and succeed smashingly with a 23. 23-13=10, I gain 10 VP and the attacker's role moves on to Tuppy, who was only able to reach the letter P in his bid for turn order.
Some rounds later, I've accumulated an enviable 56 VP, and though Tuppy isn't far behind at 48, he can only use two dice to my three. Looking to add a bit more consistency to hedge the fickle nature of Fire, I shroud him in superheated ash with Fire-Fire-Earth, and as the averaging effect of multiple dice makes the reroll more valuable in absolute terms than raw affinity he attempts to deflect it with a heavy Air-Air crosswind. f23+f7+e11 vs a4+a22, but each of us can reroll our affinities in hopes of a better result and do so, though mine is even lower while Tuppy, the rotter, manages a second 22. 23+7+11=41 vs 22+22=44, 44-41=3 means Tuppy comes out ahead of this one and gains just enough VP to put him over 50, able to use three dice as he moves on to attack the next fellow. Irked, I go to the sideboard to refresh my ginger-beer, but its cool fizzy texture and snappy flavor restores my good humor by the time the round is done.
I'll show Tuppy what for this round, equal numbers of dice or not! He shan't beat Bertie to the evening's winning VP total!
- CD,
really ought to go to bed now
ETA:
http://en.wikipedia.org/wiki/Nontransitive_dice]Wikipedia page link
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"Anko, what you do in your free time is your own choice. Use it wisely. And if you do not use it wisely, make sure you thoroughly enjoy whatever unwise thing you are doing." - HymnOfRagnorok as Orochimaru at SpaceBattles
woot Med. Eng., verb, 1st & 3rd pers. prsnt. sg. know, knows
The main hassle is that unless you can actually get physical dice with the appropriate faces, keeping track of the whole thing could be a real hassle.
On the other hand, if it's just plain numbers, it'd probably be pretty easy to cobble up a module in VASSAL as long as you didn't demand too much automated counting and such. (Which I think might be *possible*, but I'm not quite sure how at this point.)
-Morgan.
One big problem is that being primarily earth element sucks since your dice result is in effect a constant while in the single dice phase. Even at multiple dice being primarily earth is a weakness, because the rerolls occur over a very small range. Air is probably the strongest since the reroll range is 19 as opposed to 18 for the other two, with earth being weakest at a range of 5. If you want earth to be comparable to the others it should probably have a similar range, if it's supposed to be more even than the others give it a range of 17.
The Way it works out at the moment is;
Air: 1/3 very Weak, 2/3 above average (8/9 above average with reroll.)
Water: 1/2 weak, 1/2 strong (3/4 Strong with reroll)
Fire: 2/3 below average, 1/3 very strong; (5/9 very strong with reroll)
Earth: Always average. (Rerolls have minimal effect, always average.)
This means that a primary fire is weakest against a primary earth but would still win 5/9 of the rolloffs when rolling the same number of dice. Both Air and Water would do better against earth.
I would have to run some more stats to figure out if any of the other elements dominate, but the others at least seem in the same ballpark as each other.
E: "Did they... did they just endorse the combination of the JSDF and US Army by showing them as two lesbian lolicons moving in together and holding hands and talking about how 'intimate' they were?"
B: "Have you forgotten so soon? They're phasing out Don't Ask, Don't Tell."
Yeah, that is a bit more of an advantage than I had in mind, but I can't come up with an idea for how to make "primary element" a small but significant thing. Maybe a fixed +3 to each die of that element? That keeps two specialists even, but gives a tangible advantage against even their weak element against someone who doesn't have the appropriate specialty. The "concept" of earth was that it's stable and middle of the road, but it neds to keep up on average for that to work.
As to the trouble of getting physical dice, that's why I stuck with d6 rather than rearraging it for the more appealing d8s or 10s - just make six squares arranged in a cross pattern at the edges, put the numbers you want for one die in the squares, print it out and cut it out (leaving tabs to glue with) and fold into a cube. Easy peasy, hard to get wrong enough to affect probability in major ways. The larger regular poyhedra arer harder to get a high degree of accuracy with.
I didn't address ties with multiple dice, and with the new bonuses instead of rerolls that can happen even with singles... Hmm, on a tie, each player rolls one extra die of their primary element to add to the total, and keeps doing so until their is no longer a tie. One bonus VP is added to whatever final result is achieved per tie-breaker roll.
- CD, has fiddled with a couple of versions using his preferred water-wood-fire-earth-metal ring plus air and void as poles, but has nothing that looks good yet
--
"Anko, what you do in your free time is your own choice. Use it wisely. And if you do not use it wisely, make sure you thoroughly enjoy whatever unwise thing you are doing." - HymnOfRagnorok as Orochimaru at SpaceBattles
woot Med. Eng., verb, 1st & 3rd pers. prsnt. sg. know, knows
current attempt for the "elemental gyroscope" (ring off five plus two poles)
air 1d30 (avg 15.5)
metal 1 2 21 22 23 24 (avg 15.5)
water 3 4 5 25 26 27 (avg 15)
wood 6 7 8 9 28 29 (avg 14.5)
fire 10 11 12 13 15 30 (avg 15.1666~)
earth 14 16 17 18 19 20 (avg 17.333~)
void 1d30
Obviously, the trouble here is that the probabilities are not even after adding a fifth part to the sequence, and that Earth's numbers range from average-to-above-average rather than going straight across the average line. This is, however, the best I've managed to come up with. Primary Element bonus would remain +3 and determining the die used for tie-breaking. I have to admit I don't really get the math enough to really analyse it properly, though.
The other problem is that the dice do not really admit to a proper production and control cycle, only one side of it - as depicted, the production cycle is the one shown, with each element feeding on the one above it and producing the one below. For the control cycle, each element should be weak to the one two up and control the one two down, but this doesn't really work with dice. Maybe explicitly moving it to tables (and giving up on the idea of a physically produced game) and having seperate offense and defense tables for each element, with offense following the production cycle and defense using the control cycle... Meh.
- CD
ETA: To be clear, I really don't think this would work, so I'm still really only serious about hammering the four-elementss version into shape.
ETA2: Enlightenment! Okay, maybe not, but a different attempt at graphing the relationships of the number blocks on the dice made the math clearer. The following dice should be a little more even:
01 02 19 20 21 22 = 85 /6= 14.166~
03 04 05 23 24 25 = 84 /6= 14
06 07 08 26 27 28 = 102 /6= 17
09 10 11 12 29 30 = 101 /6= 16.833~
13 14 15 16 17 18 = 93 /6= 15.5
... but it's not. I just suck at math. Still going to post the edit because that weas too much work not to.
Final edit: I think
http://math.stackexchange.com/questions ... -stretched]this page would probably hold my answers, but I have no idea what the actual formula they're putting forth means. At all.
--
"Anko, what you do in your free time is your own choice. Use it wisely. And if you do not use it wisely, make sure you thoroughly enjoy whatever unwise thing you are doing." - HymnOfRagnorok as Orochimaru at SpaceBattles
woot Med. Eng., verb, 1st & 3rd pers. prsnt. sg. know, knows
If math is a problem
http://anydice.com/ can do the heavy lifting.
E: "Did they... did they just endorse the combination of the JSDF and US Army by showing them as two lesbian lolicons moving in together and holding hands and talking about how 'intimate' they were?"
B: "Have you forgotten so soon? They're phasing out Don't Ask, Don't Tell."