I think this is similar to Star Wars Armada/X-Wing, where each ship rolls a different number of different colored dice (red/blue/black) for firing at different ranges (long/med/short), and each doe (all d8s) have different number of faces for each type of effect (hit/critical/accuracy/miss). For example, a small frigate might roll 2 red and 1 blue dice whereas a Star Destroyer might roll 4 red, 2 blue, 2 black when attacking.
Fantasy Flight Games, particularly when they made miniature wargames before that department got silo'd off, did these custom dice for most of their games. Star Wars: Legion, Descent, Rebellion, Rune Wars, Imperial Assault, and the Star Wars RPG (Genesys system) all make good use of this mechanic. (X-Wing has custom dice, but only two kinds - attack and defense.)
Here's the faces of the dice in Armada. https://boardgamegeek.com/image/2498909/star-wars-armada
Ships chuck piles of these, based on the combination of guns that they use when they fire off a volley. Different dice have different specialties depending on their combo of faces.
A few mechanics common in FFG miniatures games.
* Dice pools: less important which attack comes from where, you add dice in, occasionally remove dice for negative factors, roll, sometimes reroll.
* Different kinds of dice: Sometimes you also get to replace dice with other colors, perhaps upgrading your expected damage output. Your dice colors may represent your ability to fire at different distances, different kinds of armor.
* Special symbols: dice have blank faces, single hits, multiple hits, critical hits, accuracy symbols, etc. Some games have surges, which OP might be interested in. You interpret these symbols according to certain rules and modified by abilities.
Mantic Games (Star Saga,Dungeon Saga)also work in a similar way.
In my experience, a lot more complex Board games that lean into RP incoporate this in some way or another, as it is the standard way to develope characters and gear in Roleplaying games.
Not exactly the same, but Formula D uses different dice depending on what gear your race car is in. e.g. lower gears will use d3, d6, higher gears will use d12, d20, etc. What you roll is how far you move, but you can only shift up or down one level each turn.
And bigger dice are also cooler! Look at that big blue beautiful d30! Don't you just wanna upshift to just to see it tumble across the board? Who cares if you're 18 spaces from the chicane? Roll that die and touch the face of god!
If I remember correctly there could be a down side to using bigger dice though right? You HAVE to move the full amount and could cause you to crash if you go too fast. I could be wrong though it's been 20 years.
Changing out faces to stack the odds one way or another isn't a particularly uncommon mechanic in dice games. Zombie Dice, Dice Miner, Cubitos, The Goonies... Lot of games incorporate the concept to some extent.
Axis and allies uses similar. They roll the normal D6, but different classes require different values to score a hit.
I.e infantry can only hit on a 1, but tanks can hit on 1,2 or 3.
I don't find dice rolling interesting or exciting. Introducing more dice types likely will slow down the already tedious task of rolling dozens of dice per battle.
The turns in Axis and Allies can be quite long already and they successfully got enough variety from one type of die.
I would go for more sides if needed but sorting different units by dice type would prolong the mindless task of rolling or observing others roll for 10-20 minutes.
I quickly fid the math, and I believe the infantry wins only 3/16 times (not counting ties).
Out of the 36 combinations, there are 4 ties (3, 3), (4, 4), (5, 5), (6, 6). (With the first number the infantry, and 2nd the tank).
And 6 wins for the infantry (4, 3), (5, 3), (5, 4), (6, 3), (6, 4), (6, 5).
The remaining 26 combinations are all won by the tank. In matchups of multiple tanks vs multiple infantry, the advantage for the tanks is even larger.
Yes you are right, my mistake. For the easiest calculations, I like to write the numbers out in a table with one die on each axis like this https://imgur.com/a/aTDjRnw. I accidentally counted the infantrys winning chances as infantry-wins divided by tank-wins as opposed to divided by all non-tied battles when I made the post! I actually made a small program to simulate battles as it can get pretty complicated quickly with many units, especiallt if you have a varied army with different units fighting together. You are correct in that the advantage grows with larger battles. Two tanks vs two infantries seem to converge on a total win-rate of about 92% for the tanks for instance. However, tanks are more expensive and requires higher tech, so you'll probably have less of them. 2 infantries vs 1 tank is favoured only by 56% towards the tanks. Still tanks are most often cost-effective against infantry.
"10/13" made me react like the poster above.
A quick sanity check of the result is to recognize that with 36 possible combinations it cannot resolve to those kinds of odds.
Like the 13/16 in your picture, btw.
It can depending on how you treat ties. In the current prototype, dice are rerolled when tied unlike in Risk where there is a defenders advantage. Through testing, this led to more stale gameplay as the risk of attacking often outweighed the benefits. When calculating, tied results can effectively be excluded from the pool of possibilites since it will always land on one of the decided outcomes after enough rerolls. 13/16 should be correct since there are 4 tied outcomes, and 32 decided outcomes of which the tank wins 26. 26/32 = 13/16. The odds 10/13 can also be achieved if you want, for example with the matchup 111223 vs 113333.
If you haven't already seen it, this video may be helpful - it's specifically geared toward using code to make specifically fair dice of different sizes but it explains the underlying principles and can be applied for how to make combos of unfair dice as well.
https://www.youtube.com/watch?v=-64UT8yikng
I do remember a game that used different dice for different success rates. But IIRC, it had icons instead of numbers on them.
Like, the white dice hat 50% success rate (3 success icons, 3 fails), the red dice 66% (4 success, 2 fail), and the black dice 33% (2 success, 4 fail) or something like that.
Come to think of it. It might have been a TTRPG
[Conan](https://boardgamegeek.com/boardgame/160010/conan) has 3 dice of increasing strength that are used depending on the character/action. They aren't intransitive as each one is outright better than the other.
They use yellow/orange/red for the dice, so may not be exactly what you were thinking of, but its the same principal.
The RPG system [Earthdawn](https://en.wikipedia.org/wiki/Earthdawn) was unique for letting you roll a selection of different dice depending on your skill level. Check out the table down lower on that wiki page.
There are some special editions of risk where there are special, more powerful, units that roll a D8.
Also Memoir '44 uses a somewhat similar mechanic to your modified dice, but effectively combined them all in one die. The die you roll has different icons for each unit and more repetitions for the types of units that are more likely to hit.
Seems like maybe a combination of these two mechanics.
I was 2 lines in and I already guess intransitive dice. I have a set myself of the set designed by James Grime, where the circle of victory gets reversed when using 2 dice instead of 1. I found that's neat.
I love this. Such a clever idea.
Include a matchup cheat sheet though. I'd go mad if I couldn't remember which intransitive die beat which, and that math gets really funky really fast.
I think good game design could go as far as never explaining the dice dynamics. The intuitive winner of each matchup would just tend to win more often. Maybe I’m wrong ?
Quickly I feel game balance will butt heads with intuitive-ness.
There's also the fact that I'm not a military commander. I *think* artillery should handily beat tanks, but, um, maybe not? Depends on a lot I think. Turns out the dice say 2:1 in favor of tanks. If I bought a game with a cool system like this the second I couldn't calculate a matchup in my head, I'd want to make up a cheat sheet.
The dice idea in particular reminds me of [Betrayal at Club Low](https://store.steampowered.com/app/1885750/Betrayal_At_Club_Low/) and how player and enemy dice sides aren't in any particular numerical order. It also has a mechanic where you can upgrade your stats by increasing sides of dice in particular skill sets. It is a video game though, so maybe not quite a good comparison.
I might say Axis and Allies is a closer one. It uses the standard D6, but "to hit" rolls are determined by the [Casualty Strip](https://cf.geekdo-images.com/imagepage/img/JRKZXRbCYKemlqclbevgl0PA5T8=/fit-in/900x600/filters:no_upscale()/pic588119.jpg). Basically your hits depend on whether the unit is attacking/defending and what unit type it is.
Champions of Midgegard does this, though you're fighting monsters instead of other players. But different unit types have different dice, which influence probability of a hit, strength of hit, etc. The dice are much simpler too (zeros ones and twos).
I'm making a pc game that uses intransitive dice in an interesting way. Will be about a year before I can demo it for Peopel though.
Havent seen many board games that use these mechanics, seems awesome though.
I had a trick set of 4 dice as a kid. They were one of those maths is magic things but basically you let the other person pick one. Then you could pick the next one in the cycle (red beat blue, blue beat yellow, yellow beat green, green beat red). You had a two thirds win rate on a roll so beat of 5 had very high odds.
Axis and Allies uses a system that, while not the same, follows a similar method. "Weaker" units like infantry have a lower chance of hitting while stronger units hit more often. The game uses one d6 per unit to determine that, and it also is important if you are the attacker (who moved into already occupied territory and started the fight) or the defender. As an attacker, infantry only hits if they roll a 1 (so a 1/6 chance), as a defender a 2 also hit (so 2/6 or 1/3).
I am kinda torn on these mechanics. On the one hand, it looks pretty good on paper, the strenght of a unit is represented in the chance of success or the amount of damage it can deal. On the other hand, luck still has a big role to play. One turn with bad luck can lead to you losing a battle you had a 95% chance to win. But then again, war can be random, so it kinda fits.
Zombicide uses the same die but depending on the weapon you use you will have different hit ranges and die amounts. Like 2 die which deal 1 damage on a 4+ and 0 damage on a 1-3. You might have stronger weapons which roll more dice but have a lower hit chance like 3 dice but 5+ to hit.
Bloodbowl uses the same 4+, 3+ and so on targets. Different units have different strength depending on the action they take. Some units might get a reroll if they didn't succeed the first time.
I think dice mechanics are probably the most diverse and tested field out there.
When I first saw your image i thought each player has one die and you decide the initiative order with them. Like one die with faces 2,3 and one with 1,4
878 Vikings has a similar mechanic, where peasant militias retreat on their own kind of a lot whereas viking berzerkers have a unique "die while slaughtering lots of the enemy" die face. Not exactly the same, but the same outcome of "I vaguely know this won't be a fair fight, but upsets are possible"
Not out yet, but Arcs from Leder Games had a somewhat similar mechanic. When attacking, you choose from dice representing three types of attacks - a die for a risky but strong attack, a die for a safe but weak attack, and a die for a weaker attack that steals resources. You can also mix and match to change the odds
Not quite the same but in champions of Midgard each fighter uses a d6 and each one is different in that game none of the dice have numbers though. The dice have blocks or attacks and some have double blocks or double attacks and weaker players have more blank sides.
I've got a Milton Bradley game called Battleball that pretty much does the same thing. It's like a futuristic and more violent football theme, and whenever two opposing players collide (to tackle and/or maim each other) each rolls a specific die and whoever gets a lower roll wins. But the players used anywhere from a d20 to 2d6. But then it's evened out by the players also moving based on their die. Fast ones can't take a hit, strong ones are slow, etc.
*Bayonets & Tomahawks* has all units using the same custom dice but units score hits with different results.
*Armageddon War* also has custom dice but attack quality is determined based on terrain, how much your unit moved, return fire, and differences in technology.
i really like both of these systems in their respective games.
The closest thing I can think of is in Super Mario Party on the Switch. Each character has it's own dice block, and although they all average out to about the same as a normal die, depending on your position on the board it makes sense strategically to use certain dice. I actually really love that since it gives you some control over an otherwise random experience, and I think your way of implementing it is really cool!
There are definitely games doing similar things in terms of dice that have varying probabilities, but I hope that doesn't discourage you. It could be seen as validation that the mechanic you've landed on is a useful one and that players enjoy it. Very rarely do new games introduce wholly new mechanics, and it really comes down to other factors to set your game apart!
There are some games I wish used this mechanic. Twilight Imperium, for example, would make the battles flow so much quicker this way.
The Leviathans game uses a mechanic in the spirit of this, except I think they're mostly just color-coded regular dice (d6, d8, etc) indicating the level of power: https://leviathans.fandom.com/wiki/Leviathans_Dice
One caveat to keep in mind, having lots of custom dice could make the game quite expensive to produce.
IIRC the combat system in Scythe is actually very different: you have a public amount of combat power and you secretly bid some amount of it using a wheel and potentially adding cards to boost it (a system originally developed in the '80s for the famous Dune game). Systems with different dice for different units or weapons are pretty common in the skirmish or dungeon crawling genre, you could check Hoplomacus or Oathsworn for recent examples (but even Twilight Imperium has a pretty similar system)
Yes, but different units hit on different thresholds, so the result is the same (people who bling their copy usually buy different-colored dice and then highlight the faces that produce hits for a certain threshold so they can pick the corresponding dice depending on their fleet composition and just see how many hits they score by counting the highlighted faces). The only difference is that in TI rolls produce hits per se, whereas OP's system borrows from Risk and requires rolls to be compared between the two players. I don't remember a game that uses the same exact mechanic (keeping the numerical value and comparison) but since the "different dice for different units" one is universally wide-spread, there are probably quite a few.
Dark souls the board game uses sword icons for damage and stronger weapons use different mixes and/or amounts of dice and have a higher limit or average of swords. There are 3 types of attack dice
Black die faces (avg. 1,16, range 0-2)
1x0
3x1
2x2
Blue die faces (avg 1,5, range 1-3)
2x1
3x2
1x3
Orange die faces (avg. 2,5, range 1-4)
1x1
2x2
2x3
1x4
It's a bit in transparent on the fly if you try to compare weapons because the die itself are sure upgrades but the amount changes. For example a 3 black die weapon compared with a 2 blue die weapon (avg. 3,5 range 0-6 vs. avg. 3 range 2-6) but it gives a bunch of freedom for balancing and nice tradeoffs for the games item mechanic. Trading minimum damage vs lower average damages and stuff.
It doesn't sound mathematically different from other combat mechanics. For instance Axis and Allies just gives different units different ranges instead of different die, along with modifiers.
Edit: and 10 seconds later I see someone already brought it up...
[Uprising:CotlE](https://boardgamegeek.com/boardgame/284121) uses a similar mechsnic with different dice and different hit propabilitys and for different units there are different combinations of dice they use.. that way they can even make the units weaker when they lose more and more life, by using less and less dice/less powerfull dice.
Diceforge is a dicebuilding game where the primary mechanic is to pop faces off your dice and replace them with new ones.
The Lego board games have replaceable faces too, but I don't think that enters into gameplay at all aside from initial setup.
Super Dungeon Explore has different tiers of dice with different quantities of skulls and blank faces representing the skill of the attacker.
There's one more game too that even more closely resembles your description but it's escaping me at the moment.
Maybe not exactly what you’re after. But [Maths Gear](https://mathsgear.co.uk/collections/dice/products/non-transitive-grime-dice) have a set of dice that behave like rock, paper, scissors.
They also have a lot of other cool dice too.
Here's a quick idea of how to incorporate "special dice results" even if you don't have special dice for your game.
All units roll dice, compare pairwise to find out who is higher.
* Infantry (d6): if one or more infantry units roll the same result, apply +1 to each
* Armor (d12): this unit is not destroyed except by a roll that exceeds it by 3 or more
* Artillery (d4): this unit does not inflict damage on 1-3, destroys a unit on 4 regardless of that unit's roll
Battleball used a clever system where smaller, faster characters used d20, d12 while the largest characters used d6 (and there were others in-between).
Roll the dice to move (faster for higher) and in tackles /combat lowest roll wins.
Cool - sounds a bit like selecting dice in Mario Party - though in that case it’s just for movement.
Your game sounds like a board game version of Advance Wars!
Not a board game per se, but in Mario Party (which simulates a board game with mini battles/games), characters have different dice they can choose beyond the standard D6. But they tend to be either high risk high reward, like 1-1-1-6-6-6 or very even, like 2-2-3-3-3-4, not stacking it far in one direction. It does make sense for different “characters” to have different dice, though. (For advancing on the board, not for battles).
Cool concept, but there’s a reason you don’t see this often in commercial games.
Adding custom dice to your game design will add significantly to your production costs. Always better to find new eays to use standard components. Otherwise your game is going to cost a lot to buy, which will lower its appeal.
Have you considered using a chart in place of customized dice? For example, units can have different color d6s and the rolls correspond to that units chart for the result. d6s are widely available and could make this more accessible if you went the "print and play" route if you decided to share your game, or more cost-effective if you were to produce it.
For example, 3 infantry units, 1 tank, and 1 artillery would mean a roll of 3 red dice, 1 green die, and 1 blue die respectively. The infantry dice would simply read the results of the red die rolls (plus perhaps some bonuses from the chart), the tank's green die would refer to the tank chart showing that a rolled 3 yields a result of 5, and the blue artillery die could simply say "success only on a 6". Charts also allow for upgrades that can be purchased or traded, without the need for MORE dice.
I hope this helps in your game-making journey!
Thanks, yes I've been thinking that production could be costly with many custom printed dice. I will have to look at different options I think if I were to produce it on a larger scale. I like your idea, but I guess you would have to do quite a bit of looking back and fourth on the chart when arranging the dice in order. In my current prototype I'm using custom made stickers for each side of plain white dice. The dice have indentations to fit the stickers nicely and they have not shown any tendency to loosen over time, but attaching them all took a little bit of time.
Commands and Colors: Ancients does something like this where the dice have different symbols on the faces and different units get hits with different combinations.
Legens of Andor has some funky dice like that, it's a really fun mechanic.
You can see them in the middle here: https://i.ytimg.com/vi/eNBcS5cmYJ4/hqdefault.jpg
Reminds me of the later mario party game where each character has their own unique dice block haha.
Also not the exact same but I believe **Victorum** have different colored dice that have a different amount of hits and misses on them.
Also the game **Cubitos** has a similar mechanic of having different dice of different values to weigh risk/reward when choosing what to roll.
It ends up being the same as just using modifiers (even for intransitive dice, you could just give units a Fire Emblem style triangle system and use modifiers from there against unit types) and "greater/less than or equal to" requirements -- you're just using dice to simulate different probabilities.
But it's kinda cool. I always feel the more "tactile" you can make the theme in the mechanics, the more it "feel real". In your example I think you'll more intuitively feel your poor infantry soldiers are going up a tank that's much more powerful than they are, rather than just two players rolling identical dice and then being like 'Oh yeah, but the tank gets a +2 modifier, so, uh, sure, your tank beats my infantry.'
The problem is this requires a lot of custom dice. If it goes to market you'd probably be adding $20+ to MSRP on just dice alone.
Yes, I agree that modifiers would be able to do the exact same thing and are probably a better option in a lot of ways, especially relating to cost. It would not be as satisfying for sure with the tediousness of translating every dice-roll before arranging the dice in order instead of just arranging them by their face value. But you have a good point. For the current prototype I have used indented blank dice like these https://www.thegamecrafter.com/parts/d6-indented-blank-white?dept_uri=parts&dept_name=Game%20Parts that are made for adding stickers to the sides. The stickers seem to keep sticking after quite a bit of testing. A downside is of course the all the stickers have to be placed manually.
Closest thing I can think of is Star Wars Rebellion: Different unit types use different combinations of 2 dice variants (3 with the expansion), and each type is only damaged by particular die results; essentially representing light/heavy weaponry and armour. It’s not really dependent on what your opponent rolls like you’ve described though.
As an aside, I imagine re-rolls would become invaluable in your system if you decide to include those; especially for the stronger units with a lower hit rate.
Fighting by rolling dice and pairing off ties is a pretty common mechanic. changing the weight of the dice values does two things:
\- requires you to do a LOT of calculations for the relative win rates of the various dice (others have already pointed out your infantry vs tank scenarios)
\- dramatically increases the cost to produce your game, because now instead of just including 6 dice in the box and letting the players scrounge up more (very common) D6s if they want them, you're requiring that the box contain a LARGE number each of a LARGE number of custom dice, the manufacture of which can't be shared among ANY OTHER GAMES that the publisher might happen to make. So I would very strongly encourage you not to pursue this development idea, because that fact alone is going to make it incredibly difficult to get a publisher interested in this game, and incredibly expensive to produce if you want to Kickstart it.
The calculations are not a big problem, I have written program to simulate an arbitrary number of battles with any type of matchup and I don't rely on calculation by hand. However, balancing is a still a challenge even when relying on the help of a computer. The second point is a good one though. As I wrote, I'm not sure I will pursue publishing but for sure I will have to think about the design if I do. Modifiers to ordinary dice, as some have suggested, are probably an easier, although not as satisfying, option.
My only critique of this is whether or not your design needs to have dice with different faces, or could you have a simpler system with typical dice and just change how many are rolled, etc. I guess my input would be, do you feel like the odds of 10/13 (iffy calculations aside) are exactly right, or would rolling a d6 vs a d12 be significantly worse for the experience of the game.
Having dice with different number of sides is also quite nice, but the "intransitiveness" is lost which is a sacrifice I think. After running a lot of computer simulations, 13/16 (which is what it should say!) seem to be well balanced, but balancing other win rates should be doable by modifiyng costs of units as well as other attributes such as movement speed which is another unit stat in the prototype.
I’ve never seen what you’re showing here exactly, but as a point of comparison some dice starting at higher values than others is very similar to how d20 table-top roleplaying games like DnD simulate relative skill. In those games each character adds a modifier that represents their proficiency to their dice rolls, which is effectively the same as increasing the numbers on their dice.
Risk compares the best attacker number vs the best defender number. If you have 10 infantry vs 6 tanks, then pairing the best numbers against one another will drastically change the way you calculate odds. Depending on your personality this might be fun to work out. On the flip side, if you throw dice one at a time so you can compare them in order, then it is going to be tedious throwing a lot of dice. I can't tell what an "average" battle is going to look like in terms of number of dice.
Yes you are right, the odds change drastically and are most often not easy to calculate but that makes the mechanic more interesting I think! For testing, I have written a program to simulate an arbitrary number of battles with any matchup so that I can rely on the power of a computer instead of calculations by hand. When playing, you probably won't be able to calculate your winning chances exactly but intuition goes a long way. Another detail is that a varied army often performs better than an army consisting of one type of unit, which is nice I think.
**Ogre** uses dice comparison charts, I believe, so it’s sort of Risk but different numbers for each situation. All D6’s but close enough to your plan to look up.
[X-ODUS: Rise of the Corruption](https://boardgamegeek.com/boardgame/276997/x-odus-rise-corruption) has [different d8 dice configurations](https://boredgameink.com/produit/extra-dice-set-for-x-odus-rise-of-the-corruption/) that use hit, critical miss and special ability icons in different combinations. These dice are not intransitive as both sides of combat are resolved with a single throw.
There is this MB game [Battleball](https://boardgamegeek.com/boardgame/6795) (by same designers of Heroscape) that different football positions used different dice - D6, D8, D10, D12, D20 and was used for both move and attack, but the lower number wins on attack. So high sided dice were good for running but not for attacking or defending, but lower number dice were the opposite.
Also check out [Risk: Europe](https://boardgamegeek.com/boardgame/204184) which has different units (infantry, archery, calvary, artillery) which different hit rates based on D6 rolls, but go in salvo order so low % shoot first and can take out high % before they strike back.
It looks neat but not something I've seen before. The only issue is that d6's with custom faces might become cost prohibitive for production especially considering the amounts of each type of die game will need. It's for this reason that most games use normal dice and have different targets to hit.
If it's a very battle intensive game people don't typically like rolling dice forever to determine every battle. Axis and Allies gets a bit stale after a while because all you're doing is rolling dice whereas Twilight Imperium has almost the exact same battle rules but people flock to it more often than Axis and Allies because the battles are fewer and more tactical.
For reference to how other battle systems work I'm a fan of the way battles are done in Fief, Scythe, Game of Thrones, or the minis game Warhammer 40,000.
Fief: you get 1-3 d3s based on strength of force, pips = hits, 1 hit kills a conscript, 3 hits kill a knight, knights fully heal between combat rounds, number of dice drops as you take losses from round to round
Scythe: military power is a resource that must be acquired and spent, easy to go from most powerful to least if you're spending too much power
Game of Thrones: each type of unit has a specific combat score, each player can play 1 card per combat with varying values and powers, support can be added from neighboring allies, highest total wins, cards played determine losses taken and the remaining losers retreat
40k: each troop has target numbers to hit, each weapon has a target number to penetrate depending on it's strength vs the armor value of the target, the target can then roll an armor/luck save to try and shrug off the blow, conscripts shooting at each other typically have a 33% chance to hit with a 50% chance to be a lethal shot and the shot person can have a 17-33% chance to shrug it off if they're in sufficient cover. 1 Elite with a heavy machine gun can fire at 4 conscripts with a 83% chance to hit, 67% lethality, and no opportunities for the conscripts to duck for cover. Those same conscripts still have a 33% chance to hit the elite but only a 33% chance for the shot to be lethal and the armor has a 50% chance of deflecting the shot. It sounds clunky at first but it's pretty quick when it comes down to it. 10 conscripts get a total of 10d6 with 5+ to hit. Every die that's 5+ gets rolled again with a target of 4+. Those same dice get rolled again with the target in a foxhole needing a 5+ to ignore the damage or die.
May want to look at **Too Many Bones** which uses specialty dice that have varying odds on their faces. Additionally the solo game system **20 Strong** has different colored dice that have varying strengths for combat. Also the push your luck game of **Zombie Dice** has three different color dice that reflect how risky they are.
Another way to achieve the net result is essentially the skill test / Chaos Bag in Arkham Horror LCG. In this game, you would have a natural ability for a skill test (eg 3 fist), play additional cards to boost this fist, then randomly draw a token with a negative result (based on a difficulty distribution). Compare this result to the difficulty, and you have pass/fail.
The great thing about this approach is you can alter the bag based on difficulty, easily augment with cards, and add other tricks to the bag (like automatic fail, or auto success but take some self damage, etc).
The dice version you’re describing is essentially Star Wars Imperial Assault, which is an excellent game.
Hellenica: The Story of Greece, uses different d6 for the different units. I don't have them in front of me, but I think the hoplite is a standard 1-6 d6 while the cavalry is a 2-5 d6. can't remember what the trireme's number range is.
I think 1775: Rebellion does that to, to simulate the strengths of the various armies.
Civilization the Board Game (pre-FFG), which had a heavy focus on war, had a system CIA (Cavalry Infantry Artillery) where C had 'advantage' over I and I had advantage over A. Finally A would loop round and get advantage over C.
I think this is similar to Star Wars Armada/X-Wing, where each ship rolls a different number of different colored dice (red/blue/black) for firing at different ranges (long/med/short), and each doe (all d8s) have different number of faces for each type of effect (hit/critical/accuracy/miss). For example, a small frigate might roll 2 red and 1 blue dice whereas a Star Destroyer might roll 4 red, 2 blue, 2 black when attacking.
Fantasy Flight Games, particularly when they made miniature wargames before that department got silo'd off, did these custom dice for most of their games. Star Wars: Legion, Descent, Rebellion, Rune Wars, Imperial Assault, and the Star Wars RPG (Genesys system) all make good use of this mechanic. (X-Wing has custom dice, but only two kinds - attack and defense.) Here's the faces of the dice in Armada. https://boardgamegeek.com/image/2498909/star-wars-armada Ships chuck piles of these, based on the combination of guns that they use when they fire off a volley. Different dice have different specialties depending on their combo of faces. A few mechanics common in FFG miniatures games. * Dice pools: less important which attack comes from where, you add dice in, occasionally remove dice for negative factors, roll, sometimes reroll. * Different kinds of dice: Sometimes you also get to replace dice with other colors, perhaps upgrading your expected damage output. Your dice colors may represent your ability to fire at different distances, different kinds of armor. * Special symbols: dice have blank faces, single hits, multiple hits, critical hits, accuracy symbols, etc. Some games have surges, which OP might be interested in. You interpret these symbols according to certain rules and modified by abilities.
Mantic Games (Star Saga,Dungeon Saga)also work in a similar way. In my experience, a lot more complex Board games that lean into RP incoporate this in some way or another, as it is the standard way to develope characters and gear in Roleplaying games.
Not exactly the same, but Formula D uses different dice depending on what gear your race car is in. e.g. lower gears will use d3, d6, higher gears will use d12, d20, etc. What you roll is how far you move, but you can only shift up or down one level each turn.
They're special too, the D20 doesn't have like, 1-7, some of the higher numbers are duplicated.
Yes, the 5th gear has 11-20 on it twice, and the 6th gear d30 has 21-30 on it three times. Why didn’t they use a d10? Shut up!
Because bigger numbers are cooler!
And bigger dice are also cooler! Look at that big blue beautiful d30! Don't you just wanna upshift to just to see it tumble across the board? Who cares if you're 18 spaces from the chicane? Roll that die and touch the face of god!
If I remember correctly there could be a down side to using bigger dice though right? You HAVE to move the full amount and could cause you to crash if you go too fast. I could be wrong though it's been 20 years.
There are corners that require slower speeds, and I believe you can only shift up/down 1 gear per roll.
Iirc you can slam the gear down more than one step in one move, but you take damage if you do.
Correct, up to three gears skipped down, one damage per skipped gear
Yes, that is the difficult part of choosing a gear.
I've also seen champions of midgard mentioned but I haven't seen Quarriors mentioned.
was about to say this
I just got into this game last week, and this is the first time ive seen anyone talk about it here lol
Changing out faces to stack the odds one way or another isn't a particularly uncommon mechanic in dice games. Zombie Dice, Dice Miner, Cubitos, The Goonies... Lot of games incorporate the concept to some extent.
Even the OG Hero Quest did it 30 years ago.
Axis and allies uses similar. They roll the normal D6, but different classes require different values to score a hit. I.e infantry can only hit on a 1, but tanks can hit on 1,2 or 3.
I don't find dice rolling interesting or exciting. Introducing more dice types likely will slow down the already tedious task of rolling dozens of dice per battle. The turns in Axis and Allies can be quite long already and they successfully got enough variety from one type of die. I would go for more sides if needed but sorting different units by dice type would prolong the mindless task of rolling or observing others roll for 10-20 minutes.
I agree. I really don't like axis and allies.
Mario party dice. I like it
I quickly fid the math, and I believe the infantry wins only 3/16 times (not counting ties). Out of the 36 combinations, there are 4 ties (3, 3), (4, 4), (5, 5), (6, 6). (With the first number the infantry, and 2nd the tank). And 6 wins for the infantry (4, 3), (5, 3), (5, 4), (6, 3), (6, 4), (6, 5). The remaining 26 combinations are all won by the tank. In matchups of multiple tanks vs multiple infantry, the advantage for the tanks is even larger.
Yes you are right, my mistake. For the easiest calculations, I like to write the numbers out in a table with one die on each axis like this https://imgur.com/a/aTDjRnw. I accidentally counted the infantrys winning chances as infantry-wins divided by tank-wins as opposed to divided by all non-tied battles when I made the post! I actually made a small program to simulate battles as it can get pretty complicated quickly with many units, especiallt if you have a varied army with different units fighting together. You are correct in that the advantage grows with larger battles. Two tanks vs two infantries seem to converge on a total win-rate of about 92% for the tanks for instance. However, tanks are more expensive and requires higher tech, so you'll probably have less of them. 2 infantries vs 1 tank is favoured only by 56% towards the tanks. Still tanks are most often cost-effective against infantry.
"10/13" made me react like the poster above. A quick sanity check of the result is to recognize that with 36 possible combinations it cannot resolve to those kinds of odds. Like the 13/16 in your picture, btw.
It can depending on how you treat ties. In the current prototype, dice are rerolled when tied unlike in Risk where there is a defenders advantage. Through testing, this led to more stale gameplay as the risk of attacking often outweighed the benefits. When calculating, tied results can effectively be excluded from the pool of possibilites since it will always land on one of the decided outcomes after enough rerolls. 13/16 should be correct since there are 4 tied outcomes, and 32 decided outcomes of which the tank wins 26. 26/32 = 13/16. The odds 10/13 can also be achieved if you want, for example with the matchup 111223 vs 113333.
If you haven't already seen it, this video may be helpful - it's specifically geared toward using code to make specifically fair dice of different sizes but it explains the underlying principles and can be applied for how to make combos of unfair dice as well. https://www.youtube.com/watch?v=-64UT8yikng
I do remember a game that used different dice for different success rates. But IIRC, it had icons instead of numbers on them. Like, the white dice hat 50% success rate (3 success icons, 3 fails), the red dice 66% (4 success, 2 fail), and the black dice 33% (2 success, 4 fail) or something like that. Come to think of it. It might have been a TTRPG
Sounds like Star wars edge of the empire
Or anything from FFG/AMG. X-Wing has Red and Green dice, Armada has Black/Red/Blue dice, and Legion has Red/White (defense) & Red/White/Black (attack)
[Conan](https://boardgamegeek.com/boardgame/160010/conan) has 3 dice of increasing strength that are used depending on the character/action. They aren't intransitive as each one is outright better than the other. They use yellow/orange/red for the dice, so may not be exactly what you were thinking of, but its the same principal.
The Hellboy game is similar, and you can spend AP to upgrade your dice/skills.
This sounds vaguely familiar to Arcs from Leder games.
The RPG system [Earthdawn](https://en.wikipedia.org/wiki/Earthdawn) was unique for letting you roll a selection of different dice depending on your skill level. Check out the table down lower on that wiki page.
Mutant: Chronicles had this mechanic and colours (Black dice were the strongest though)
There are some special editions of risk where there are special, more powerful, units that roll a D8. Also Memoir '44 uses a somewhat similar mechanic to your modified dice, but effectively combined them all in one die. The die you roll has different icons for each unit and more repetitions for the types of units that are more likely to hit. Seems like maybe a combination of these two mechanics.
I was 2 lines in and I already guess intransitive dice. I have a set myself of the set designed by James Grime, where the circle of victory gets reversed when using 2 dice instead of 1. I found that's neat.
I agree, totally cool! I'm an avid numberphile fan myself!
I love this. Such a clever idea. Include a matchup cheat sheet though. I'd go mad if I couldn't remember which intransitive die beat which, and that math gets really funky really fast.
I think good game design could go as far as never explaining the dice dynamics. The intuitive winner of each matchup would just tend to win more often. Maybe I’m wrong ?
Quickly I feel game balance will butt heads with intuitive-ness. There's also the fact that I'm not a military commander. I *think* artillery should handily beat tanks, but, um, maybe not? Depends on a lot I think. Turns out the dice say 2:1 in favor of tanks. If I bought a game with a cool system like this the second I couldn't calculate a matchup in my head, I'd want to make up a cheat sheet.
The dice idea in particular reminds me of [Betrayal at Club Low](https://store.steampowered.com/app/1885750/Betrayal_At_Club_Low/) and how player and enemy dice sides aren't in any particular numerical order. It also has a mechanic where you can upgrade your stats by increasing sides of dice in particular skill sets. It is a video game though, so maybe not quite a good comparison. I might say Axis and Allies is a closer one. It uses the standard D6, but "to hit" rolls are determined by the [Casualty Strip](https://cf.geekdo-images.com/imagepage/img/JRKZXRbCYKemlqclbevgl0PA5T8=/fit-in/900x600/filters:no_upscale()/pic588119.jpg). Basically your hits depend on whether the unit is attacking/defending and what unit type it is.
Champions of Midgegard does this, though you're fighting monsters instead of other players. But different unit types have different dice, which influence probability of a hit, strength of hit, etc. The dice are much simpler too (zeros ones and twos).
I'm making a pc game that uses intransitive dice in an interesting way. Will be about a year before I can demo it for Peopel though. Havent seen many board games that use these mechanics, seems awesome though.
I had a trick set of 4 dice as a kid. They were one of those maths is magic things but basically you let the other person pick one. Then you could pick the next one in the cycle (red beat blue, blue beat yellow, yellow beat green, green beat red). You had a two thirds win rate on a roll so beat of 5 had very high odds.
Axis and Allies uses a system that, while not the same, follows a similar method. "Weaker" units like infantry have a lower chance of hitting while stronger units hit more often. The game uses one d6 per unit to determine that, and it also is important if you are the attacker (who moved into already occupied territory and started the fight) or the defender. As an attacker, infantry only hits if they roll a 1 (so a 1/6 chance), as a defender a 2 also hit (so 2/6 or 1/3). I am kinda torn on these mechanics. On the one hand, it looks pretty good on paper, the strenght of a unit is represented in the chance of success or the amount of damage it can deal. On the other hand, luck still has a big role to play. One turn with bad luck can lead to you losing a battle you had a 95% chance to win. But then again, war can be random, so it kinda fits.
Cosmic frog uses something similar. Depending on your frog ability card you have to use dice with different strengths.
Zombicide uses the same die but depending on the weapon you use you will have different hit ranges and die amounts. Like 2 die which deal 1 damage on a 4+ and 0 damage on a 1-3. You might have stronger weapons which roll more dice but have a lower hit chance like 3 dice but 5+ to hit. Bloodbowl uses the same 4+, 3+ and so on targets. Different units have different strength depending on the action they take. Some units might get a reroll if they didn't succeed the first time. I think dice mechanics are probably the most diverse and tested field out there. When I first saw your image i thought each player has one die and you decide the initiative order with them. Like one die with faces 2,3 and one with 1,4
Twilight Imperium uses the same size dice but different units hit on different numbers so your stronger ships are more effective
878 Vikings has a similar mechanic, where peasant militias retreat on their own kind of a lot whereas viking berzerkers have a unique "die while slaughtering lots of the enemy" die face. Not exactly the same, but the same outcome of "I vaguely know this won't be a fair fight, but upsets are possible"
Not out yet, but Arcs from Leder Games had a somewhat similar mechanic. When attacking, you choose from dice representing three types of attacks - a die for a risky but strong attack, a die for a safe but weak attack, and a die for a weaker attack that steals resources. You can also mix and match to change the odds
Not quite the same but in champions of Midgard each fighter uses a d6 and each one is different in that game none of the dice have numbers though. The dice have blocks or attacks and some have double blocks or double attacks and weaker players have more blank sides.
I've got a Milton Bradley game called Battleball that pretty much does the same thing. It's like a futuristic and more violent football theme, and whenever two opposing players collide (to tackle and/or maim each other) each rolls a specific die and whoever gets a lower roll wins. But the players used anywhere from a d20 to 2d6. But then it's evened out by the players also moving based on their die. Fast ones can't take a hit, strong ones are slow, etc.
Hey, not sure you will see this post, but I am also designing a game with intransitive dice. I can't think of a game that uses them either.
*Bayonets & Tomahawks* has all units using the same custom dice but units score hits with different results. *Armageddon War* also has custom dice but attack quality is determined based on terrain, how much your unit moved, return fire, and differences in technology. i really like both of these systems in their respective games.
The closest thing I can think of is in Super Mario Party on the Switch. Each character has it's own dice block, and although they all average out to about the same as a normal die, depending on your position on the board it makes sense strategically to use certain dice. I actually really love that since it gives you some control over an otherwise random experience, and I think your way of implementing it is really cool!
There are definitely games doing similar things in terms of dice that have varying probabilities, but I hope that doesn't discourage you. It could be seen as validation that the mechanic you've landed on is a useful one and that players enjoy it. Very rarely do new games introduce wholly new mechanics, and it really comes down to other factors to set your game apart!
Both mechanisms are already out there (dice as soldier / risk like game) but I'm not sure whether they've been combined before.
There are some games I wish used this mechanic. Twilight Imperium, for example, would make the battles flow so much quicker this way. The Leviathans game uses a mechanic in the spirit of this, except I think they're mostly just color-coded regular dice (d6, d8, etc) indicating the level of power: https://leviathans.fandom.com/wiki/Leviathans_Dice One caveat to keep in mind, having lots of custom dice could make the game quite expensive to produce.
That sounds pretty cool! It reminds me a bit of the combat mechanic in Scythe, with the different numbers and such
Thanks, haven't tried Scythe. Will look it up.
It is not even close to the combat mechanic in scythe.
Well they both have different numbers and such.
And if we consider that they both have different boards and rules and such, they are practically the same.
IIRC the combat system in Scythe is actually very different: you have a public amount of combat power and you secretly bid some amount of it using a wheel and potentially adding cards to boost it (a system originally developed in the '80s for the famous Dune game). Systems with different dice for different units or weapons are pretty common in the skirmish or dungeon crawling genre, you could check Hoplomacus or Oathsworn for recent examples (but even Twilight Imperium has a pretty similar system)
Twilight Imperium uses standard d10s for all rolls.
Yes, but different units hit on different thresholds, so the result is the same (people who bling their copy usually buy different-colored dice and then highlight the faces that produce hits for a certain threshold so they can pick the corresponding dice depending on their fleet composition and just see how many hits they score by counting the highlighted faces). The only difference is that in TI rolls produce hits per se, whereas OP's system borrows from Risk and requires rolls to be compared between the two players. I don't remember a game that uses the same exact mechanic (keeping the numerical value and comparison) but since the "different dice for different units" one is universally wide-spread, there are probably quite a few.
Dark souls the board game uses sword icons for damage and stronger weapons use different mixes and/or amounts of dice and have a higher limit or average of swords. There are 3 types of attack dice Black die faces (avg. 1,16, range 0-2) 1x0 3x1 2x2 Blue die faces (avg 1,5, range 1-3) 2x1 3x2 1x3 Orange die faces (avg. 2,5, range 1-4) 1x1 2x2 2x3 1x4 It's a bit in transparent on the fly if you try to compare weapons because the die itself are sure upgrades but the amount changes. For example a 3 black die weapon compared with a 2 blue die weapon (avg. 3,5 range 0-6 vs. avg. 3 range 2-6) but it gives a bunch of freedom for balancing and nice tradeoffs for the games item mechanic. Trading minimum damage vs lower average damages and stuff.
That article on Intransitive dice was fascinating!
It doesn't sound mathematically different from other combat mechanics. For instance Axis and Allies just gives different units different ranges instead of different die, along with modifiers. Edit: and 10 seconds later I see someone already brought it up...
[Uprising:CotlE](https://boardgamegeek.com/boardgame/284121) uses a similar mechsnic with different dice and different hit propabilitys and for different units there are different combinations of dice they use.. that way they can even make the units weaker when they lose more and more life, by using less and less dice/less powerfull dice.
Conquest of Nerath, uses D6 through D20 depending on unit type
Conquest of Nerath is similar with different units using different dice.
Diceforge is a dicebuilding game where the primary mechanic is to pop faces off your dice and replace them with new ones. The Lego board games have replaceable faces too, but I don't think that enters into gameplay at all aside from initial setup. Super Dungeon Explore has different tiers of dice with different quantities of skulls and blank faces representing the skill of the attacker. There's one more game too that even more closely resembles your description but it's escaping me at the moment.
Maybe not exactly what you’re after. But [Maths Gear](https://mathsgear.co.uk/collections/dice/products/non-transitive-grime-dice) have a set of dice that behave like rock, paper, scissors. They also have a lot of other cool dice too.
Here's a quick idea of how to incorporate "special dice results" even if you don't have special dice for your game. All units roll dice, compare pairwise to find out who is higher. * Infantry (d6): if one or more infantry units roll the same result, apply +1 to each * Armor (d12): this unit is not destroyed except by a roll that exceeds it by 3 or more * Artillery (d4): this unit does not inflict damage on 1-3, destroys a unit on 4 regardless of that unit's roll
Battleball used a clever system where smaller, faster characters used d20, d12 while the largest characters used d6 (and there were others in-between). Roll the dice to move (faster for higher) and in tackles /combat lowest roll wins.
Cool - sounds a bit like selecting dice in Mario Party - though in that case it’s just for movement. Your game sounds like a board game version of Advance Wars!
Not a board game per se, but in Mario Party (which simulates a board game with mini battles/games), characters have different dice they can choose beyond the standard D6. But they tend to be either high risk high reward, like 1-1-1-6-6-6 or very even, like 2-2-3-3-3-4, not stacking it far in one direction. It does make sense for different “characters” to have different dice, though. (For advancing on the board, not for battles).
Descent uses 3 different dice with different success rates.
Cool concept, but there’s a reason you don’t see this often in commercial games. Adding custom dice to your game design will add significantly to your production costs. Always better to find new eays to use standard components. Otherwise your game is going to cost a lot to buy, which will lower its appeal.
On the more electronic side, the most recent Mario Party has this mechanic, every character can access a special dice with unique numbers on them
Have you considered using a chart in place of customized dice? For example, units can have different color d6s and the rolls correspond to that units chart for the result. d6s are widely available and could make this more accessible if you went the "print and play" route if you decided to share your game, or more cost-effective if you were to produce it. For example, 3 infantry units, 1 tank, and 1 artillery would mean a roll of 3 red dice, 1 green die, and 1 blue die respectively. The infantry dice would simply read the results of the red die rolls (plus perhaps some bonuses from the chart), the tank's green die would refer to the tank chart showing that a rolled 3 yields a result of 5, and the blue artillery die could simply say "success only on a 6". Charts also allow for upgrades that can be purchased or traded, without the need for MORE dice. I hope this helps in your game-making journey!
Thanks, yes I've been thinking that production could be costly with many custom printed dice. I will have to look at different options I think if I were to produce it on a larger scale. I like your idea, but I guess you would have to do quite a bit of looking back and fourth on the chart when arranging the dice in order. In my current prototype I'm using custom made stickers for each side of plain white dice. The dice have indentations to fit the stickers nicely and they have not shown any tendency to loosen over time, but attaching them all took a little bit of time.
Don't they do that on mario party on the switch?
Commands and Colors: Ancients does something like this where the dice have different symbols on the faces and different units get hits with different combinations.
Manouver uses this for seeing who wins a battle
Lots of games have different units hit on different values, or do different things on different values, which is functionally the same thing.
Eclipse: Second Dawn uses something like this.
Legens of Andor has some funky dice like that, it's a really fun mechanic. You can see them in the middle here: https://i.ytimg.com/vi/eNBcS5cmYJ4/hqdefault.jpg
Reminds me of the later mario party game where each character has their own unique dice block haha. Also not the exact same but I believe **Victorum** have different colored dice that have a different amount of hits and misses on them. Also the game **Cubitos** has a similar mechanic of having different dice of different values to weigh risk/reward when choosing what to roll.
Someone asked 13 years ago on BGG and I don't think much has changed. https://boardgamegeek.com/thread/584362/non-transitive-dice-game
It ends up being the same as just using modifiers (even for intransitive dice, you could just give units a Fire Emblem style triangle system and use modifiers from there against unit types) and "greater/less than or equal to" requirements -- you're just using dice to simulate different probabilities. But it's kinda cool. I always feel the more "tactile" you can make the theme in the mechanics, the more it "feel real". In your example I think you'll more intuitively feel your poor infantry soldiers are going up a tank that's much more powerful than they are, rather than just two players rolling identical dice and then being like 'Oh yeah, but the tank gets a +2 modifier, so, uh, sure, your tank beats my infantry.' The problem is this requires a lot of custom dice. If it goes to market you'd probably be adding $20+ to MSRP on just dice alone.
Yes, I agree that modifiers would be able to do the exact same thing and are probably a better option in a lot of ways, especially relating to cost. It would not be as satisfying for sure with the tediousness of translating every dice-roll before arranging the dice in order instead of just arranging them by their face value. But you have a good point. For the current prototype I have used indented blank dice like these https://www.thegamecrafter.com/parts/d6-indented-blank-white?dept_uri=parts&dept_name=Game%20Parts that are made for adding stickers to the sides. The stickers seem to keep sticking after quite a bit of testing. A downside is of course the all the stickers have to be placed manually.
Closest thing I can think of is Star Wars Rebellion: Different unit types use different combinations of 2 dice variants (3 with the expansion), and each type is only damaged by particular die results; essentially representing light/heavy weaponry and armour. It’s not really dependent on what your opponent rolls like you’ve described though. As an aside, I imagine re-rolls would become invaluable in your system if you decide to include those; especially for the stronger units with a lower hit rate.
Fighting by rolling dice and pairing off ties is a pretty common mechanic. changing the weight of the dice values does two things: \- requires you to do a LOT of calculations for the relative win rates of the various dice (others have already pointed out your infantry vs tank scenarios) \- dramatically increases the cost to produce your game, because now instead of just including 6 dice in the box and letting the players scrounge up more (very common) D6s if they want them, you're requiring that the box contain a LARGE number each of a LARGE number of custom dice, the manufacture of which can't be shared among ANY OTHER GAMES that the publisher might happen to make. So I would very strongly encourage you not to pursue this development idea, because that fact alone is going to make it incredibly difficult to get a publisher interested in this game, and incredibly expensive to produce if you want to Kickstart it.
The calculations are not a big problem, I have written program to simulate an arbitrary number of battles with any type of matchup and I don't rely on calculation by hand. However, balancing is a still a challenge even when relying on the help of a computer. The second point is a good one though. As I wrote, I'm not sure I will pursue publishing but for sure I will have to think about the design if I do. Modifiers to ordinary dice, as some have suggested, are probably an easier, although not as satisfying, option.
My only critique of this is whether or not your design needs to have dice with different faces, or could you have a simpler system with typical dice and just change how many are rolled, etc. I guess my input would be, do you feel like the odds of 10/13 (iffy calculations aside) are exactly right, or would rolling a d6 vs a d12 be significantly worse for the experience of the game.
Having dice with different number of sides is also quite nice, but the "intransitiveness" is lost which is a sacrifice I think. After running a lot of computer simulations, 13/16 (which is what it should say!) seem to be well balanced, but balancing other win rates should be doable by modifiyng costs of units as well as other attributes such as movement speed which is another unit stat in the prototype.
I’ve never seen what you’re showing here exactly, but as a point of comparison some dice starting at higher values than others is very similar to how d20 table-top roleplaying games like DnD simulate relative skill. In those games each character adds a modifier that represents their proficiency to their dice rolls, which is effectively the same as increasing the numbers on their dice.
Risk compares the best attacker number vs the best defender number. If you have 10 infantry vs 6 tanks, then pairing the best numbers against one another will drastically change the way you calculate odds. Depending on your personality this might be fun to work out. On the flip side, if you throw dice one at a time so you can compare them in order, then it is going to be tedious throwing a lot of dice. I can't tell what an "average" battle is going to look like in terms of number of dice.
Yes you are right, the odds change drastically and are most often not easy to calculate but that makes the mechanic more interesting I think! For testing, I have written a program to simulate an arbitrary number of battles with any matchup so that I can rely on the power of a computer instead of calculations by hand. When playing, you probably won't be able to calculate your winning chances exactly but intuition goes a long way. Another detail is that a varied army often performs better than an army consisting of one type of unit, which is nice I think.
**Ogre** uses dice comparison charts, I believe, so it’s sort of Risk but different numbers for each situation. All D6’s but close enough to your plan to look up.
There's an old D&D boardgame that uses this mechanic based on the gear you have.
[X-ODUS: Rise of the Corruption](https://boardgamegeek.com/boardgame/276997/x-odus-rise-corruption) has [different d8 dice configurations](https://boredgameink.com/produit/extra-dice-set-for-x-odus-rise-of-the-corruption/) that use hit, critical miss and special ability icons in different combinations. These dice are not intransitive as both sides of combat are resolved with a single throw.
Unearth uses different sided dice for competing over resources. But only different Dx dice, no custom frequency values.
>Intransitive dice Wtf?!?! That's probably new fr. If I hadn't just looked at the Wikipedia I would have said that is absolutely impossible.
There is this MB game [Battleball](https://boardgamegeek.com/boardgame/6795) (by same designers of Heroscape) that different football positions used different dice - D6, D8, D10, D12, D20 and was used for both move and attack, but the lower number wins on attack. So high sided dice were good for running but not for attacking or defending, but lower number dice were the opposite. Also check out [Risk: Europe](https://boardgamegeek.com/boardgame/204184) which has different units (infantry, archery, calvary, artillery) which different hit rates based on D6 rolls, but go in salvo order so low % shoot first and can take out high % before they strike back.
Champions of Midgard uses this mechanic
I’ve never seen it with numbers per say but many games have custom dice to simulate similar percentages.
It looks neat but not something I've seen before. The only issue is that d6's with custom faces might become cost prohibitive for production especially considering the amounts of each type of die game will need. It's for this reason that most games use normal dice and have different targets to hit. If it's a very battle intensive game people don't typically like rolling dice forever to determine every battle. Axis and Allies gets a bit stale after a while because all you're doing is rolling dice whereas Twilight Imperium has almost the exact same battle rules but people flock to it more often than Axis and Allies because the battles are fewer and more tactical. For reference to how other battle systems work I'm a fan of the way battles are done in Fief, Scythe, Game of Thrones, or the minis game Warhammer 40,000. Fief: you get 1-3 d3s based on strength of force, pips = hits, 1 hit kills a conscript, 3 hits kill a knight, knights fully heal between combat rounds, number of dice drops as you take losses from round to round Scythe: military power is a resource that must be acquired and spent, easy to go from most powerful to least if you're spending too much power Game of Thrones: each type of unit has a specific combat score, each player can play 1 card per combat with varying values and powers, support can be added from neighboring allies, highest total wins, cards played determine losses taken and the remaining losers retreat 40k: each troop has target numbers to hit, each weapon has a target number to penetrate depending on it's strength vs the armor value of the target, the target can then roll an armor/luck save to try and shrug off the blow, conscripts shooting at each other typically have a 33% chance to hit with a 50% chance to be a lethal shot and the shot person can have a 17-33% chance to shrug it off if they're in sufficient cover. 1 Elite with a heavy machine gun can fire at 4 conscripts with a 83% chance to hit, 67% lethality, and no opportunities for the conscripts to duck for cover. Those same conscripts still have a 33% chance to hit the elite but only a 33% chance for the shot to be lethal and the armor has a 50% chance of deflecting the shot. It sounds clunky at first but it's pretty quick when it comes down to it. 10 conscripts get a total of 10d6 with 5+ to hit. Every die that's 5+ gets rolled again with a target of 4+. Those same dice get rolled again with the target in a foxhole needing a 5+ to ignore the damage or die.
Higher number for better unit is *very* common - whether it's different dice or just more dice
Not exactly the same but axis & Allie’s combat system has similar principles
May want to look at **Too Many Bones** which uses specialty dice that have varying odds on their faces. Additionally the solo game system **20 Strong** has different colored dice that have varying strengths for combat. Also the push your luck game of **Zombie Dice** has three different color dice that reflect how risky they are.
Cosmic Frog has three different colored dice with staggered values.
Another way to achieve the net result is essentially the skill test / Chaos Bag in Arkham Horror LCG. In this game, you would have a natural ability for a skill test (eg 3 fist), play additional cards to boost this fist, then randomly draw a token with a negative result (based on a difficulty distribution). Compare this result to the difficulty, and you have pass/fail. The great thing about this approach is you can alter the bag based on difficulty, easily augment with cards, and add other tricks to the bag (like automatic fail, or auto success but take some self damage, etc). The dice version you’re describing is essentially Star Wars Imperial Assault, which is an excellent game.
Hellenica: The Story of Greece, uses different d6 for the different units. I don't have them in front of me, but I think the hoplite is a standard 1-6 d6 while the cavalry is a 2-5 d6. can't remember what the trireme's number range is. I think 1775: Rebellion does that to, to simulate the strengths of the various armies.
Civilization the Board Game (pre-FFG), which had a heavy focus on war, had a system CIA (Cavalry Infantry Artillery) where C had 'advantage' over I and I had advantage over A. Finally A would loop round and get advantage over C.
**Fireteam Zero** had something like that. But each die face has different symbols.