The skeleton of a simple wargame

Skulls in the stars has a neat little post about unusual dice. Check it out. I am especially enamored of the rock/paper/scissors (“Nontransitive”) dice, and it got me thinking about how you could use those dice in a war game.

Image from Skulls in the Stars

Delta’s D&D Hotspot has a chart with a simplified schematic of troops types, and it reminded me of a similar schematic.  I was thinking this diagram was from one of Richard Gabriel’s books, but the magic of Google Image Search tells me it first appeared in Archer Jones’s book The art of war in the Western world. Happily someone has already scanned it:

“A” = attacks successfully; “D” means defends against successfully; in either case it is a tactical edge

So the “nontransitive” dice each have an advantage over one other die and thus a disadvantage versus another die, with something like a 2/3 advantage in each case!  I think the “3” die is equally matched vs. the “1-5” die (each has a 1/2 chance of beating the other in any roll-off), but the “0-4” vs. “2-6” dice gives a very slight edge to “2-6” (5/9 of rolls will favor the 2-6 according to my calculations).

The mechanics I envision for the wargame would give each of four unit “types” a specific die, and when they fight each other, they roll that die, high = winner.  So Heavy Cavalry (HC) is the 6-2 die, Light Infantry (LI) is the 5-1 die, Light Cavalry (LC) is the 4-0, and Heavy Infantry (HI) is the 3-3 die.

That would make: HI evenly matched with LI, and having an advantage vs. HC, but disadvantaged vs. LC.  But HC is at an advantage over LI, a slight edge over LC, and at a disadvantage vs. HI.  (This make HC a little better than they “should” be, since LC should actually have an advantage over HC.)

So, you assign one nontransitive die type to each troop type, and they always roll that die, and high roll wins. There are no ties.  Except when Heavy Infantry fights Heavy Infantry.  At first I was thinking this was bug, but my brother convinced me that this could be a feature.  Two lines of HI would fight to a standstill, if they are lined up to all fight each other head-on.  But if any advantage arises from position (flanking, concentration of forces, etc.), then the side with the advantage wins.  All you need to do is add a rule that should two units of a given type contact a single enemy, you add their dice.

I should note that I am conceiving this with DBA/HOTT style “elements” — one base of several figures represents a “unit” (or “element” in DBA jargon) and they move, fight, and die as a unit.  This is obviously an abstraction; a unit that is “destroyed” might be merely routed, dispersed, etc. and not necessarily killed to a man.  However big you want your units, you just make sure both armies are scaled to the same ratio of men:figures and figures:element.  Since a real unit might be hundreds of men and horses, movement and shooting ranges would be very small (1-3 element’s base widths would be all a unit could or shoot).  So you could just lift DBA’s movement rules wholesale.

I think you’d want to preserve the possibility that some kinds of units are not necessarily destroyed when they lose.  Cavalry defeated by infantry would be able to ‘retire’ (fall back) rather than be destroyed, assuming the infantry can’t shoot and is not flanking or surrounding them. Infantry defeated by cavalry would be destroyed/routed in any case.

One further kink is we have not thrown a regular d6 into the mix yet.  I’d probably adopt the DBA/HOTT mechanic of rolling a die to determine how many of your units can move on your turn (an abstract way of handling command & control issues, like were the orders understood, were they obeyed, did the messenger reach the right troops, etc.).  But you could also reserve the regular die for another troop type, such as the commander’s unit, or maybe irregular/fanatical units.

Heavy Infantry: “Use” the 3-die (there’s no real reason to roll).

Light Infantry: Use the 0-4-die.

Light Cavalry: Use the 1-5-die.

Heavy Cavalry: Use the 2-6-die.

Fanatics/expendibles/hordes: Use d6. Always lose ties. This gives them even chances versus HI, even chances vs. LC, and an advantage versus LI, and a disadvantage versus HC and Commanders.  But they do have a chance to beat any other unit, and do not stalemate versus HI.

Commanders: Use a d6. Always win ties. This gives them an advantage versus all troops.

Movement: Roll d6 for PIPS, and use DBA in all respects, treating Light Infantry & Fantatics as Auxilia (300 paces)  and Heavy Infantry as Spears (200 paces), Light Cavalry as Cavalry (800 paces) and Heavy Cavalry as knights (600 paces). Commanders move as whatever unit they are represented by, usually Heavy Cavalry or Heavy Infantry.

Shooting: As per DBA.  If the shooter loses, no effect unless opponent has missiles.  If defender loses, they are destroyed.

Combat: Roll your troop’s die for each attacker, and the only difference from DBA is that troops attacking the flank or rear roll their die and add to their side rather than subtract a point from enemy’s die, and overlapping units add one to their side’s roll. (Use DBA for definitions of overlapping and flanking).  Loser destroyed. Cavalry of any type may retire (as per Fleeing in DBA) rather than being destroyed.  I am thinking that “rough” terrain (“bad going” in DBAese) will carry a penalty.

Any army will have one Commander (optionally you might add one or two more for subgenerals/allied generals/heroes/monsters).  The other units are basically equal, except that Knights are a little better than the others, so let’s say all units are 2 points except knights are 3 and Commanders are 4.  I would also make it an option to give a unit missile weapons like bows, slings, or crossbows (thrown weapons would be used only once in contact with the enemy), which shoot at a distance (I’d just use DBA/HOTT shooting ranges).  Missile armed units cost an extra point.  Cavalry do not get to fall back when fighting missile armed infantry. Any unit may have missiles, but this would be rare for knights, and for the Heavy troops this probably means the unit is “mixed” like the ancient Persians with spears & shield in the front ranks and bows behind, or mixed Byzantine units of knights and horse archers, etc.  I’ve gotten rusty on ancient and medieval troop types but I believe that there were medieval Egyptian troops who fired volleys of arrows from horseback and wore heavy armor…

I am not sure how the capacity to shoot, or higher move rates of cavalry, will affect their “value” in terms of points.  But that’s a starting point for play-testing.  First I guess I need to make or buy nontransitive dice. 🙂

Published in: on May 2, 2011 at 6:00 am  Comments (5)  
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5 CommentsLeave a comment

  1. Crazy cool! You could also make the heavy foot die with one 4 or one 2 to have some action in the mirror match.

    I’ve seen other nontransitive relationships in various wargames from DBA to the Total War series. For example, archers > spear > horse > archers, or light horse > heavy horse > blades > spear > light horse.

    • Good point about the 3-die. Otherwise you’re not really rolling. However adding any 4s or 2s will muck up it’s superiority over/inferiority to its neighbor dice. I’ll have to see how big a difference it makes. 2s will weaken HI relative to HC and 4s will strengthen them relative to LC…but LC is already the “weakest” overall, and HC the “strongest”. I guess I’d be more inclined to weaken LC than strengthen HC. Maybe letting LC shoot like LI would be enough to balance that.

  2. Nice post! Incidentally, there are a couple of math papers that discuss how one can extend non-transitivity to d8, d12, d20; if you’re interested, I’ll dredge them up and send them to you! (They don’t look too technical.)

    • Wow, yeah, I would be very interested!

      • I’ll try and send you the papers in the next couple of days — feel free to remind me if I forget! (End of teaching semester is crazy!)

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