Author’s Note: My math skills are not great. It’s why I became a writer, but this is a math-heavy subject and one I will do my best to do justice to. Any errors of math are thus, mine and mine alone.
Since Avalon Hill published Tactics in 1958, we’ve all seen various forms of the oldest convention in wargaming – the Lancastrian (or ratio of attacker to defender) based Combat Results Table (CRT). It seems a simple thing for wargames, but we’ve been arguing bell curves and square roots ever since. And, since the 1980s, we’ve been arguing over which dice work best. One six-sided? Two six-sided? Maybe a ten-sided, or perhaps, the heresy of heresy, a twenty-sided die?
I’ve seen many combat results tables in my time, and for the record, I prefer the bloody ones. The bloodier they are, the faster the combat goes. But history doesn’t always support my point of view. Most armies throughout history have rarely fought to the last man. In fact, as Boneparte put it, “In war, three-quarters turns on personal character and relations; the balance of manpower and materials counts only for the remaining quarter.” What that means is, raw numbers is far from the only thing. We try in hex and counter wargames to reflect this through a variety of means: be it die roll modifiers, odds column shift modifiers, or different dice rolled for various tables (a unique version of this I saw implemented in the game Red Tide West), and a myriad of other methods that don’t bear repeating here.
But is one method better than any other? I am probably the least qualified to say, as I am the guy who got a “C” in Algebra and felt fortunate enough for it. My main question would be, “does it reflect the period being simulated, and does it make sense?” For example, 3-1 odds unmodified does not mean most of the results are “Attacker Eliminated.” Now, if it were a prepared defense, then I’d say there’s a good chance of that, as 3-1 isn’t traditionally enough to overcome such a position.
But not all CRTs are odds-based. For example, look at the Infantry Fire Table from the Advanced Squad Leader Series:
Advanced Squad Leader and its predecessor, Squad Leader, was always a firepower-driven game, and it didn’t rely on traditional odds-based tables for its combat results. Instead, it had an Infantry Fire Table (IFT) that one rolled against with effects for range, cover, and the leader’s own modifiers combined as modifiers against the roll. As you can see, lower is better in this system, which is a throwback to older rules. The newer standard tends to be higher die rolls have more positive results. But this system makes a lot of sense for a game like Squad Leader. One well-placed machine gun or two men with a radio and an off-table mortar battery can cause a lot of potential havoc out of proportion to their numbers.
These firepower-based tables are common in tactical games, but they’re not the only kind of table one sees. Other games, such as GMT’s Panzer and MBT series, rely on rolling a pair of ten-sided dice as percentile dice to determine if the target is hit and what damage, if any, is done. These games are often quite detailed and have rules for facing the target vehicle, the slope of the armor, and so forth.
Simply put, there are many combat systems out there, and all of them are meant to handle different levels of game. Even the results of a given combat can be interpreted differently depending on the game and what it’s trying to simulate. That seems obvious, but there’s been some controversy with some systems over others, and everyone has their favorites.
I personally like the traditional roll of six-sided dice and a consult of the odds table. It’s what I grew up with. I get it instinctively. That said, I think times are changing. I don’t see as many single six siders being used for CRTs anymore, as I think designers want more granularity in their results, and many seek to avoid the pitfalls of the almighty probability distribution. See, I told you I’d try to work in some math somewhere, right?
The X-axis is the die roll result, and the y-axis is the percentage chance of a given result. You’ll notice six, seven, and eight are the most likely outcomes, with the other results being outliers. Many wargames’ CRTs have been tied to this since time immemorial. That’s why I think many designers are seeking to break free of this to gain more granularity and increased chaos in the potential combat results, just like the real thing they are modeling.
It’s all a lot of food for thought. As always, Good Gaming, Everyone.
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(This article is credited to Jason Weiser. Jason is a long-time wargamer with published works in the Journal of the Society of Twentieth Century Wargamers; Miniature Wargames Magazine; and Wargames, Strategy, and Soldier.)