ROLL THE BONES
More ways to interpret dice results
One of the key elements in all our games – figures, RPGs, boardgames – is ‘luck’, that unknown, unquantifiable element of randomness which humans have feared and craved since we were so rudely woken up by some alien dumping their recycled black obelisks in our camp (at least, according to Arthur C. Clarke). Whilst packs of cards can be a very interesting alternative (and may be the subject of a follow-up article), what I would like to discuss are some simple ideas for how the use of dice can be interpreted, without resorting to computational engines or A-level maths books.
NUMBERS, PREDICTIONS AND WHAT?
First off, I’d like to present some of the problems with the good old dice. For a single die (assuming it’s well made!), the various faces all have an even chance of being rolled (unless I’m rolling them, when the low numbers are more frequent!). And it’s not a new phenomenon – the Roman hexagonal ‘long dice’ were still prisoners of the same mathematics.
However, when you get into multiple dice, the results/probability curve starts to kickin. To illustrate:
Anyways, you get the idea. By simply adding the dice to a single total, the overall result is ‘skewed’ towards the centre of the range – the more dice you add, the greater the distortion. But what else can you do with a handful of D6s?
READING THE RUNES: MEAN, MEDIAN & MODE
Let us say you are rolling a handful of D6s – say, seven of them. If you were to roll scores of 1,2,2,2,4,5,6 this can be read four different ways right from the off:
◗ Simple total is 22
◗ Mean (average) is 3- ish (total of 22 divided by number of dice)
◗ Median (middle number in any sequence). There are then two ways of looking at this:
◗ Either the absolute middle (in this case the 4th position which is 2)
◗ Or the middle of the unique numbers which have occurred – 1,2,4,5,6 (so 4)
◗ Mode (or ‘most common’ in any set) in this case is 2
How can any of these be used in a game? Well, my own corps-level ACW rules use brigades as the basic unit. But to get the ‘ebb and flow’ of combats,
I use buckets of dice with most bonuses or penalties etc being reflected by the addition or removal of dice from the ones to be rolled. However, not only does the resultant roll provide info on the normal range of ‘hits’, I also use the roll:
◗ Any doubles and trebles are used to generate ‘special effects’ such as running short on ammunition, death of a key commander etc. I use different tables for the two types, with increasing severity.
◗ The mode (most common) score sets the unit’s perceived level of success as the starting point for any subsequent morale rolls, as this often did not match up to actual performance or tactical situation! True, it can still be adjusted by the usual veteran/ green etc, but only adjusted…
This approach is especially useful for the ACW, where some units would break at the first reverse, while others merrily kept going even when losing people right and left. I’m sure that players with other period interests can think of suitable adaptations. But there are yet more interesting things you can do with multiple dice…
You can also use the ‘buckets of D6s’ approach to represent in simplified form much more complex actions such as fire-fights. About a thousand years ago I was involved in the development of the rules for the Werelords’ award-winning ‘MoonGrunt’ game. This was a near-future 15mm game with different fireteams engaging each other. Skill levels set a basic number of dice, then weapons and tactical situations added or subtracted from said number. The difference was that the defender also rolled a number of D6s and results were then computed by laying-out the rolls in descending order and comparing attacker/defender 1:1 in sequence. Anti-vehicle effects could also be achieved (or increased in severity) in a similar manner.
DICE COMBINATIONS
There are many systems out there which have taken a multi-dice approach, especially since the arrival of ‘RPG’ dice giving results in 1-4,8,10,12 and 20 ranges. The fantastic space combat game Silent Death used a three-dice system for combat:
◗ Skill levels set one of the dice (d4 up to d12)
◗ Weapons then set other dice, depending on range etc (so 3d6 or 2d8 etc)
The resulting roll was first checked against a total required to hit a target, but then the scores were examined for the weapon effect, which might be expressed as ‘low +2’ or ‘high’. Thus a roll of 1d10 (good gunner) and 2d8 (med-range laser) might score 5,7,5. If the weapon hit and the result was ‘low +2’, the lowest score was 5, but there are 2x 5’s, so in this case the final effect would be 12 (5+5+2): ouch!
My first introduction to D10s was with the venerable Lou Zocchi space combat rules, but my most frequent use was in numerous wild west skirmish games by Mike Blake and Steve Curtis. This was the first time I had seen a pair of said D10s used as ‘percentage based’ answer: a brilliant means of addressing that damned probability curve with multiple D6s. In more recent years, the D20 has grown in popularity with some game designers. It is often seen in an attempt to claw-back the use of multiple stage results into a single computation. The Chicago Way by Great Escape Games is a 28mm skirmish game in Prohibition era United States and uses both specialised card decks and a D20 to provide both hit, wound and ‘morale’ effects from a combat round.
The old WRG Ancient rules famously used a combination of different dice to reflect the steadier results to be expected from trained, disciplined ‘regulars’ as opposed to more volatile but quite violent ‘barbarians’. Thus the ‘regulars’ used a six-sided Average Dice (faces 2,3,3,4,4,5) whilst the other mob still had D6s. This had the effect of smoothing the results curve for the regular units, grouping possible results more towards the centre of the curve (three AvD can only score between 6 and 15, but with a massively increased weighting towards the 9-12 band).
And now of course there are other dice on sale, showing ‘binary’ results (ones and zeros), increasing bases (1,2,4,8,16,32) and – well, all manner of numbers. My own favourite Fibonacci series (next number is the sum of two previous numbers) is banned by my (socalled!) friends as it reminds them too much of school, but with loads of blank dice now around the limit is really your ability to see small print!
OTHER SIMPLE DISTRIBUTION SYSTEMS
In several US boardgames, pairs of D6s are sometimes used on ‘special event’ charts which really bring period flavour to the basic strategic goings-on. In this case, however, to prevent the skewing discussed earlier, the two dice are treated as ‘tens’ and ‘units’. Thus a roll of
4 and 3 is read as 43. There are of course still only 36 possible combinations which can be rolled, but the basic result range is now 11-66, and by judicious construction of effects charts it is possible to still include some +/adjustments to give 60 or more outcomes – from just two dice! It is also useful to ‘band’ the results in each range to different types of result, so – in a tankfest or Starship encounter – the 11-16 might affect tracks/drive, whilst 61-66 could be the bridge/crew and so on…
GET ROLLING!
I hope that this has piqued the interest of budding designers out there. But the best way to learn is by exploring – grab some friends (ideally vaccinated ones by the time you see this) and roll some dice.
My thanks to the long-suffering members of South London Warlords, SELWG and Maidstone Wargames Society for putting up with my experiments over the years… ■