09 March 2023

Words by Arthur Harman, Illustrations by the Editor
Mr Harman offered this article in Miniature Wargames Magazine which I was tempted to subtitle ‘Mercy Buckets’ (on the basis of comedic French as opposed to real Latin!). Arthur and I have often disagreed with the use of dice in games – in the nicest possible way, you understand – and I have an opinion that some gamers display an almost ‘phobic’ approach to using anything other than ‘normal’ dice (as the Author would call them!). Being the sort of chap he is, Mr Harman has actually come up with some ideas and solutions rather than my usual approach of just banging on about pet peeves so – preamble aside – over to Arthur Harman. Ed.
MY POSITION
Gaius Julius Caesar famously said, “Alea iacta est” (the die is cast) when he crossed the Rubicon to march on Rome to seize power. Some wargame rules require players to throw large numbers of dice – sometimes referred to as ‘buckets of dice’ – to resolve musketry or close combat.
Whilst this randomness may offer a very realistic recreation of the erratic performance of volley fire by flintlock muskets, for example, counting out the appropriate number of dice, throwing them, counting how many have the appropriate scores, and ten picking them all up again afterwards is both timeconsuming and extremely tedious. And some of the dice always seem to bounce out of the dice tray and have to be retrieved, either from amongst the ranks of your troops or from the floor!
MY PROPOSITION
Here is an idea to replace ‘buckets of dice’ with only six dice to reduce the time spent on dice throwing and speed up play. I don’t claim it exactly replicates the probabilities created by ‘buckets of dice’ but it should certainly save you time – and the expense of buying lots of dice in the first place.
MY PROCESS
All you need is six, differently coloured normal dice. For purposes of this explanation, let’s assume you have black, red, green, yellow, purple and blue dice. Allocate individual scores to each die, so that the score of the black die is the number of ones thrown; the score of the red die, the number of twos, and so on.
Construct a chart like this:
Black 
Red 
Green 
Yellow 
Purple 
Blue 
1’s 
2’s 
3’s 
4’s 
5’s 
6’s 
MY DIFFICULT EXAMPLE
Suppose that the situation in your tabletop battle requires you to throw a die for each of twentyfour figures shooting and only fives or sixes will count as hits on the target. Throw the six coloured dice. Let’s say the purple die, representing fives, scores 3 and the blue die, representing sixes, scores 2. Since the number of men shooting is an exact multiple of the number of dice, you could simply multiply the total of the scores on the purple and blue dice, five, by four to discover the number of hits obtained, giving twenty hits. That’s pretty good shooting.
But suppose the purple die had scored 4 and the blue die, 5: using the method described above would give 9 x 4 = 36 hits – impossible if only twentyfour figures are shooting! We need to resolve the casualties in a different way.
MY BETTER EXAMPLES
Assume the scores of the six dice are
as follows:
Black 
Red 
Green 
Yellow 
Purple 
Blue 
6 
5 
2 
6 
3 
2 
The total of their scores is 24, the same as the number of men shooting, so we can regard each score as a number of shots. Using this method, the number of shots that hit their targets is only five, much lower, but quite realistic.
Suppose the number of men firing had been fortyeight, twice the total
of the dice scores, we could simply double the number of hits to ten. If the number of men had been thirtysix, we would multiply by 1.5, giving 7.5 hits, or eight hits when rounded to the nearest whole number.
If the total of the scores is more than the number of men firing, we can reduce the number of hits by the appropriate proportion. For example, if the six dice scores for twentyfour men were:
Black 
Red 
Green 
Yellow 
Purple 
Blue 
3 
5 
2 
4 
3 
2 
We simply multiply by 0.75, giving 3.75 hits or four hits when rounded up to the nearest whole number. (Arthur, do you think on the fly multiplication by fractional numbers is a simple process? I’ll confess I disagree! Ed.)
If the total of the dice scores only exceeds the number of potential hits by between one and six, then disregard the die whose score is equal to the excess, meaning that, when all the dice were thrown, no die scored that particular number. Suppose twenty figures were firing and the dice scores were:
Black 
Red 
Green 
Yellow 
Purple 
Blue 
5 
5 
3 
4 
3 
2 
This totals 22 – an excess of 2 – and we would disregard the Blue die and imagine no sixes were scored, giving only 3 hits.
Should two die scores equal the excess, and one – or both – of the dice represent potential hits, throw one die to decide which score to disregard. If the dice scores for twenty men had been:
Black 
Red 
Green 
Yellow 
Purple 
Blue 
5 
6 
2 
4 
3 
4 
This totals 24 – an excess of 4 – scored by both the Yellow and Blue dice, so we would throw one die: odds indicating that the Yellow die would be disregarded; evens, the Blue die. If the Yellow die is disregarded, then no fours were thrown and seven hits were obtained; if the Blue die, then this means that no sixes were thrown and only three hits were scored.
Of course, if none of the dice whose scores equal the excess are potential hits, there is nothing else to do.
A similar procedure can be followed if the number of firers only exceeds the total of the coloured dice scores by between one and six.
Why not give it a try?
Are ‘buckets of dice games’ something you play or representative of systems you are keen to avoid? Me? I'm quite the 'polyhedral' kind of chap. But what do the readership think? Ed.
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