Some Fridays ago, I presented two games to a total of four PW participants... Bob and Cleo Liebl, Stephan Patejek, and Bruce Zorn. I thought that, in this article, instead of talking about the nitty-gritty of the individual games, I'd mention some of the topics that came up in our post-battle discussions.
Discussion the 1st.
The first game I presented had a medieval setting... that is to say, my idea of what a medieval setting should be... we had wimpy untrained foot, and crossbows and archers and men@arms and foot knights and mounted knights. These troops were arranged in groups called 'retinues', each under control of a Big Guy, a Leader Knight.
Each retinue had a data sheet on which its losses (in terms of loss points) were tracked. When a certain number of losses accumulated, stands were removed. And when it came time to take stands off, we tossed percentage dice, referring to the following table:
- 01 - 25 Remove 1 stand of untrained foot
26 - 50 Remove 1 stand of archers
51 - 75 Remove 1 stand of men@arms
76 - 100 Remove 1 stand of foot knights
It was Bruce's thought that this table was off kilter. You'll note that there was the same probability (25 percent) of removing a stand of foot knights (powerful guys) as there was of removing the wimpy untrained foot.
Bruce's idea was that the table should be biased in favor of the more powerful units, i.e., there should be less chance of a stand of foot knights being taken off then one of the weaker types of troops. A table, perhaps, similar to this one:
- 01 - 40 Remove 1 stand of untrained foot
41 - 70 Remove 1 stand of archers
71 - 90 Remove 1 stand of men@arms
91 - 100 Remove 1 stand of foot knights
Here, there's only a 10 percent chance of having a foot knight stand fall victim to casualties while there's a 40 percent chance of the untrained foot being removed. An excellent suggestion, thought I, and I'll incorporate it in future rules sets.
Discussion the 2nd
Referring back to the medieval game, each time a unit was hit (from enemy fire, or melee, or simply failing a morale test), it was given a casualty marker. At the end of the half-bound, a separate phase in the sequence then assessed the effect of the various casualty markers being dragged around by the units on the field.
A record was kept for every retinue, and the casualty markers 'translated' into Loss Points on the retinues' data sheet. When a unit recorded 10 Loss Points, one of its stands was removed.
The translation of the effect of the casualty markers into unit losses was done by referring to the following table, using percentage dice:
- 01 to 33 Each casualty marker results in 2 Loss Points
34 to 66 Each casualty marker results in 4 Loss Points
67 to 100 Each casualty marker results in 6 Loss Points
Each time a total of 10 Loss Points was reached, we'd remove one stand, and carry over the unused Loss Points for the next assessment.
On the first or second bound, one of Stephan's retinues had accumulated a total of 7 casualty markers. When it came time to find out the effect of these injuries to the unit, Stephan's dice toss on the above table was a bad one, extremely high... each marker resulted in 6 Loss Points. Since we all know that 6x7 equals 42, and every 10 points results in a stand removed... Stephan's retinue lost four of its five stands... it simply blew up!
And the next bound, another of Stephan's units accumulated the same number of markers, 7, and again a high dice throw resulted in the loss of an entire retinue!
"Too much! Too much!", said Stephan. He indicated that the table we used, in dividing the potential Loss Point conversions into three equal sections, with each one having the same 33 percent chance of occurring, should have been organized differently.
It should follow a sort of 'bell curve', he said, with the extreme events being less likely to occur than those in the middle. For example:
- 01 to 15 Each casualty marker results in 2 Loss Points
16 to 85 Each casualty marker results in 4 Loss Points
86 to 100 Each casualty marker results in 6 Loss Points
Here, the chance of either extreme occurring (low Loss Points or very high Loss Points) is only 15 percent... while the middle ground occupies 70 percent of the field.
Another good point, sez I, and I'll follow up on this.
Discussion the 3rd
The second game I presented was that of a WW II encounter. Each stand... representing a squad? platoon? company?... was tracked, and its losses recorded.
During the bound, the stands accumulated casualty markers, and in good ol' Simon tradition, one of the phases of the bound required a determination of the accumulative effect of the casualty markers on the units.
Reading current REVIEWS, you'll discover that I'm in my "translation" mode... in past rules sets, I had casualties from fire and melee recorded instantly on the units' data sheets, and when a magic total was reached, POOF!, one stand was immediately removed. Nowadays, I let units accumulate casualties via series of casualty markers, and it's only on a specific phase of the sequence that disaster strikes, the markers are translated into points, and stands are removed.
Stand removal was accomplished using the following table. Note that, here again, I used an "equal results distribution", i.e., the probability of any of the outcomes was the same... they all had a 33 percent chance of occurring.
- 01 to 33 Unit loses 1 point, regardless of number of casualty markers
34 to 66 Unit loses 2 points for each casualty marker
67 to 100 Unit loses 3 points for each casualty marker
When a stand accumulated 10 points, it was destroyed, and removed from the game.
Note the unusual result accompanying a very loss die toss. Occasionally, a unit would be inundated with casualty markers during the bound, and when the assessment phase came, a lucky, low percentage dice roll (33 or below) would result in only a single point lost.
This didn't sit well with the audience for two reasons.
- First, because of the probability distribution, i.e., the equal 33 percent increments, which were the topic under Discussion the 2nd. The chart should reflect more of a 'bell curve' configuration.
Second, the gamers noted the results of a low dice throw (33 or below). They deemed it unreasonable to have a unit.. -.. purportedly taking so many casualties during the bound (as evidenced by accumulating a huge number of casualty figures).. -.. get off "scott free" by suddenly having a lucky low dice throw pop up, and suffer only a single, dinky loss point.
I'm not sure I agree with this assessment. If, despite a fairly large number of casualty markers, a unit escapes crippling casualties, all it means is that the guys were under cover, and the majority of wounds for that period of time were light wounds, and the unit quickly recovered. The casualty markers are only a temporary method of indicating that the unit was under intense fire... it doesn't necessarily mean that the casualties were high.
I think that if I modified the loss table to reflect a bell curve result, then the chance of the unit escaping would be more palatable. A distribution such as this one:
- 01 to 10 Unit loses 1 point, regardless of number of casualty markers
11 to 90 Unit loses 2 points for each casualty marker
91 to 100 Unit loses 3 points for each casualty marker
Here, the above table shows that the two extremes happen only a total of 20 percent of the entire time. A low dice toss benefits a unit only 10 percent of the time.
Discussion the 4th
Here, the topic concerned the method I used to determine melee outcome, i.e., which unit wins a specific combat. A 10-sided die toss is used, and Bob Liebl thought that the die roll was completely determinative... toss high and you won, toss low and you lose.
The die roll acts as the multiplier for the sum of two parameters:
- a. The number of your stands in the melee, and
b. The number of casualties you caused on the opposition
Bob's thought was that the sum of these parameters was insignificant when compared to the die roll itself. And he emphasized... "...toss high and you won, toss low and you lose."
Digression. Some background on this issue. Years ago, I looked at two 'efficiency factors' to determine melee outcome:
- a. The first concerned how efficient your unit was in staying alive during the melee. Or, to put it another way... your survival efficiency, SE. To obtain this efficiency factor, divide your survivors by the number of troops in your original force.
- SE = (Your surviving troops)/(Your original number of troops)
b. The second looked at how efficient you were in killing the enemy. Here, too, the efficiency factor was based on your original number of troops... how good were they in knocking off the enemy... this was your hit efficiency (HE).
- HE = (Number of casualties on the opposing unit)/(Your original number of troops)
Combine the two efficiencies by adding them... SE + HE... and to randomize the outcome, toss in a multiplier of a 10-sided die to get a melee product, which I call MP:
- MP = 10-sided die roll x (SE + HE)
But note that here, there were several calculations to be made, since the efficiencies were fractions, and valuable game time was taken up by having to divide the numerators by the denominators of the fractional elements.
And it turned out that, most of the time, the sizes of the opposing forces going into a melee were equal... to put this another way, the term "Your original number of troops" in the fractions of both sides, was a 'wash'... which meant that we could eliminate the irritating dividing business, and simply compare numerators. Which is how I derived my present system:
- MP = 10-sided die x (Your survivors + Enemy casualties)
When each side tossed its 10-sided die, this set up a matrix of 100 possible outcomes. As an example, if the die multiplier (survivors + enemy casualties) for Side B was 3 times that of Side A's, the matrix would look like the chart on the next page.
In the chart, I've marked all the squares in which, when A and B toss their dice, the higher number wins, i.e., 'A' indicates that A's number is higher, while 'B' indicates that B's number is higher..
Note that there are 3 boxes in which possible ties occur, 3 out of the matrix of 100 possible outcomes. Since all ties are tossed again, we ignore ties. This leaves 97 boxes of interest.
Of the 97, Side A wins in only 12 of all the possible outcomes, while Side B wins in 85 of the total number of outcomes. On the matrix, therefore, we have the following probabilities:
- Probability of A winning = 12/97 12.37, say 12 percent
Probability of B winning = 85/97 87.6, say 88 percent
| Side A's Die | Side B's Die | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| 3 x Side B's Die | ||||||||||
| 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | |
| 1 | B | B | B | B | B | B | B | B | B | B |
| 2 | B | B | B | B | B | B | B | B | B | B |
| 3 | TIE | B | B | B | B | B | B | B | B | B |
| 4 | A | B | B | B | B | B | B | B | B | B |
| 5 | A | B | B | B | B | B | B | B | B | B |
| 6 | A | TIE | B | B | B | B | B | B | B | B |
| 7 | A | A | B | B | B | B | B | B | B | B |
| 8 | A | A | B | B | B | B | B | B | B | B |
| 9 | A | A | TIE | B | B | B | B | B | B | B |
| 10 | A | A | A | B | B | B | B | B | B | B |
The above analysis says that when A and B each toss their die, B will win 88 percent of the time, i.e., his resultant number will top that of Side A's 88 percent of the time.
This is no different than stating that B can toss percentage dice, and he will win if he tosses 88 or less. End of digression.
I realize I've roamed far afield, but now we can get back to Bob Liebl's point that the two opposing die rolls are the key factors, the sole factors, the one-and-only deciding factors.
Yes, they are key factors, but they are not the one-and-only... they are simply the mechanism that, in essence, picks out the specific box on the matrix that will apply. And in the example I've given, 88 percent of these boxes 'belong' to Side B, and he'll win 88 percent of the time.
In a game, each melee, with its different number of casualties and size of opposing forces, will set up a different melee product, MP. When these MP's are compared, they, in effect, will result in a chart of 100 different values, similar to the above.
To me, the calculation of melee results, using the MP factor, is fast, it's simple, and it's logical. While it doesn't take into account all pertinent factors, the two that it does consider are extremely important.
There are many rules sets that simply state: "...the side that scores the most casualties wins the encounter". I've always thought this sorta silly, and, to my mind, it stems from the fact that the author really doesn't know which parameters to consider, or for that matter, how to factor then into the equation. There are other rules that state that the side with the most casualties will take a morale test. It's always the side with the most casualties that is selected.
But do you think that Persippius, in the center of the third rank of the fourth cohort, really knows that his unit has lost more men than the enemy? Why pick on Persippius?
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© Copyright 1999 Wally Simon
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