[SG2] Speeding Up Stargrunt

Two weeks ago I posted a Stargrunt 2 game report. One of the things I
bemoaned was the length of time it was taking to resolve combat... in
particular, the amount of time it was taking to resolve Impact vs.
Armour
rolls. Well, gang, I may have a solution! Warning, I include some
statistics. If the thought of numbers with "%" signs behind them scares
you,
you might want to jump to the conclusion section...

THE PROBLEM

Simply SG2 combat can take a long time, particularly with good armour.
Not
enough deaths means that attrition in the game is slow. 

The slow part is the rolling off of impact versus armour dice. With
three
potential casualties this means three armour vs. impact dice rolls
essentially
doubling the number of rolls in a round of combat. Also needed is a
mental
note of how many rolls succeeded in causing casualties. In the game I
played,
I was often getting 3 and 4 potential casualties. The problem is that
with D12
Power Armour, not enough figures drop quickly enough! The same guy can
take
three or four hits on his armour before one penetrates. This means lots
of
time resulting in a null result.

THE STATISTICS AND THE SOLUTION

In an effort to speed up the game I thought I'd find some way of
reducing the
impact vs. armour step to a single dice roll. My original idea was to
come up
with some sort of chart on which a single dice roll gave the casualties.
This
would have been against the spirit of the game, though, and turned out
to be
unworkable in any case.

However, in my efforts to build the chart I decided to write a computer
programme to work out the possible combinations of all the dice results
for
impact vs. armour. I wanted to find out the percentage chance of causing
0, 1,
2, 3, or 4 casualties in the case where there were 4 potential
casualties. I
limited it to 4 because the number of possible combinations was getting
pretty
high at that point, and it's rare to have more than 4 casualties anyway.

I came up with the information. I looked for correlations between
different
rolls in the hope of finding some simple algorithm. None presented
itself.

In the course of this I thought of different potential ways of resolving
armour vs. impact. One idea struck me: what if the attacker only rolled
one
die and the defender rolled an armour die for each potential target? 

Well, of course the probabilities would be off. I mean, just think of a
situation where non armoured guys were attacked by a D12 impact SAW. If
the
SAW rolled a 1 none of the men would be wounded, a situation that would
be
very, VERY unlikely to happen when rolling D12 vs. D4 four times. Still,
it
was simple and did reduce impact vs. armour to one roll. 

So, I worked out the probabilities for this. As expected, there were
greater
chances of hitting the extremes. That is, the percentage chance of
producing 4
casualties and the chance of producing 0 casualties increased. 

I went one step further. I did a weighted average. I multiplied the
percentage
chance of doing a certain number of casualties by the number of
casualties.
For instance, if the percentage across the board for 0, 1, 2, 3, and 4
casualties was 20% each, the weighted average would be 0 x .2 + 1 x .2 +
2 x
.2 + 3 x .2 + 4 x .2 = 0 + .2 + .4 + .6 + .8 = an average of 2
casualties per
combat. 

The results surprised me: the weighted average for my method and for the
method in the rules was the same!

Oh, sure, the probabilities were different, with the extremes coming out
more
often in my case, but the weighted averages were the same. In other
words, my
method created the same number of casualties as Jon's, on average, but
my
standard deviation was higher. 

Here's an example of D10 impact vs. D12 armour:

SG2 method:
0 casualties: 15.26%  weighted average: 0
1 casualty: 36.62%  weighted average: 0.366210938
2 casualties: 32.96%  weighted average: 0.659179688
3 casualties: 13.18%  weighted average: 0.395507813
4 casualties: 1.98%  weighted average: 0.079101563

Total weighted average: 1.5

My method: 
0 casualties: 29.27%  weighted average: 0
1 casualty: 23.55%  weighted average: 0.235474537
2 casualties: 22.49%  weighted average: 0.449826389
3 casualties: 17.30%  weighted average: 0.518923611
4 casualties: 7.39%  weighted average: 0.295775463

Total weighted average: 1.5

A quick perusal will see that the averages for 0, 3 and 4 casualties is
higher, but the averages for 1 and 2 casualties is lower in my method.
But in
this case the averages are within 15% of each other (and in the case of
3 and
4 casualties, are only out by 5%). 

I won't show all the work, but what is interesting is that the
percentages are
closer when the larger dice are used, or the spread between dice is
great. For
instance, D4 vs. D4 has the highest deviation, while D4 vs D12 is within
about
5% for all numbers of casualties. 

Of course, with higher deviations, the more rolls you make the closer
things
come to the average. Since this method is intended to work with larger
forces,
there WILL be more rolls, and the deviations will all wash out in the
end.

CONCLUSION

For impact vs. armour rolls, try rolling the number of armour dice
indicated
by the number of potential casualties, but only one impact die. Apply
the
impact die's result to each of the armour rolls.

This will create more of a deviation where the extremes on the casualty
results will be more prevalent. However, the results won't be that
radically
different from what is obtained in the usual way, and the dice rolling
will be
greatly reduced.

This may also result in more morale checks, due to the greater liklihood
of
the higher casualties in one combat result (not necessarily a bad thing,
mind
you!!!)

On the plus side, this method does yield fast results without taking a
hatchet
to the combat system as happens when using the quick play rules
suggested in
the rulebook.

Let me know if you want more of the statistics. I can send it by e-mail
to
anyone who is after it. I'm looking forward to everyone's comments...

Allan Goodall		       agoodall@interlog.com

"Surprisingly, when you throw two naked women with sex
toys into a living room full of drunken men, things 
always go bad." - Kyle Baker, "You Are Here"