THE AMERICAN CIVIL WAR GAMING CLUB
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Est.
1997
Opportunity Fire Explained
For many years we have all wondered just how the A/I Controlled Opportunity Fire works but have never been able to quite explain it or test it to anyone’s satisfaction. But with little else to do in 2020 outside the home I dedicated some of my time to figuring out all I could about Opportunity Fire and trying to decipher the mystery of how it operates. Here are my findings.
To begin with – what is Opportunity Fire? From the User’s Guide:
Defensive Fire is possible by the opposing side under the control of the computer.
They do not even give the process a name in the User’s Guide! So how did it get its name? There is a brief mention of the term “opportunity fire” in the User’s Guide section on artillery ammunition expenditures:
As each artillery battery fires, this amount (artillery ammunition) is reduced for that side by one. During opportunity fire, the value will decrease by one only half the time on average however.
Or, maybe the name Opportunity Fire was popularized when the optional rule directly addressing it was released. That rule states:
Select Proportional Opportunity Fire to have the computer controlled opportunity fire modified so that small stacks have a lower probability of triggering opportunity fire when they fire while larger stacks have a higher probability of triggering opportunity fire.
Those brief mentions of Opportunity Fire are all the documentation I could discover on the subject. Needless to say there are many gaps left in our understanding of this important function of our beloved Civil War games.
Any member can rattle off a half-dozen or more questions about Opportunity Fire they have always wondered about. Just to get us started:
What process does the A/I use to determine “Opportunity”?
Why do certain units fire and others don’t?
What causes the same unit to fire twice but others not at all?
Does the range of the enemy matter?
What is the probability of firing if the enemy moves or fires?
Can I do anything to increase my Opportunity Fire?
Honestly, I had no clue about the answers to the questions listed above. I always figured someday someone who designed the games would give us a full explanation of Opportunity Fire and how it works exactly. But, for whatever reason, I have never found an answer aside from the basic, “firing happens.”
The most helpful ‘starting point’ I found was a paper written years ago by Robert Frost who undertook his own study of Opportunity Fire. In it he tested the Opportunity Fire mechanism of the game by using the Devil’s Den/Little Round Top scenario from HPS Gettysburg. He was able to compile quite a few results but concluded, understandably, that there were too many variables and that further testing would net few tangible conclusions. He did identify one idea which became my guide in this study – probabilities. He concluded that each range corresponded to a certain “probability of fire” which controlled whether or not the A/I fired. To quote his work:
Why a fixed percentage for a given distance? Unless the program is constrained in some manner, it will fire equally across all hexes within range. One could attach no value to a given hex and have the program check every unit within range applying the same percentage. This would be very inefficient and would give the same results as making the check up front.
The problem he ran into was sample size. He just couldn’t gather enough data to really make a convincing case. As it turns out some of his conclusions were, in fact, accurate, while others were not. He simply needed more data to examine.
So, how does one collect data on Opportunity Fire? One plays games, right? Wrong! You could play for years and not be able to collect enough data to eliminate variables and isolate singular occurrences. What you need to do is create your own data. That is where I began.
Testing Setup
What I required was a way to test, not a few, or a few dozen, but hundreds of Opportunity Fire occurrences at a time. The only way to do that was by utilizing the scenario editor and creating my own Order of Battle to use. I also needed a giant sandbox to play in without any possible variables I could not control myself. Luckily, the HPS Atlanta game has a perfect map called “Open Space” which is a gigantic piece of Clear, level, ground. It is impractical for any actual scenario but for my purposes it was a Godsend. Using this terrain I could eliminate any variables, have an endless amount of space to set up a thousand tests at once, and control any possible variables I chose to implement. Because I did not alter the PDT file from the game itself the results would mirror those of an actual game.
To run all my tests I created 2,000 average quality 200-man units. I would alter their numbers and quality for a few tests but generally kept them at that size and quality throughout. For my Optional Rules I played with everything checked except Manual Defensive Fire and Proportional Opportunity Fire. I wanted to test Opportunity Fire as it is in theory and not altered by an Optional Rule. I would, towards the end, test Proportional Opportunity Fire as well. The Adjust Auto Defensive Fire option was set to “Max” for all my tests.
How do you run a thousand tests at once? Easy – if you have the A/I. My method was to place my men on the map in whatever way I wanted and then to start up the scenario as the player for both sides. I would then click on “A/I” to automatically conduct all my firing. The A/I, luckily for my sanity, would then conduct all the firing the same as if I were doing it myself. The A/I, having no script to follow, would never move or change formation, it would just fire if there were any units within range. This was exactly what I wanted. Each test was constructed where only one available target was given to each “offensive” unit. That limited any possible deviation from the control side of the experiment. As the A/I conducted offensive fire it also conducted Opportunity Fire in response. My role then was to record the results. Does having the A/I conduct offensive firing alter the results? No. They mirror other tests I did in live action battles. Using the A/I was a sanity-saving measure. There was no other way this could have been done on the gigantic scale it was without using the A/I’s assistance. Each test was done as a separate event. There were no 2nd turns. Each firing phase was its own event and then the game was closed and reopened for the next test. This eliminated any variables from the results as each batch of tests was done using the same set of units (unless notated of course).
A Starting Point
About the only pieces of information which are common knowledge about Opportunity Fire are based on years of playing and observation. We all know two things, for sure, about Opportunity Fire:
1) Stationary/non-firing units will not be fired upon.
2) Fire Values are halved by Opportunity Fire.
Part One: A Journey of a Thousand Tests…
Where to begin? Using Robert Frost’s thesis that there was a probability of fire for different hex ranges I decided to pursue that idea and see where it led me. I would start with the range of 1. Starting at that range made the most sense and from there I could establish if there were any definite probabilities or patterns with Opportunity Fire. With that idea in my head… I opened up the scenario editor and began to place my units one hex apart.
Question 1:
What is the probability of Opportunity Fire at a range of 1?
1A. 1 vs. 1 in Line Formation at a range of 1
I lined up 1000 Federal units and 1000 Confederate units in adjacent hexes across the map. As you can see from the setup picture below, the only units able to fire at one another were those facing one another. That left only one possible hex/unit to return fire against the only other hex/unit that was opposite them. I then opened up the game, hit the A/I firing button, and began recording the results.
RESULTS:
485/1000 = 48.5% Opportunity Fire responds
CONCLUSIONS:
I had my first probability.
Question 1: Answer
What is the probability of Opportunity Fire at a range of 1?
The probability of Opportunity Fire at a range of 1 is ≈50%.
Question 2:
Does a unit’s movement draw the same amount of Opportunity Fire as a unit which fires?
This was the obvious next step in the testing – and my least favorite. There was no way the A/I could run this test for me.
2A. 1 vs. 1 in Column at a range of 1
I placed half the units on the map in column formation two hexes away from their designated opponent. I then, manually (and this was incredibly time consuming), moved from 2 hexes away forward in column to 1 hex away. The result I was looking for was ≈50%.
RESULTS:
495/1000 = 49.5% Opportunity Fire responds
CONCLUSION:
After a grueling few hours spent clicking on units I arrived at the determination that the A/I does not differentiate between movement and firing actions. For the A/I they are the same event taking place at a range of 1 hex.
Question 2: Answered
Does a unit’s movement draw the same amount of Opportunity Fire as a unit which fires?
Yes. Whether you are firing or just moving the A/I see’s the event in the same way and responds a fixed percentage of the time.
This was a major revelation for me. Having established this control number for all subsequent tests at a range of 1 I could add as many variables as I wanted. It reduced all the variables significantly. If the game responded differently to actions such as formation changing, facing changes, etc. then I would have lost my mind trying to test them all.
Question 3:
Does the number of units in a targeted hex increase the probability of Opportunity Fire?
Next, I wanted to test whether or not you could increase the probability of Opportunity Fire by placing more units in the defending hex. This seems like a logical idea. More units should equal a better chance of return fire, right? I was only recording whether or not the targeted hex responded to the enemy action. I was not looking to see if more total firing occurred – I would test that later on in another test.
3A. 2 vs. 1
I placed two units in the same defensive hex opposite the single firing unit one hex away. I then recorded the results of 1,000 firing occurrences. I had two probable outcomes in my mind as I began:
1. The additional unit would improve the chances of the hex returning fire and the result would be greater than the 50% probability established earlier.
2. Opportunity Fire would still be activated the same amount of the time regardless of the additional unit.
RESULTS:
494/1000 = 49.4% of the time the hex fired in response.
CONCLUSION:
The addition of the second unit made no difference in the probability of the targeted hex responding to Opportunity Fire. If your goal was to increase your chances beyond a 50% response rate by placing more units in the hex then you would be unsuccessful.
3B. 3 vs. 1
Not wanting to assume too much I decided to run the test two more times. First, I would place three units in the hex opposite the single firing unit.
RESULTS:
514/1000 = 51.4% chance that the hex fires.
CONCLUSION:
The result was exactly as I anticipated. No appreciable difference.
3C. 4 vs. 1
Lastly, I brought in a fourth unit just to be sure.
RESULTS:
513/1000 = 51.3% of the time the hex responds.
CONCLUSION:
This put the final nail in the coffin of the idea that you could increase your probability of Opportunity Fire by adding more units to the hex.
Question 3: Answered
Does the number of units in a targeted hex increase the probability of Opportunity Fire?
No. The probability of Opportunity Fire is not alterable by increasing the number of units in the hex.
In the three tests I conducted I fired offensively a total of 3000 times against opposing hexes. I had the 1 vs. 2, 1 vs. 3, and 1 vs. 4 units each conduct 1000 tests. That created 3000 Opportunity Fire chances for the A/I to respond to. In total the A/I controlled Opportunity Fire was triggered 1521/3000 times – or 50.7% of the time.
This idea really made me optimistic that countless other variables would be negated by the overriding rule of probability the game had adhered to thus far. I decided to take the plunge and begin to test each variable one by one to see if they changed the probability of Opportunity Fire at all for a range of 1.
Part Two: Variables
What really tripped up countless other studies of Opportunity Fire was the fact that, in a real game, the variables are too many to control. You could never be sure whether or not the results were based on an X, Y, or Z variable if you could not isolate them. Using the scenario editor I was able to fully isolate each possible variable and test them without any interference. And, so began, a long and dull process of testing as many variables as I could stomach.
I chose to test these variables 200 times as a base number. If I ran into any unexpected results I would increase that number to a thousand in an effort to eliminate any possible variance and arrive at a solid conclusion. Otherwise, for my sanity’s sake, 200 would have to do. I ran all tests at the range of 1 as that continued to be the control part of my experiments.
Question 4:
Does the quality of units in a targeted hex alter the probability of their Opportunity Fire?
It is a reasonable idea. The game does allow higher quality units some luxuries and perhaps increased Opportunity Fire was one of them. It was worth testing.
4A. Quality
I made all the units on the board an “A” in quality. I ran the test 200 times to see if there was any chance that it could affect the result.
RESULT:
98/200 = 49%
CONCLUSION:
The quality of a unit will not increase its probability to fire.
Question 4 Answered:
Does the quality of units in a targeted hex alter the probability of Opportunity Fire?
Nope. The probability of firing is still the same regardless of the quality of the units involved. I tested this at a range of 1 where, you would think if there was any possible alteration in the rule of probability, it would be most likely to occur. Therefore, I chose not to test this idea again at increased ranges. A unit’s quality does not change the Opportunity Fire probability of a hex. If it did, the game would have to be designed to differentiate between unit qualities within the same hex and create numerous equations to determine the firing probabilities of mixed quality hexes.
Were the designers lazy then or was it just easier to make a straight up probability equation for each hex range? To quote Robert Frost again, “Simplicity in programming – and there is nothing wrong with this approach – probably carries greater weight than the development of some highly complex outcome.” As a computer programmer he knows more about gaming codes than I ever will, and I believe he is right in this instance.
He is saying that there are times programmers do not try and make overly complicated equations for each individual outcome. It would become too complicated at some point and would add little to the overall enjoyment of the game and much to the cost and time of development. Those of you in the Armed Forces or in the Civil Service might look at that and think of the KISS method – Keep It Simple Stupid.
With that in mind I had no fear testing all the other possible variables… just in case.
Question 5:
Does the terrain in a targeted/firing hex alter the probability of Opportunity Fire?
Basically, I was wondering if terrain mattered at all in Opportunity Fire probabilities? I doubted it but I had to try. To do so I needed to take a “field trip” from my Open Space sandbox of clear fields I was using and venture over to the Kennesaw Mountain map to take advantage of its natural terrain features.
5A. Terrain
For this test I placed 25 units from each side on the board at a range of 1 from their opponent. Both units were located in Forest hexes. I ran the test eight times for a total of 200 Opportunity Fire chances.
RESULTS:
96/200 = 48%
CONCLUSION:
The result was what I expected.
Question 5 Answered:
Does the terrain in a targeted/firing hex alter the probability of Opportunity Fire?
No. The probability remains 50% despite the terrain of the hexes the units are located in.
Question 6:
Does elevation make a difference in the probability of Opportunity Fire being initiated?
Perhaps, I thought, a hex’s probability of Opportunity Fire would alter with elevation changes. I decided to try it and find out.
6A. Elevation
I returned to Kennesaw Mountain where I placed the same 25 units I previously used on a higher elevation than their 25 targeted opponents. I ran the test eight times to gather 200 results. I then ran the test eight more times and reversed the targeted and firing hexes to have the targeted units on the high ground instead.
RESULTS:
104/200 = 52%
and
101/200 = 50.5%
CONCLUSION:
Elevation changes had no effect on the probability of Opportunity Fire.
Question 6 Answered:
Does elevation make a difference in the probability of Opportunity Fire being initiated?
No. Just like with hex terrain modifiers there was no difference when it came to elevation changes and Opportunity Fire.
Question 7:
Does weapon type matter in the probability of Opportunity Fire?
At this point I was running out of variables to test and wondered if the weaponry had any chance of altering the probability of Opportunity Fire.
7A. Muskets
For this test I took 500 units from both sides and armed them with Muskets. I then placed them 1 hex apart and opened fire.
RESULTS:
247/500 = 49.4%
CONCLUSION:
The weaponry, just like terrain and elevation, had no effect on the probability of 50% already established.
Question7 Answered:
Does weapon type matter in the probability of Opportunity Fire?
Nope.
Question 8:
Does the service type of the units in the hex change the probability of Opportunity Fire?
I decided I would remove my infantry from the equation and substitute artillery, and then, cavalry, and see if that made any difference at all in the probability of Opportunity Fire.
8A. Artillery
I started out by placing 200 artillery units from both sides adjacent to one other. Each unit was only able to fire at one other unit on the map.
RESULT:
102/200 = 51%
CONCLUSION:
It was at this point I knew that the probability rule was unbreakable.
8B. Cavalry
I carried on though and tried it again with cavalry.
RESULT:
100/200 = 50%
CONCLUSION:
I love easy math.
8C. Mixed Hexes
For the final test I mixed the targeted hex up with two infantry units and an artillery section.
RESULT:
102/200 = 51%
CONCLUSION:
Very predictable by this point.
Question 8 Answered:
Does the service type of the units in the hex change the probability of Opportunity Fire?
Not in the slightest. Whether it is artillery, cavalry, or infantry in the hex they have the same probability of Opportunity Fire.
Question 9:
Does the number of units in the firing hex change the probability of Opportunity Fire from the targeted hex?
​
The last thing I could think of was to change the number of firing units, as opposed to targeted units, on the off chance a defender would be more apt to fire if additional units were attacking.
9A. Firing Units
I placed three firing units in the same hex against a single defender for this test.
RESULT:
100/200 = 50%
CONCLUSION:
Dead on the money once again.
Question 9 Answered:
Does the number of units in the firing hex change the probability of Opportunity Fire from the targeted hex?
It does not. This is why people are always moving around in our games using large stacks – to minimize Opportunity Fire checks. It is an effective strategy.
Part Three: Multi-Firing
The phenomenon of multiple Opportunity Fire from the same hex is always a welcome sight to any defender. But I never could decipher if there was any rhyme or reason to how it was determined or conducted. Having established that the 50% probability rule was unbreakable at the range of 1, I decided to test how multiple firing was conducted at a range of 1.
Question 10:
How often do you get repeat fires from the same hex at a range of one?
​
I knew that any enemy hex, at a range of 1, had a 50% probability of being triggered by an Opportunity Fire check. When that fire happens it always occurs as a single event for a single unit. There may be multiple units in the hex but the A/I will only choose one unit in the hex to return fire – most of the time. In my mind I imagined that the next step for the A/I would be to check subsequent units in the hex to see if they were able to fire as well.
10A. 2 Units Stacked
I began by placing one unit opposite two targeted units at a range of 1. I then fired 1,000 times to determine the probability of repeat firing. In my mind I thought the outcome would be a 25% multi-fire rate. This was based on the idea that a hex with a 50% chance to fire would then have a 50% chance of firing twice. Or, in math terms, a ½ x ½ = .25 or 25% chance of firing twice.
RESULTS:
519/1000 = 51.9% at least one unit fired
481/1000 = 48.1% nobody fired
Of the firing occurrences there were:
420 single occurrences of firing
99 double occurrences of firing (99/519 = 19.1% chance)
CONCLUSION:
This was my first real unexpected result in testing Opportunity Fire. I believed the result for double firing should have been ≈ 25%. Instead it was just 19.1%. I decided it must be some sort of error on my part and so I ran another test to verify the results.
10B. 2 Units Stacked
RESULTS:
518/1000 =51.8% at least one unit fired
482/1000 =48.2% nobody fired
Of the firing occurrences there were:
425 single fire occurrences
87 double fire occurrences (87/518 = 16.8% chance)
CONCLUSION:
Not only did my probability of repeat firing fail to rise to the level of 25% but it actually dropped to 16.8%. Why would the probability of repeat firing be set so low? To confirm my findings, I had to run it just one more time.
10C. 2 Units Stacked
RESULTS:
526/1000 = 52.6% at least one unit fired
474/1000 = 47.4% nobody fired
Of the firing occurrences there were:
449 single fire occurrences
77 double fire occurrences (77/526 = 14.6% chance)
CONCLUSION:
By this point I was positive that the game determined the possibility of multiple fires using a different probability than the 25% I had believed in. The only way I could hope to answer this question was to accumulate more data.
10D. 3 Units Stacked
For this test I placed three units in the same targeted stack to see if multi-firing increased as a result of more units. I knew the probability of the hex firing would stay at 50%.
RESULTS:
518/1000 = 51.8% at least one unit fired
482/1000 = 48.2% nobody fired
Of the firing occurrences there were:
437 single fire occurrences
75 double fire occurrences
6 triple fire occurrences
81 Multi-fire occurrences (81/518 = 15.6% chance)
CONCLUSION:
The good news was that the 50% probability remained stable. The interesting part of it was that the percentage of multiple fires continued to remain around 15 – 20%. If one adds the double and triple fires together and divides by the total number of opportunity fires then you arrive at a 15.6% chance of multiple fires. This was on average with the previous tests 10A – 10C. The third unit did not increase my chances to fire more than once.
10E. 4 Units Stacked
I then placed four units opposite a single one and ran the test 1000 times. By now I had identified the pattern of multiple firing occurring about 15 – 20% of the time with Opportunity Fire.
RESULT:
502/1000 = 50.2% at least one unit fired
498/1000 = 49.8% nobody fired
Of the firing occurrences there were:
412 single fire occurrences
82 double fire occurrences
7 triple fire occurrences
1 quadruple fire occurrences
90 Multi-fire occurrences (17.9% chance)
CONCLUSION:
At this point I had come up with my answer.
All Tests Combined:
First, I was curious what all the numbers added up to during these tests on multiple firing from the same hex. They are as follows:
2583/5000 = 51.7% at least one unit fired
2417/5000 = 48.3% nobody fired
Of the firing occurrences there were:
434 Multi-fire occurrences (434/2583 = 16.8% chance)
Question 10 Answered:
How often do you get repeat fires from the same hex at a range of one?
Sometimes, in life, you just have to go by what the numbers are and not worry too much about the “why?” I believe the answer to multi-firing from a single hex boils down to a probability between 15 – 20%. The additional units in the hex do not alter the probability of Opportunity Fire at a range of 1 (50%) nor did they raise the chances of multi-firing at all either. Whether you had two units in the hex, or four, the probability of multi-fire remained in that same 15 – 20% range. How, or why, the multi-fire comes in the form of a double, triple, or quadruple shot… I have no idea. Multi-fires of more than two are freak occurrences happening only about 2% of the time.
Question 11:
If you have units in multiple hexes, all with a range of one, against an enemy unit, what is the probability they will fire?
​
Having already established that a single hex has a 50% chance of Opportunity Fire I began to wonder if I could increase my total firing 25% by occupying two hexes instead of one.
​
11A. 2 Hexes vs. 1
The above picture will display how I aligned the units for this test. I knew that the math indicated by occupying two hexes, instead of one, I should be able to fire 25% more often (½ x ½ = ¼ or 25%). But how would it play out?
RESULTS:
754/1000 = 75.4% at least one unit fired
246/1000 = 24.6% nobody fired
Of the firing occurrences there were:
626 times one hex fired
128 times both hexes fired at once
CONCLUSIONS:
Everything continued to be based off the probability of 50% for firing at a range of 1. I was able to increase my firing by occupying more hexes. This was a major revelation as it was the first hint of how to easily increase your probability of firing.
11B. 3 Hexes vs. 1
Following the same train of thought that says occupying two hexes is better than one I decided to test just how much better three would be. The math pointed to a probability of 87.5% firing vs. not firing.
RESULTS:
866/1000 = 86.6% at least one unit fired
134/1000 = 13.4% nobody fired
Of the firing occurrences there were:
604 times one hex fired
230 times two hexes fired
32 times three hexes fired at once
CONCLUSION:
Just as predicted the combination of ½ x ½ x ½ = 12.5% to not fire, or 87.5% to fire, came out as expected. This is a very real way to increase your chances of Opportunity Fire occurrences.
Question 11 Answered:
If you have units in multiple hexes, all with a range of one, against an enemy unit, what is the probability they will fire?
Technically, the same – 50%. But because you have more total chances of firing your probability increases. If someone asks you to bet $50 on the flip of a coin you might hesitate a moment. A 50/50 chance isn't the best odds in the world. But if they offered to flip it twice… you might stop to do the math:
½ x ½ = 25% chance of losing, 75% chance of winning.
What if they offered to flip it three times?
½ x ½ x ½ = 12.5% chance of losing and a 87.5% chance of winning.
As this relates to our game – the more chances you have to win an Opportunity Fire check the higher your firing rate will become. Occupy more hexes!
Question 12:
If you have multiple units in multiple hexes, all with a range of one, against an enemy unit, what is the probability of multi-firing?
​
I ran this test before I did the math and realized it was redundant. I include it here as it proves the validity of the previous two tests.
12A. 2 Units Apiece in Two Hexes vs. 1
Here I was testing the probability of multiple defensive hexes, occupied by more than one unit, firing at the same offensive firing hex. I placed two units apiece in hexes 1 and 2 (as seen in the picture above 11A) and then ran the test 1,000 times. I knew the probability of firing vs. not firing was going to be the same as we had above in test 11A. That part wouldn’t be altered by the addition of more units to the two hexes. I should have also realized that the probability of multi-firing would be 15 – 20% per hex based on the results of question 10 earlier.
RESULTS:
752/1000 = 75.2% at least one unit fired from the 2 hexes
248/1000 = 24.8% nobody fired
This confirmed my answer from question 11 concerning probability of firing from multiple hexes.
From Hex A there were:
416 total fires
78 multi-fires (78/416 = 18.8% chance)
From Hex B there were:
471 total fires
71 multi-fires (71/471 = 15.1% chance)
And this confirmed my conclusions drawn from question 10.
Question 12 Answered:
If you have multiple units in multiple hexes, all with a range of one, against an enemy unit, what is the probability of multi-firing?
The probability of Opportunity Fire will be 50% for each hex at a range of one. Regardless of anything else that remains constant. The probability of multi-firing also remains at between 15 – 20% per hex at a range of 1 with multiple units.
By this point I felt that I had made serious progress and had learned all I could about Opportunity Fire at a range of 1. I felt that it was all probabilities and that, despite increased ranges, the same rules would continue to apply.
Part Four: Moving Back to Two Hexes
Having established a number of rules concerning variables and probabilities at a range of 1 I believed that the same rules would still apply at a range of 2. Would they?
Question 13:
What is the probability of Opportunity Fire at a range of 2?
​
The key to Opportunity Fire seems to be determining the probability of Opportunity Fire at a given range. We start there.
13A. 1 vs. 1 at a Range of Two
Here we will place one unit vs. another unit as a range of two to establish what the probability of fire is at this range.
RESULTS:
346/1000 = 34.6% fired
654/1000 = 65.4% no fire
CONCLUSION:
A noticeable drop from the probability of range 1.
Question 13: Answered
What is the probability of Opportunity Fire at a range of 2?
The probability of Opportunity Fire is 35% at a range of 2.
Question 14:
What is the probability of multiple fires from the targeted hex at a range of 2?
​
If you recall we established that at a range of 1 multiple fire occurred an average of 15 – 20% of the time during Opportunity Fire. Would increased range affect that?
14A. 2 vs. 1 at a Range of Two
For this test I placed two units in the same hex and moved them two hexes back from the firing hex. At a range of 1 the multiple fire rate was roughly a third of the 50% opportunity fire rate (17% chance). If we assume the same odd rule holds true here then I should get multiple fires in about 10.9% of the occurrences.
RESULTS:
346/1000 = 34.6% at least one unit fired
654/1000 = 65.4% no fire
The above is NOT a typo. I, literally, got the same exact numbers as in test 13A.
Of the firing occurrences there were:
313 single fire occurrences
33 double fire occurrences
Chances of a double fire are 9.5%.
CONCLUSION:
At least the 35% rule was verified by this second result at a range of 2.
Question 14 Answered:
What is the probability of multiple fires from the targeted hex at a range of 2?
The multiple firing percentage may seem a bit low in test 14A, but, when dealing with small sample sizes the variants become harder to control and chance begins to play a role. Usually over thousands of results the true answer would be found but, with just 33 occurrences in a thousand, it is simply not worth pursuing to any great extent. Basically, your chances to fire multiple times from the same hex at a range of 2, and beyond, will continue to decrease rapidly.
Question 15:
Will occupying more hexes still increase your Opportunity Fire occurrences at a range of 2?
​
I knew this one was a given but wanted to show, again, how spreading out your line could increase your fire combat output.
15A. 1 and 1 vs. 1 at a Range of Two
In this test I placed two units in adjacent hexes and then an opposing unit two hexes away from them. If you reference question 11 you will see a noticeable increase over multiple hexes because the game does not reduce the probability of single-hex firing per event. Therefore, in this test there should be a 57.75% firing rate.
RESULTS:
560/1000 = 56% at least one unit fired
440/1000 = 44% no fire
Of the firing occurrences there were:
497 single fire occurrences
63 double fire occurrences
CONCLUSION:
The result came out as expected.
Question 15 Answered:
Will occupying more hexes still increase your Opportunity Fire occurrences at a range of 2?
Absolutely. With each hex having a 35% chance of firing the math equals .65 x .65 = 42.25% of it not happening and a subsequent 57.75% of it happening. Once more, it benefits the defender to occupy more hexes.
Question 16:
What happens if you occupy two different hexes, one is adjacent to the enemy and the other is two hexes away, does the A/I fire at 50% or 35%?
16A. Multiple Ranges at Once
I will admit I had a few different theories on what the answer to this one might be. One of them was, “I have no idea!” But then I looked at the results.
RESULTS:
449/1000 = 44.9% of the time the hex at a range of 1 fired
316/1000 = 31.6% of the time the hex at a range of 2 fired
Of the 1000 Opportunity Fire chances there were 324 times that no firing occurred at all.
CONCLUSION:
Did you catch it?
Question 16 Answered:
What happens if you occupy two different hexes, one is adjacent to the enemy and the other is two hexes away, does the A/I fire at 50% or 35%?
At first, I was confused as to why the probabilities for both hexes dropped by about 5 percentage points. And then I did a little math and realized the reason why – the game was averaging the probabilities for Opportunity Fire.
For the range 1 hex you have a 50/100 chance of firing. The other hex, at range 2, has a 35/100 chance of firing. If we do .50 x .65 then we arrive at an answer of 32.5% of the time there will be no firing at all and 67.5% that there will be. Over a thousand tests the end result was within a single instance of that! There were 324 instances of not firing and 676 instances of firing. The game simply finds the probability of the result given the odds of the two distances.
Part Five: Past a Range of Two
Having already discovered all I could, or would, about Opportunity Fire at the ranges of 1 and 2 I decided it was time to test more ranges. The first step was to identify the most common probabilities for the rifle fire. That included the hexes 3 – 5. Beyond that I would just take a sampling of the ranges for long distance artillery fire.
Question 17:
If the Opportunity Fire is initiated 50% of the time by a hex at range 1, and 35% at range 2, what about 3, 4, and 5?
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Expanding outwards from two hexes I then tested the probability of Opportunity Fire at range 3, 4, and 5.
17A. 1 vs. 1 at a Range of 3
Testing the probability of Opportunity Fire at a range of 3.
RESULTS:
248/1000 = 24.8% fire rate
CONCLUSION:
The Probability rate continued to decrease. It dropped from 50 at 1, to 35 at 2, and to 25 at 3.
17B. 1 vs. 1 at a Range of 4
I then pushed my men back another hex to test this range.
RESULTS:
203/1000 = 20.3% fire rate
CONCLUSION:
The probability dropped another 5 points. Remember, I set the Auto Adjust Defensive Fire setting to max. So, this is the default probability.
17C. 1 vs. 1 at a Range of 5
Moving out to maximum rifle range.
RESULTS:
152/1000 = 15.2% fire rate
CONCLUSION:
Another 5 point drop in probability.
Question 17 Answered:
If the Opportunity Fire is initiated 50% of the time by a hex at range 1, and 35% at range 2, what about 3, 4, and 5?
The answers are – 25%, 20%, and 15%.
Question 18:
What are the probabilities of Opportunity Fire beyond the range of 5?
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There was no way I was testing ranges all the way up to 70! But I went ahead and tested ranges: 8, 10, and 15.
18A. 1 vs. 1 at a Range of 8
I placed two units 8 hexes away to determine the probability of firing at that range.
RESULTS:
146/1000 = 14.6%
CONCLUSION:
The range probability of 8 was still the same as the range probability of 5 (about 15%). It may sound odd at first but, at some point, the designers would have used a fixed percentage for a range of numbers. I concluded that the probability of fire was the same from 5 – 9.
18B. 1 vs. 1 at a Range of 10
Upping the range to 10.
RESULTS:
51/1000 = 5.1%
CONCLUSION:
At a range 10 probability drops down to just 5%.
18C. 1 vs. 1 at a Range of 15
Moving on up to 15.
RESULTS:
47/1000 = 4.7%
CONCLUSION:
The probability of Opportunity Fire stayed 5% from 10 – 15.
Question 18 Answered:
What are the probabilities of Opportunity Fire beyond the range of 5?
It appears that the probability of Opportunity Fire dwindles down to 5% after a range of 9. From range 10 and beyond it is, at most, 5%. I could have continued to test more ranges but, to be honest, who is wasting ammo at that range anyways? Also, the percentages would be so small as to be useless to even discover.
Part Six: Dead End
There was one thing that always bugged me about Opportunity Fire – how did the A/I choose which unit to fire with and which unit to fire at? I had to test it out.
Question 19:
When firing into a stack of units is there any reason to which unit is targeted or which unit fires?
Question 19 Answered:
I will spare you my long-winded test summaries, my different theories, and my many failed guesses and cut to the chase. The answer is no. I tried everything I could think of to make any sense of what the A/I used to decide which units to fire with and at. But nothing affected them. I tried quality changes, weaponry changes, fatigue, disrupted status, etc. but the A/I had its own reasons it would not share. It doesn’t feel “random” though. But it doesn’t feel “intelligent” either. It just seems like some sort of programming code that runs in some meaningless pattern. It got to the point where it wasn’t worth pursuing anymore and I moved on.
Part Seven: Tying up Loose Ends
At this point I was running out of tests I wanted to conduct. I could have continued investigating multiple fires from the same hex or why certain units are targeted over others. In the first instance I realized that it was unlikely I could arrive at a better probability than the 15 – 20% I established at a range of 1. Beyond that range the probability shrunk to a point where it was not worth the time to establish it precisely. As for the idea of trying to nail down how units were chosen – no, thank you. I had tried that and found that there was no intelligent method that the game used to decide such things. It, also, would have been a waste of time.
There were questions and ideas that I still wanted to verify though. Before I presented this report to you all I wanted to double-check my findings against any possible errors. I chose a few of the tests I wanted to run again in a slightly different way just to confirm that the rule I came up with still applied despite different specifics being tested.
Question 20:
Does every action by an offensive unit really draw the same rate of Opportunity Fire?
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Going back to Question 2 I concluded that any “action” was an “action” and that the form of it did not matter to the A/I in determining whether to run an Opportunity Fire check. This was a major conclusion as it greatly reduced the number of probable tests I would have to run.
20A. 1 vs. 1 at a Range of 2
I populated the map with 100 units from both sides located 2 hexes apart. I then had one side begin building breastworks to see if Opportunity Fire occurred the expected 35% of the time. I decided to run this test 100 times rather than a 1000. My experience of manually moving a thousand units from question 2 scarred me for life.
RESULTS:
36/100 = 36% fire initiated
CONCLUSION:
I was thrilled when this happened, otherwise, I’d have had to test a ton of variables moving forward.
Question 20 Answered:
Does every action by an offensive unit really draw the same rate of Opportunity Fire?
Yes. That is confirmed.
Question 21:
Does having more hexes occupied really increase Opportunity Fire?
This question came out of question 11 where I discovered that by occupying more hexes you could increase your chances of firing defensively. Just for fun let’s briefly try it a few more times.
21A. 1 vs. 4 at a Range of 1
Picking up where I left off earlier in question 11 I decided to add a fourth unit to the defensive line. This should, in theory, allow my defenders to use Opportunity Fire in 93.75% of the tests.
RESULTS:
186/200 = 93% fire initiated
CONCLUSIONS:
Just as anticipated firing rose to new heights.
21B. 1 vs. 3 at a Range of 3
In this test I decided to see if I could match the results of question 11 and test 21A at a greater distance. The probability of not firing should be .253 = 42.2% and then firing would be a 57.8% probability.
RESULTS:
58/100 = 58% fire initiated
CONCLUSIONS:
I just stopped testing after 100 because I was exactly on the estimated probabilities. You can, absolutely, increase your firing probability by occupying more hexes.
Question 21 Answered:
Does having more hexes occupied really increase Opportunity Fire?
This might just be the biggest takeaway from all these tests. Want to increase your chances of Opportunity Fire? Occupy more hexes.
Question 22:
Does moving by stacks cause the same amount of Opportunity Fire as moving singly?
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If I didn’t test this someone would point it out. I had to. But I think we all know the answer.
22A. 1 vs. a stack of 4 units at a Range of 2
In this test I stacked up four units at a range of 3 and then moved them, in column, to a range of 2 from the enemy. Fire should be initiated 35% of the time.
RESULTS:
36/100 = 36% fire initiated
CONCLUSION:
That’s the reason everyone moves in stacks.
Question 22 Answered:
Does moving by stacks cause the same amount of Opportunity Fire as moving singly?
This was an easy one to predict. Members have been moving in large stacks for years because this was obvious to all.
Question 23:
Can you repeat the results of question 16?
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It was question 16 that established that a probability of Opportunity Fire was established by finding the combined probability of two units at different ranges to fire defensively at an enemy unit. In question 16 it was a hex at a range of 1 and another at a range of 3 that created a 67.5% probability of Opportunity Fire. The result landed within a single instance of the predicted result. Was it a fluke?
23A. 1 vs 1 at range 2 and 1 at range 4
I had to mix it up some. The math on this one came out as .65 x .80 = .52 or a 52% chance of no firing versus a 48% chance of firing.
RESULTS:
95/200 = 47.5% fire initiated
CONCLUSION:
Couldn’t ask for better results.
What if I made this more complicated? Could I confuse the A/I by adding more units?
23B. 1 vs 1 at range 2, 3, and 5
Why not? The math on this would work out as .65 x .75 x .85 = .41 or a 41% chance of not firing and a 59% chance of firing.
RESULTS:
116/200 = 58% fire initiated
CONCLUSION:
The number continues to come out as expected.
One more time just to really try and confuse the A/I – and myself.
23C. 1 vs two 1-unit hexes at range 1, 1 hex at range 2, and 1 at range 3
In this instance we have four total units facing a single unit. The ranges are 1, 1, 2, and 3. According to the math the probability of not firing is .5 x .5 x .65 x .75 = 12.2% and an 87.8% chance of firing.
RESULTS:
178/200 = 89% fire initiated
CONCLUSION:
About what expected.
Question 23 Answered:
Can you repeat the results of question 16?
Yes! If you have multiple units at different distances from an enemy unit who triggers an Opportunity Fire check your probability of fire is determinable.
Part Eight: Proportional Opportunity Fire
Gentlemen, to find out my unexpected findings about this Optional Rule please read DIS-Proportional Opportunity Fire Error? located at the conclusion of this report. Continue reading below to find out how this Optional Rule ideally works. Remember the section below is based on the idea that Proportional Opportunity Fire works – which it might not.
The User’s Guide states:
Select Proportional Opportunity Fire to have the computer-controlled opportunity fire modified so that small stacks have a lower probability of triggering opportunity fire when they fire while larger stacks have a higher probability of triggering opportunity fire.
How does this effect our games and what does “modified” actually mean? I was determined to find out. I opened back up the scenario editor once again placed my units on the map. Only this time I would click on “Proportional Opportunity Fire”.
Question 24:
How does Proportional Opportunity Fire work?
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In theory the following probabilities are the ideal settings for Proportional Opportunity Fire.
24A. 100 vs 1 unit at a Range of 1
In this test I have taken 100-man units and placed them opposite an enemy unit.
RESULT:
92/1000 = 9.2%
CONCLUSION:
We saw a major drop in probability with this rule checked! The Proportional Opportunity Fire decreased the probability of firing at range 1 from 50% to just 10% using this rule.
24B. 200 vs 1 unit at a Range of 1
Here I have placed a 200-man unit opposite an enemy unit to test the probability of fire.
RESULTS:
198/1000 = 19.8% chance of firing
CONCLUSION:
It would seem that the larger the unit size the greater the probability of firing.
24C. 300 vs 1 unit at a Range of 1
Since we have already seen the probability go up with each 100-man addition we will continue to increase our manpower and see if there is a plateau to this rule.
RESULTS:
308/1000 = 30.8% chance of firing
CONCLUSION:
Just as expected!
24D. 400 vs 1 unit at a Range of 1
Up to 400.
RESULTS:
400/1000 = 40% chance of firing
24E. 500 vs 1 unit at a Range of 1
RESULTS:
510/1000 = 51% chance of firing
24F. 600 vs 1 unit at a Range of 1
RESULTS:
618/1000 = 61.8% chance of firing
24G. 700 vs 1 unit at a Range of 1
RESULTS:
708/1000 = 70.8% chance of firing
24H. 800 vs 1 unit at a Range of 1
RESULTS:
821/1000 = 82.1% chance of firing
24I. 900 vs 1 unit at a Range of 1
RESULTS:
919/1000 = 91.9% chance of firing
24J. 1000 vs 1 unit at a Range of 1
RESULTS:
998/1000 = 99.8% chance of firing
CONCLUSION:
Proportional Opportunity Fire – as designed – is very effective. It makes moving by stacks a much more painful endeavor and guarantees more defensive fires against you.
Question 24 Unanswerable:
How does Proportional Opportunity Fire work?
I have no idea. See DIS-Proportional Opportunity Fire Error? below for a ton more information on why this is. I assumed all the general rules for Opportunity Fire carry over when using Proportional Opportunity Fire. I tested movement vs. firing and both actions draw enemy fire the same percentage of the time in tests. Beyond that I could test little more because of inconsistencies with the data.
Opportunity Fire Rules
The entire purpose of these tests was to finally establish a set of rules concerning Opportunity Fire. Why the actual User’s Guide has so little information on Opportunity Fire is a mystery to me.
Opportunity Fire functions well. For many years people have thought it dysfunctional in some way but I believe I have narrowed that issue down to the addition of the Proportional Opportunity Fire Optional Rule. If you do NOT check that rule then Opportunity Fire works perfectly well. The following is my own list of rules I have established concerning Opportunity Fire.
1. Stationary/non-firing units will not be fired upon.
No unit which does not move in some way, or fire offensively, can trigger a response from Opportunity Fire.
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2. Fire Values are halved by Opportunity Fire.
This is based on information provided to us from the User’s Guide.
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3. Any action (defined as any movement or firing of any kind) is treated the same by the A/I and is subject to an Opportunity Fire check.
This was established during tests 2A, 20A, and 22A.
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4. Opportunity Fire is determined using a set probability for different ranges.
The probability of Opportunity Fire decreases as the range becomes greater. The known range probabilities of Opportunity Fire are as follows:
1: 50%
2: 35%
3: 25%
4: 20%
5 – 9: 15%
10+: 5%
This was firmly, and repeatedly established. Most notably in tests 1A and 13A, along with questions 17 and 18.
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5. Increasing the number of units in a hex does not alter the probabilities of Opportunity Fire.
For evidence of this reference question 3.
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6. Occupying additional hexes can increase your odds of firing using Opportunity Fire.
Questions 11 and 15 addressed this issue.
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7. Firing multiple times from the same hex during one Opportunity Fire sequence is a unique event which happens less than 15 – 20% of the time at best. The probability decreases rapidly with distance.
I exhaustively researched this in question 10.
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8. The units chosen to fire and chosen as targets are done so randomly.
This was addressed in question 19. Unless anyone finds a better answer, I am sticking to mine.
Do not forget to occupy more hexes when possible! This will increase your fire combat output naturally.
I now have come to the end of what was an unbelievably fascinating, yet incredibly frustrating, project. The revelations revealed to me concerning Proportional Opportunity Fire have dampened my enthusiasm for using Turn-Based Play in the future with that rule checked. Opportunity Fire, by itself, works perfectly well and was designed intelligently. It combines a set of probabilities coupled with differing ranges to create a dynamic experience which has challenged and entertained us for decades. I would not advise using Proportional Opportunity Fire in the future if you can help it. If something is as inconsistent and inexplicable as that rule is then it does more harm than good to the outcome of a game.
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NOTE: Since writing this in 2020 I continue to use Proportional Opportunity Fire in my games. I am 100% convinced it has an error in the coding but because the error affects everyone equally it sort of evens things out. Nonetheless it continues to be an issue.
I hope everyone who has read all of this through to this point have learned all they ever wanted to know about Opportunity Fire. I sure as hell have! But, if you have any questions, comments, or ideas, please do not hesitate to email me directly.
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Proportional Opportunity Fire Error:
An error we all live with
This will, undoubtedly, be the most controversial of my findings. I wish I could say that I have “solved” the riddle of Proportional Opportunity Fire but can only report that I have found vast inconsistencies in the way the rule is used and how it effects gameplay.
By this point I believe you understand that I have ran thousands and thousands of tests using Opportunity Fire and have been able to pinpoint probabilities and patterns extremely well. But, once you check the optional rule box for Proportional Opportunity Fire all those probabilities and patterns go out of the window. Or, at least, sometimes they do. That’s the problem. It works. Then it doesn’t. I have found no variable that explains the inconsistency.
When testing with a singular regiment the rules work 100% of the time. A 700-man unit draws fire 70% of the time at a range of 1. I think that is the way the rule was designed to work. It is with the addition of multiple units in the same stack that things become dysfunctional.
As some examples:
While testing to see the probability of firing at a range of 1 with different size stacks of multiple units, the game, repeatedly, did not include the entire number of men in the stack and would only account for the “top” regiment in the stack. If you had a 100-man unit stacked with a 500-man unit you would only draw fire in 10% of the firing tests. The result should have been 60%. At least that’s what happens when you use this rule and fire against a single regiment of 600 men – the probability is 60%. How can I account for the discrepancy? Maybe if you flip the units position in the stack it will fire more. Right?
I would flop the 100-man unit with the larger unit on bottom, the 600-man unit, and then the results would be totally different. Suddenly results were closer to 60%. Did that mean the game only saw the regiment on top of the stack and determined probability of fire from that? I thought so.
The problem was that further testing debunked that as well. I could duplicate the results only part of the time. Sometimes the result would be based on the top regiment alone, other times it was based on the size of the whole stack, and others it simply found a middle point between the two sizes of the regiments to use as a probability.
Why does it work in some instances and not in others? I don’t know.
I have tested each variable I could think of to alter the probabilities: terrain, quality, odd vs. even numbers, OOB order, and even rotating turns, but nothing can account for the inconsistencies.
In another insistence I thought I had “figured it out.” Each result was precisely as the tests predicted. The key seemed to be to use a pre-made factory scenario and move the men manually to achieve the correct results. This worked great in one test. In the second test the numbers were vastly different. I ran it again and again and could never duplicate the correct numbers in the first test. What variable did I change? Not a single one.
At that point… defeat. For some unknown reason Proportional Opportunity Fire alters something in the game which I cannot pinpoint.
Personally, I like playing a game using rules I understand and can account for. Using Proportional Opportunity Fire seems to cause chaos and inexplicable results. If it works, or when it works, it does so very well. But, when and if it doesn’t, it can cripple the defender whose opportunity fire is inconsistent at best. Using Opportunity Fire without this rule checked is FAR superior because at least you know the rules going in and can account for why things happen and why they don’t.
This, friends, is the end of my testing for the foreseeable future regarding Proportional Opportunity Fire. Life is far too short to try and figure it out any longer. I really hope someone reads this and tries to build upon my findings and discover what I have overlooked and correct any mistakes I may have made. That probably will never happen, and that's okay. These are just games at the end of the day.