"Pseudo random Numbers" Topic

Gamblers seem to love rare events, me I hater them. I have had good games spoiled by both good and bad luck. No point winning if its just down to luck. Losing due to unusually bad look is also takes the game out of the set of interesting games.

In a wild fit of insanity I set a sort of simulation up.

1000 random numbers generated in sequence representing a D20 and compared the rolling total to that of the equivalent number of average rolls. Assuming an infinite number of rolls the value of the random and average would be equal.

For 1000 rolls that's 10500 pretty much.

Now interestingly I recorded the variation Plus or Minus of the cumulative value Average to Random score average.

I was surprised that in some cases the discrepancy between the expected average deviated by over 300, a couple of times in 100 checks. While messing around I got a 500 discrepancy. A fair way from an average score.

So if you could find a cheap effective way you could load say 1000 numbers into a machine that dealt them out sequentially knowing that they were all random but the deviation to the mean was acceptable.

There were sequences where the variation from the average peaked at only Plus or Minus values in two digit range. Still all random numbers.

It is interesting that it maybe possible to select random streams that avoided game ruining wild extremes. The "Bound termination" card coming out so often it stops a player doing anything, completely ruining an already not great random game is a case in point at the extreme end. Even in our own simulations having a more typical result while having a level of unpredictability has serious merits.

Note a rough guesstimate is that with Maneouvre Group running at the limits of the authors capabilities we might roll 600 die in an evening.

So do you think it has merits and how would you implement it simply and cheaply if it did.

For the really mathematical what would be a good acceptance limit be?

You're talking about the expected value of a fair die. You solved numerically and got the analytical result. The expected value is half of the lowest value plus half of the highest value. So, for a D20 you get 10.5. Not a value you can get, but on average it's what should be designed for.

You would expect fair dice to give a uniform distribution, but they never do. Same with random number generators (RNG) over so small a sample. And yes, 1000 is a small sample when trying to show uniform distribution. The other standard statistical distributions will show themselves pretty quickly but uniform is really only revealed by not finding another distribution that better fits the data.

You could replace the randomness of the dice rolls by supplementing them with modifiers or bonus points, but there are already games that use similar mechanics out there.

Looking at this from a different angle, on a D20 which numbers are you objecting to? Do 1, 2, 19 and 20 cause the problems? If so it might be simpler to just have a house rule that requires those results to be re-rolled.

So do you think it has merits and how would you implement it simply and cheaply if it did.

No. Your extreme wild variation works out as +/-0.5 per d20 roll over the course of two full games. This is a problem you don't have to solve, except by a more phlegmatic approach.

I have just re-watched the film "Midway" this afternoon. The US commanders ask themselves at the end "were we better, or just luckier"? If they can ask themselves that, you probably can too.

Tell you what UshCha I have a suggestion for you. I think 99.99% of gamers would loathe this (including myself) but I genuinely think you might like it: why don't you start recording all the die rolls made in the game by each side? Then you can actually work out which side was luckiest. You might even be able to code them for high-leverage and low-leverage situations. Obviously don't interrupt the game in progress to do it, but you could start filming them for subsequent analysis…

LaserGerenadier, its more subtle than that, to some extent it is rejecting long series of rolls lower (or higher) than average, rather than just rejecting extremes.

Wakeney you are correct the problem is inherently that statistics of small numbers are a bit of a problem. In small samples the deviations from the mean are higher. If I did 1000000 roles I expect the overall result to be identical. However at any given time there will be statistical variations. Rolling 4 "1's" in a row for instance would of itself give a simple value of 40, although not a great chance it is about 1 in 16000. However longer combinations of value below the norm or above are far more likely, as evidenced in some of the extremes in my simple analysis.

Really we are talking of selecting sets of random numbers based on a criteria. Effectively some sets are rejected. So they are "not" genuine random numbers as they are in a set of acceptable random streams. The actuality is simple but my Maths is not esoteric enough to express the means of selection in precise mathematical terminology.

You could mitigate the long runs of high/low results by abandoning the straight D20 roll for two D10s added.

Dilbert Random Number Generator
link

War Artizan that is not an equivalence that is useful. 2 D10 is a Massively different statistical distribution unworkable with our current system. Basically the system as is, is the least worst, only a few games are degraded as typically the distributions of random numbers does not feature high drifts so the games proceed well. The above was a thought experiment about how to deal with statistics of small numbers. It might trigger somebody else to have a completely different idea.

Drawing chits from a bag with enough chits for the whole game would add some constraints but probably not as much as selecting random distributions to a criteria, but the maths are a bit complex for me without again more time.

I was hoping we had a "proper" mathematician. I'm an engineer so I can deal with basic statistics but this either needs an expert or more numerical modelling than I have time to devote.

OK so this is just pointless but interesting. Taking 100 chits labeled 1 to 20 so 5 chits of each number, instead of throwing a die I draw a chit out of the a bag and then discarding it until the bag is empty.

By the time I finish the bagI will have 5 of each number. If I roll 100 die randomly Variations can be huge. In roughly 5 runs I got one number occurring only once, not the expected 5 times.

Running quite a few more iterations one number occurred 14 times not the expected 5 times. These differences are in the range of 4 to 11%. So perhaps drawing from a fixed population of say 100 would limit anomalies significantly. 100 die would represent about a small game.

Depressingly this needs significant thought on the implications but for a simulation where excessive randomness takes the game out of the set of interesting games it may have serious implications.

It may be the case some love the idea some will hate it. I guess its why some gamble and some are less keen.

On the practical side can you get a card dispenser that you can just draw a card from a loaded deck quickly? This would minimize time drawing the "chits" and could be drawn by the nearest player without issue. so the game would not waste time in evaluation random numbers. The occasional re-load and reshuffle would be quite quick.

Why not remove the randomness. If your game is based on D20, just give the player cards for 1-20. Let it be up to them to determine which ones to "burn" for each check. When they run out, they get the 20 cards back and start over.

As long as the game doesn't allow for spurious die rolls, like in RPGs, then it shouldn't be too bad.

Yes, in many games players will use the really good value cards for their single, most powerful unit. But it may balance out over time as other units get eliminated.

Just to run the sims, if you are worried about the gap between the highest result count and the lowest result count, I set up the following in Matlab:

runs = 1000000;
rolls = 100;

dSides = 20;

allRollsTable = ceil(dSides*rand(rolls, runs));

[n, xout] = hist(allRollsTable, dSides);

maxN = max(n);
minN = min(n);

gaps = maxN – minN;

The mean of the gaps is 8.2 and the standard deviation is 1.6. That means that on average the most frequent result will occur 8 times more than the least frequent result. More rolls will in crease this but decrease this as a total percentage.

If you can only get an outcome from a decreasing number of possibilities then the system would be massively open to gaming I.e. I know the last couple of outcomes must be a 17 or a 19.

The real world IMO operates according to a bell curve distribution of event likelihoods. 2D6 (or 2 of any numerically denominated die for that matter) provides an easily understood framework for random generation along a bell curve, with the added advantage of always maintaining the same standard range of possible outcomes with every throw. Card decks or bags of chits cannot deliver this standard of neutrality. Every draw from a deck or bag of "n" cards or chits incrementally and unavoidably alters the percentages of every future draw.

The only solution is to return the draw to the deck or bag. If you are going to take that step, dice are simpler.

Strictly my opinion, of course.

B

Blutarski,
You are in some ways correct. However for simplicity we add factors to our die rolls. Adding one to a single die roll changes the proability by a defined value (5% for a D20). Now in 2 D6 or even 2 D20 adding a factor of one onto a base of 11 (most likely occoring single value) changes the proabilities diffrently to adding 1 to a base requirement of 2. Not a good system in many ways.

We do use a sort of bell curve at one point but simply buy a table which represents a Very Rough normal distribution, but that is after the factors are applied.

Wakeney, What you are proposing I am sure has its merits as it has no Random element at all. However its not ideal for our purposes purpose.

Thanks for the statistics. As I understand it on average there will on average be a diffrence of 8 between the overrepresented rolls and under represented rols of 8. However that value could vary by about 4, so 4 to 12 to cover most of the population.

Thanks.

So the fastest way would be to draw cards from a Dealer Shoe. However as Bulutarski ponts out is it worth it. Yet more stuff to transfer to the Club twice a week, thats a definite downer to avoid the odd game where things are moving out of the set of interesting games.

However it is a thought provoking issue.

Don't forget that some dice rolls are also much more important then others. A roll where you need to roll a 5 or less on a D6 and roll a 6 is more "unbalanced" then one where you need to roll a 1 to pass and roll anything else. Or even one where you need a 2 or less to pass a morale check with half your units and 4 or less with the others. If you always roll a 5 with the units that need a 4 and a 3 with the units that need a 2 then things seem "balanced" when looking at the rolls in the aggregate but are no help to the poor player that rolled them.

Play games like 1642 where nothing happens. Push the cavalry together on turn one and play 10 turns each doing one casualty a turn to no significant result.

Dynaman8789, random roles even if screened somewhat are still random. Sod's law is not applicable, its just the nature of a random selection. Attributing it to anything else is unfounded unless one person is cheating.

random roles even if screened somewhat are still random. Sod's law is not applicable, its just the nature of a random selection. Attributing it to anything else is unfounded unless one person is cheating.

I think you misunderstand his point (I made broadly the same one). You wrote:

I have had good games spoiled by both good and bad luck. No point winning if its just down to luck. Losing due to unusually bad look is also takes the game out of the set of interesting games.

But many (most?) die rolls are going to have a very small cumulative effect towards producing that result, especially if you are rolling 600 times per game. The 'luck' will come down to how both sides roll on a much smaller number of high leverage rolls. Nothing you have talked about addresses this, so you are still going to leave your gaming table feeling unsatisfied.

UshCha wrote –
"However for simplicity we add factors to our die rolls. Adding one to a single die roll changes the probability by a defined value (5% for a D20). Now in 2 D6 or even 2 D20 adding a factor of one onto a base of 11 (most likely occurring single value) changes the probabilities differently to adding 1 to a base requirement of 2. Not a good system in many ways."

I indeed take your point, UshCha. A lot depends upon the degree of "granularity" desired (or required) in the rule mechanics. From my own point of view, however, a coarser degree of granularity forces me to focus upon important factors and prevents me from adding long lists of minor factors (otherwise known as "chrome") – I treat it as a self-imposed discipline. Otherwise, at modifier increments = 5 pct, I could justify an almost limitless array of influencing factors ("check gun crew for head cold in winter season; if Gunner Asch has a head-cold, then -1 on D20 die throw to hit"). Silly, of course, but a note of caution nevertheless.

- – -

While on the topic of "pseudo-random numbers", there is a very interesting YouTube video regarding the manufacture of gaming dice. According to the gentleman on screen, cheap dice very often display manufacturing flaws ( offset centers of gravity, differently rounded edges and corners on the same die that will over time statistically favor the appearance of certain number results and disfavor others. I tend to believe him, although I have no idea what I would do about it.

B

"So if you could find a cheap effective way you could load say 1000 numbers into a machine that dealt them out sequentially knowing that they were all random but the deviation to the mean was acceptable."

Get a Random Number Table, randomly pick a starting point, then use the numbers following it. (and being a table, you have 8 potential directions you can count in. You can randomize that too. ;-) You should rarely have the same sequences repeat. (And if you need a result from 1 to 20, simply divide the random # by 5.)

I'll make it simple. Rolling 600 D6 and getting 100 of each result over the course of a game does not eliminate good or bad luck being a factor.

I'll make it simple. Rolling 600 D6 and getting 100 of each result over the course of a game does not eliminate good or bad luck being a factor.

One interesting side note to this is that if you or I attempted to write down 100 1-6 numbers attempting to make them as random as possible, any statistician would be able to tell that what was recorded wasn't the record of 100 die rolls. How? Too random. Not enough runs of 1's, or 2's etc.

Dynaman, you are in some ways correct, its still random but it MAY and perhaps only MAY, reduce the extreemes. in that all numbers are fairly represented. Over representation of a number by 5 to 10% being possible otherwise. However as you point out if such extreemes are not at critical points its impact could be minimal. At the wrong point the player could get a sring of "bad" numbers even in the Pseudo random system. However the restriction statisicaly may not be that significant. Its has to a an overrepresented number that HE wants.

For instance an over representation of 1's for a player may not be too bad. Often you need more than 1 anyway in our system, which means there may be an over representation of say 6's. This would help becase a player more often would like 6+ than less than 6.

Again as a though experiment it highlights lots of interesting issues. It is now far more clear to me that once statisticsl proability's are invoked its wider implications are not easily understood. This little thread is shining a light on the realities. Changing that reality to a "better" one is not simple. Asas Dynaman 8789 notes, without so much bias the numbers are no longer random. Even a small run of and it may be bound and player dependentas game critical number (wihich will be bound and player dependent) and whether one player shared of the specific run between takes it all or is them. ( which actaully a bad run is a bad run for the player so a bad run could be for example 1,20,1,20 extreem but you get the idea Player 1 gets 1's Player 2 gets 20's.

Come to think of it in our own games it gets a bit dishertening when a staticticaly sound strategy seems to fail due to unfortunage "localy sound bets" failing. However later the same thing happends to the opposition and "balance" is restored. IF its not restored it can make an unsatifying game.

Ensuring you battle plan is not locally tolerant of bad luck or dependant on good luck to achieve its effect is in effect a general making his own luck. So was it me or luck that made it an unsatisfying game? Thats a hard one now I think about it.

McLaddie I read somwhere similarly, folk do not include a representative number of repeat numbers in writeing down random numbers for a LOTO ticket or similar.

For myself, I try really hard to avoid rules and scenarios which can be decided by a very small number of die casts. (The Evil Three are usually unit activation, reinforcement arrival and bridge demolition. Weather might make a fourth.) Everything else, I figure eventually averages out. But anyone who thinks luck averages out over the short haul and there is no such thing as a streak of bad luck clearly had a very different life.

robert piepenbrink, I'dont like rolling for re-enforcements. but if some unpredictability is needed, the role increases significantly each time its rolled for, so its automatic after a few bounds otherwise you are correct it can ruin the interest.

Random number generation war story from My Age of Sail rules -

My rules require passing an "Initiative Test" whenever a player desired one of his ship to undertake a new action (commencing a turn or change of heading, for example). A ship with a veteran crew passes any Initiative Test on a D6 score of 1-5. I once threw six failing 6's in a row trying to get a Veteran British frigates to wear away from a reef ahead. Fortunately, the wind in the scenario was very light and I finally succeeded before striking the rocks.

The likelihood of throwing six such failures in succession on a D6 = (o.1667)^6 = 0,00002, or about 1 in 47,000. I can happily rationalize such unusual events as the result of a foul-up so obscure and unlikely as to not merit inclusion in a rule set – the officer of the deck was reading the chart upside down or was personally unaware of the reef, the helmsman suffered a heart attack, the tiller ropes jammed. Unexpected bad stuff happens even to the best.

- – -

Another random number generation war story from My Age of Sail rules -

Ships with poor crews fire slowly (half the rate of a veteran crew) and are unable to focus fire upon the opponent's hull (trained and veteran crews capable of hulling fire produce about twice the hulling effect per broadside or discharge).

I've played a few games where the odd Poor quality French or Raw quality Spanish ship is throwing gunnery dice like James Bond at Casino Royale and inflicting far more damage than the rules might suggest as the norm. This is IMO not a bad thing within the scope of a scenario. Things like this do in fact happen in real life: in the Gut of Gibraltar battle (1801), Llinois' previously beaten up flagship Formidable (80) under jury masts engaged HMS Venerable (74) in close action for nearly two hours, shooting away the British ship's foremast and mainmast and leaving her completely disabled to drift aground.

Removing that sort of unlikely deviation from the expected norm removes all possible drama from the game and reduces it to an artificially controlled statistical exercise.

- – -

OK ….. one more war story, but this time from the annals of the venerable Column, Line & Square Napoleonic rules. A regiment of French infantry marching in column down a road through a large stretch of Type 3 woods discovers a roadblock consisting of one single Armored guard sapper figure defending behind works. The French player, for some unknown reason, disdains to engage with him with musketry and charges into melee. After a lengthy dicing session, the Hungarian grenadier remains standing, but the entire French regiment, as a result of massive melee casualties and bad morale, is GONE.

Unlikely in real life? Sure. Impossible? Look up the Battle of Saragarhi (1897), where 21 Sikhs held off somewhere between six and ten thousand Afghan tribesmen.

Stuff happens.

B

Blutarski.
There you have it both those examples would be ones which I would fined, as either side, an appaling waste of time. There may be elements of validity in the real world but noting is learnt except that statistics can very occationaly screw up even a good plan. That is self evident and of no interest. Occationally a battalion is kept on the move by one soldier of Victoiria Cross bravarey but again that teaches nothing on the underlying stategy and tactics, so to me again a wates of valuable playing time.

Clearly there is an enoumouse variation on what is defined as a set of interesting games. The random element is clearly one of the deciding paramaters.

One of our first forays into design was to modify Stargrunt 2 Mele, as it was far to unpredictable ruining our game completely. Again this is personal preference. Interestingly, we has stuck with its. Mele results are one of the few times we have gone very deliberately for a Rough Normal distribution, as it is a statistics of small numbers issue so the randomness could be very wide and uninteresting. Controlled as a normal distribution its variation is acceptable to us.

I believe I understand your thinking here, UshCha, and I do not necessarily dispute your intent. It's just that I have a great deal of respect for "The Law of Unintended Consequences". One might argue, for example, that a good plan is one that allows for friction, internal screw-ups, unsuccessful taking of a calculated risk, and "unintended consequences".

Strictly my opinion, of course.

B

Blutarski, Yes indeed a plan must be toretant of a level of upredictability but ther are limits to the extent a plan can tolerate that. A plan that requires a flanking unit turn up is vital. One that has suffient miss fortune/bad planning never to turn up is realistic but uninteresting and not usefull as a learning experience. I can understand there are many diffrent views on what makes an entertaining game.

UshCha, if I understand your original post correctly, you are talking about 2 different things.

In a wild fit of insanity I set a sort of simulation up.

I think the statistical interpretations of this have been well covered above.

I have had good games spoiled by both good and bad luck.

This I guess is your main topic? How to modify games so they are not spoiled by extreme luck? For a D20 system, this means the extreme outliers of 1,2,19,20 being much more rare or not happening at all.

2 very practical suggestions were already submitted but I think you didn't care for them:
1) agree with the other players to throw out extreme rolls (1,2,19,20 on D20).
or
2) switch your probability generator so the extreme numbers can't occur or are much less likely. Paired dice would do this and make the middle range more likely due to the bell curve effect (this is an implied corollary of your intent).

One suggestion was 2D10, so 1 can't occur, and outliers of 2,19,20 have 1/5th the probability (1/100 instead of 1/20).

You could also use 2D8+1 so 1,2,18,19,20 can't occur.

For a flat probability curve, you could use D16+2, so 1,2,19,20 can't occur and you have equal odds of results in the range 3-18. (D16 can be simulated with D6 + D8 where D6:1-3 is ignored and D6:4-6 adds 8 to the D8 result.)

load say 1000 numbers into a machine that dealt them out sequentially knowing that they were all random but the deviation to the mean was acceptable.

The problem with this is first it takes preparation, and second it is susceptible to bias, or the perception of bias, since there might be fore-knowledge of the sequence. Some players care about this a lot.

Substituting a different dice method is ad hoc and avoids this.

Interesting discussion.

CeruLucifus,
The aim if it were to be invoked would be to stop extreems being over or under represented. So in say 100 die trows of a D20 the order would be random(soert of) but no number would be over represented or under represented. (or not by much). Iterestingly drawing 100 chits out of a bag of 100 numbers containig equal numbers of each value would be one way. Thecnicaly ists peudo randum, but of course if you did draw out one number 5 times in a row at the start there would be no more draws of that number, not ideal.

I think the answer is there is no answer its either random, or its not and pseudo random systems may have at least as many issues though perhaps not the same ones as a random system.

The aim if it were to be invoked would be to stop extremes being over or under represented.

"over or under represented" compared to what?

Well, the questions would be:

1. If compared to a good, less frustrating game, then go for whatever limit on extremes pleases you and other gamers.

OR

2. IF compared to whatever portion of past or current reality you've chosen, the you need to determine what are the actual extreme limits in reality.

UshCha:
The aim if it were to be invoked would be to stop extremes being over or under represented.

So decide with the other players how many 20s should be allowed, and track them with hash marks. When you've hit the limit, re-roll every 20 that comes up thereafter.

Do the same for any other numbers with the potential for game disruption if over represented: 19,2,1.

If you can't decide how many is right, pick some inconsequential number as a reset result, say 9. Every time someone gets a 20, play it but declare 20s now must be rerolled until someone gets a 9. That way you've tied 20s to have the same representation as 9s.

So decide with the other players how many 20s should be allowed, and track them with hash marks. When you've hit the limit, re-roll every 20 that comes up thereafter.

Then that will likely front-load any '20' results in game play… They all happen at the beginning of the game and are used up by the end. [depending on the limit of '20' rolls being allowed]

Then that will likely front-load any '20' results in game play…

Yes, the consequence would be after an arbitrary point, 20s are shut out.

However from a simulation standpoint, that is what the OP is after, for the deserving player in the endgame to not be robbed of a rightful win by a lucky occurrence of a 20. No 20s = no chance of a simulation-defying upset from a lucky roll.

However from a simulation standpoint, that is what the OP is after, for the deserving player in the endgame to not be robbed of a rightful win by a lucky occurrence of a 20. No 20s = no chance of a simulation-defying upset from a lucky roll.

Uh, that limiting of die rolls defies simulating too. The limitation has been discussed as a game need, not as representative of some reality. Game need is certainly a legitimate reason, it just has nothing to do with simulating history/reality.

In reality, upsets from luck did happen. The question is why, how and how often. Those are simulation-building questions about representing luck in a wargame.

IF you don't want that aspect represented, terrific, but it doesn't have anything to do with simulating.

McLaddie,
You are correct, the desire for a more "even" simulation is like listening to "the sound of one hand Clapping" it can be said but it has no reality. Truth is a random factor is just that a random factor and this thread abounds with the reality that random is random and all attempts to "tame" it are flawed in so many ways. Still I understand more intrinsically what random means and its implications. So a fun and informative thread that I think has had its day. But thanks for all your insights, I leave it with a better understanding of the way the universe works.

Still I understand more intrinsically what random means and its implications. So a fun and informative thread that I think has had its day. But thanks for all your insights, I leave it with a better understanding of the way the universe works.

UshCha:

It is a fascinating topic. For a simulation, random isn't without order or unanswerable when asking the how often, where, and why. And a simulation doesn't NEED random or luck to be a simulation… it all depends on what you want to simulate.

But if you want to simulate, say the lucky happenings during the Utah landings for instance, the how often, where, and why can be answered.

The old saw of "For the want of a nail, the shoe was lost; For the want of a shoe, the horse was lost…" isn't totally random. The horse wasn't any old horse, but a courier's horse, the courier carrying important messages. That narrows down the where and the why. All we have to do is determine how often such 'lost messages' occurred on the battlefield by some study and statistical [e.g. probability] analysis.

Perfect? No, but that is the simulation approach to variables, luck and randomness. Depending on how well the researcher does, answers will be a light-years closer to reality than simply rolling a 20 sided die, then limiting the outliers with whatever feels good.

<Q>Gamblers seem to love rare events, me I hater them. I have had good games spoiled by both good and bad luck. No point winning if its just down to luck. Losing due to unusually bad look is also takes the game out of the set of interesting games.

UshCha:

You originally started this thread because of what was basically a game issue…luck and rare events spoiling the fun for you. Considering the time and effort it takes to organize a tabletop game, having a die roll decide the game can be really frustrating--the same is true of a boardgame.
How many times have I had a bad roll or the wrong card in playing "For The People" destroy my chances of winning? Players have to accept the reasons for such chances and accept them if they are going to play.

Truth is a random factor is just that a random factor and this thread abounds with the reality that random is random and all attempts to "tame" it are flawed in so many ways.

Not all attempts are equally flawed depending on what you want. It is just as easy to limit the range of outcomes by going from 20 sided die to a ten-sided die--then again, the bottom line is what those 20 possible results have been designed to represent. It is your design after all.

The Gamblers comment was aimed at a lot of games that inroduce to me excessive random events. The "end of turn card" being one which can have disaterous results, my co author failed to get a turn in on such a game in the whole afternoon game. Simuilarly many commecial games seem excessivly random to me. However the thread on How many games of cold war do you play was enlightening. If you play only two or 3 games a year you will NEVER master the tactics and random makes more sence.

Unfortunately random is an interesting issue. It would be better if on one die rolle we could quickly alter the mean and standard distribution of the population we are drawing from but retaining the same "granuality". Multi die rolls favored by some, changes the standard deviation of the popultaion but not the mean. I guess you could do somthing on a small hand held device but again it may take more time.

Trouble is rare(ish) events like the very occational destruction of a trench by a long artillery barrage do occour but juat not very often. I guess thety are quite random but a standard desviation may be difficult to estimate never mind implement.

Oh and the more I think about the above the more difficult it would be for me to get a grip in such effects should be nevermnind the implementation ;-).

Trouble is rare(ish) events like the very occasional destruction of a trench by a long artillery barrage do occur but just not very often. I guess they are quite random but a standard deviation may be difficult to estimate never mind implement.

UshCha:

It is simple, but difficult. For instance, Dave Brown's Pickett's Charge. He said on the TMP that the probability of any brigade without extra support 'hesitating' was 1 in 3 chances. Why? Because it worked with the game system. A game decision.

If you what to establish how often ACW brigades actually hesitated to simulate that probability, you have to answer some generic questions:

1. What behaviors and incidents does the term'hesitated' cover. The designer is free to define it as long as it is specifics and not vague generalization.

2. Then you have to go to the sources and start counting how many times such brigade events can be found during different battles. At this point, many will state that those are only the recorded incidents and how many weren't recorded. While that is a reasonable question, it is unanswerable. Any game designer who is recreating history only has the historical record to go by…imagining what wasn't recorded is a waste of time--and as easily wrong as right.

3. When you have found at least 30 events among those battles, then you can start reasonably determining the probability of them occurring, where, why and how many.
The more examples in your base, the better the validity. That is how you determine 'how rare' an event it. It works the same way in determining how rare the destruction of a trench is by long-range artillery.

It's simple in approach, but obviously the research is a lot of work. It is far simpler just to find probabilities that work in the game.

This also can address the tendency of contemporaries to record the rarer or unexpected events. Statistical analysis can do that.