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Subject: Variance in Combat Resolution rss

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Robb Minneman
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There's a really good discussion going on in a thread about combat resolution in wargames (http://www.boardgamegeek.com/thread/416878), and it's ranging over Bucket 'o Dice vs. CRT and factor counting and positive reinforcement and a whole bunch of other interesting topics.

I wanted to take one bit out and talk about it in detail. This really smart guy made a comment (http://www.boardgamegeek.com/article/3611584#3611584) a few days ago that I think deserves re-emphasis:

robbbbbb wrote:
I find that gamers understand means and probabilities pretty well, but they do not understand variance well at all.


I've been playing Asia Engulfed solo on the tabletop over the weekend. I also picked up a copy of Bonaparte at Marengo recently. The two make an interesting contrast on this particular point of wargame design.

Asia Engulfed uses the bucket 'o dice combat resolution mechanic. Not only that, but the numbers of dice being tossed at any one time are relatively small, and the chance of a hit on each roll is relatively small. This means that huge swings in fortune for each side are dependent on a roll of the dice.

Bonaparte at Marengo, on the other hand, uses a no-dice resolution mechanic for combat. The only thing that matters is how much mass you've got at the point of attack. If you know what you've got and what the enemy's got before the battle's announced, then you know how it's going to come out.

These are radically different design philosphies, but each works within the context of the game being produced. BaM is designed to emphasize the players' decisions without letting dice get in the way.

AE, on the other hand, abstracts out WWII naval combat, which is an inherently high-risk venture. Battles in the Pacific turned on a few minutes of action, and wild swings in fortune occurred at critical junctures. (The Battle of Midway is most famous, with the offensive capability of the IJN crippled within a few minutes. The Great Marianas Turkey Shoot was another. How would the war have been different had these swings of luck played out in the Japanese's favor, instead of ours?)

Just as much as mean and median results, variance plays a part in the games we play, and we'd do well to understand it.

(Incidentally, does anyone know how to embed links in text for forum posts? I'm not finding it, for some reason. This probably dilutes my brilliance.)
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Luca Iennaco
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robbbbbb wrote:
Incidentally, does anyone know how to embed links in text for forum posts?

Use the [url = www.mylink.something ] tag, without the spaces.
Then write the text that you wish to see on the screen as a link (redirecting to what you've indicated after the "=" sign in the tag).
Finally use [/url] to end the whole thing.

Example: click here to see the start of this thread!
Use "quote" on my post to see how I've done.

meeple
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Timothy Young
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Personally I would look for something in-between the two solutions. While too much randomness and dice emphasis will reduce a strategy game to nothing more than chance, I think the pure statistic based play removes a lot of the uncertainty of a real war.

History after all is full of amazing stories of soldiers defeating very long odds. Look at the 1297 Battle of Stirling Bridge where a British army of 11,000 were thoroughly routed by a Scottish force of 2,500. This is something that would simply not happen in a game of statistics.

Without the random factor I certainly wouldn't be interested in playing a game as it would simply remove a lot of the fun of playing.
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Mark Mokszycki
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When I first discovered the buckets o' dice approach, I really liked the idea. Every combat factor counts for something, and there is no math involved with setting up a perfect odds break with no wasted factors (something I always found "gamey" in wargaming). However, after playing plenty of buckets o' dice style games, I've come to the following conclusions:

1. Sometimes it takes too long.

2. It can produce really sporadic results (Hmmmmm. I just rolled 28 dice, and not a single 6! Then my enemy returned fire with 8 dice, hitting me on 5 of them)

3. The CRT isn't so bad after all. It speeds gameplay and normalizes results.

Of course, my preference depends on the game. I can't imagine playing Europe/Asia Engulfed with a CRT. It would spoil half the fun. I also can't imagine Russian Campaign with buckets o' dice. ...Actually, I can. It was called Defiant Russia.

My favorite version of CRT is the bell curve approach, such as rolling 2d6. The SCS/OCS games are a good example. It can be used to produce occasionally wild results (2's and 12's), but no more wild than what the designer intends.
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Robb Minneman
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Jackasses? You let a whole column get stalled and strafed on account of a couple of jackasses? What the hell's the matter with you?
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Luke: Thanks for the tip! I knew it had to be something like that, but I didn't know exactly how.

I supppose I didn't clarify above, but I was making a point that variance, in and of itself, isn't a design evil. Sometimes (and Asia Engulfed is a prime example) variance isn't a bug, it's a feature. Sometimes, high variance in combat resolution makes no sense. But variance is an inherent part of wargaming, and understanding its role is crucial.

Not only that, but designers should take variance into account in their designs. Designers should select high- or low-variance resolution systems to reflect the design effect they're looking for.

For those who are having difficulty resolving Bucket 'o Dice systems (length, etc.), I might recommend looking into Microsoft Excel. Specifically, the critical binomial function (CRITBINOM) will allow you to roll convert any dice roll you like into a Bucket 'o Dice resolution. Geekmail me, if you need details, but the Excel help file is good on this subject. It's similar in effect to the 3d6 conversion charts included with Europe Engulfed, and easy to do with a d20 or with percentile dice.
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Dr ?
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threads like these are a big part of the reason BGG is a fun place for gamers! This is the kind of talk that strikes a chord with those that like wargames!

I think some element of chance actually more accurately depicts the fortunes of war. How many conflicts were a totally known quantity--even considering unit density?! We know approximately this many units have been sited from this directions. We know this ground is more defensible. But what actually happens? An order gets miscommunicated an one group arrivers 15 minutes later that the charge because of a provisioning screw up somewhere down the road...

For a fun factor, dice are important to me as well. It is actually when outcome are based on few dice that things can come unglued. The more dice rolled, the better chance at a forseeable result, knowing each cast of the dice can go either way. Don't enter battles that spell doom if less than perfect results occur!

Or make a decision and realize that there is variability in the dice and average may not happen...
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Seth Owen
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For those who might be interested, Bowen Simmons wrote about why he went with a diceless combat system in Bonaparte and Marengo and about chance in wargames generally here: http://www.simmonsgames.com/design/Chance.html
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Robb Minneman
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Jackasses? You let a whole column get stalled and strafed on account of a couple of jackasses? What the hell's the matter with you?
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wargamer55 wrote:
For those who might be interested, Bowen Simmons wrote about why he went with a diceless combat system in Bonaparte and Marengo and about chance in wargames generally here: http://www.simmonsgames.com/design/Chance.html


That's a terrific article. Thanks for the pointer!
 
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Seth Owen
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In theory it slows play down, but only if there are a similar number of combat resolution events.

In reality most bucket of dice style games have relatively fewer combat events than similar scale CRT games. Does it really take more time to throw a bunch of dice for a couple of rounds in one or two big battles than it does to compute the odds and resolve the die rolls for a dozen or more individual battles in a CRT system?

Generally I would say BoD games have a reputation for playing quickly, as a rule.
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Lee Kennedy
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I agree the number of resolutions is important, and so is the number of checks per resolution. Those are more important than dice vs CRT to speed. A dice system that has you add up a bunch of die modifiers, roll to hit, then add up more modifiers and roll for damage, etc is much slower than a single die roll lookup on a CRT. On the other hand a single set of die rolls to hit (like Asia Engulfed) is much faster than multiple CRT resolution systems.
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Lee Kennedy
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duckweed wrote:
I also can't imagine Russian Campaign with buckets o' dice.


EastFront II is a great russian campaign that uses BOD.

I think BOD actually works well in strategic games like Asia Engulfed or the East Front series. It introduces a large amount of variance, which is realistic, but combat resolution is only one aspect of the game. Supply, command and control, unit placement, combined arms, and so mnay other things all feed into the strategy.
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John Bobek
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I generally design games to use 2 six sided dice for a bell shaped curve result. Instead of a CRT, I have modifiers that are added or subtracted from the die roll. It's fast (you tend to get into patterns of the same modifiers), and flexible (If you have a special situation in a game, you can tamper with the modifiers). Keeping the old brain fresh with basic math is an additional bonus!
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Robb Minneman
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Jackasses? You let a whole column get stalled and strafed on account of a couple of jackasses? What the hell's the matter with you?
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Wargamer204 wrote:
I generally design games to use 2 six sided dice for a bell shaped curve result. Instead of a CRT, I have modifiers that are added or subtracted from the die roll. It's fast (you tend to get into patterns of the same modifiers), and flexible (If you have a special situation in a game, you can tamper with the modifiers). Keeping the old brain fresh with basic math is an additional bonus!


I'm gonna quibble with the notion that 2d6 gets a bell-shaped curve. It doesn't. It gets a V shaped curve. Yeah, it gets more results in the middle than on the edge, but it's a linear relationship, up and down.

If you want anything remotely resembling a bell-shaped curve, you've got to get up to or past 5d6. Even 3d6 doesn't get a "bell." It just gets more reps in the middle of the results than on the edges.

The bell curve is a funky bit of math. Really. Nothing really replicates it except making a bunch of trials at a target. Even the binomial distributions that we get off of rolling a bucket 'o dice, like in EastFront II or Europe Engulfed aren't true bell curves, in the mathematical sense.

Now, this only really, really matters to people with serious math degrees, and for the purposes of game design this is way overblown. But hey, I'm like Lawrence Pritchard Waterhouse, sometimes, and I like precision in my math.
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John Bobek
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Quote:
If you want anything remotely resembling a bell-shaped curve, you've got to get up to or past 5d6. Even 3d6 doesn't get a "bell." It just gets more reps in the middle of the results than on the edges.

Yeah, I know it's not a true bell shaped curve, but it's rather impractical to keep adding dice for a single outcome. However, for game purposes, it does the job rather nicely and speedily.
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Jason Roach
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robbbbbb wrote:
wargamer55 wrote:
For those who might be interested, Bowen Simmons wrote about why he went with a diceless combat system in Bonaparte and Marengo and about chance in wargames generally here: http://www.simmonsgames.com/design/Chance.html


That's a terrific article. Thanks for the pointer!



It is a very good article, was well written, well reasoned, and an enjoyable read. However, although I agree with much of it, I do not agree with the generlization of "the simulation ends when the mechanism for chance is utilized.”

-Jason
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James Lowry
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wargamer55 wrote:
In theory it slows play down, but only if there are a similar number of combat resolution events.

In reality most bucket of dice style games have relatively fewer combat events than similar scale CRT games. Does it really take more time to throw a bunch of dice for a couple of rounds in one or two big battles than it does to compute the odds and resolve the die rolls for a dozen or more individual battles in a CRT system?

Actually, that sounds like the definition of 'taking longer'. You're just compensating by having fewer of the longer combats to come out to an equal or lesser total time.

Which is a fine way of pointing up the potential limitations of a BoD approach. Though really, the amount of time is a big variable in BoD since it also depends whether the combat can go multiple rounds, and the actual number of dice involved. And both BoD and CRT can take a while to go through if there's a large number of modifiers involved.

About as short as you can get is an old-fashioned single-die odds CRT with minimal modifier adjustments (think The Russian Campaign). About the longest would be a BoD with multiple rounds and other considerations (think Napoleon: The Waterloo Campaign, 1815; battles are practically a game in themselves).

The longest CRT resolution I can think of would be Onward, Christian Soldiers, which has a lot of modifiers to work out, including rolling dice just to get some of the modifiers. I'm not thinking of anything that would qualify as the 'shortest BoD' game I've come across off-hand.

All three examples I give, I consider to be great games.
 
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Rindis wrote:
wargamer55 wrote:
In theory it slows play down, but only if there are a similar number of combat resolution events.

In reality most bucket of dice style games have relatively fewer combat events than similar scale CRT games. Does it really take more time to throw a bunch of dice for a couple of rounds in one or two big battles than it does to compute the odds and resolve the die rolls for a dozen or more individual battles in a CRT system?

Actually, that sounds like the definition of 'taking longer'. You're just compensating by having fewer of the longer combats to come out to an equal or lesser total time.

Which is a fine way of pointing up the potential limitations of a BoD approach. Though really, the amount of time is a big variable in BoD since it also depends whether the combat can go multiple rounds, and the actual number of dice involved. And both BoD and CRT can take a while to go through if there's a large number of modifiers involved.

About as short as you can get is an old-fashioned single-die odds CRT with minimal modifier adjustments (think The Russian Campaign). About the longest would be a BoD with multiple rounds and other considerations (think Napoleon: The Waterloo Campaign, 1815; battles are practically a game in themselves).

The longest CRT resolution I can think of would be Onward, Christian Soldiers, which has a lot of modifiers to work out, including rolling dice just to get some of the modifiers. I'm not thinking of anything that would qualify as the 'shortest BoD' game I've come across off-hand.

All three examples I give, I consider to be great games.


I think The Napoleonic Wars (Second Edition) would qualify as a short BoD game system. There are only a few battles per turn and the game can end in ONE turn! You simply add up the factors (battle dice), roll for 5s (retreats) and 6s (kills). The side with the most hits wins. It only goes a 2nd round if there is a tie. But the HUGE variance in combat and completely ahistorical results leave me thinking this is the A&A of Napoleonic Games...
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Combat and the D6.

As terrain gets more difficult, and other things, combat dice rolls add 1D6 to the normal 1D6 resolution. Pretty nifty; it makes terrain itself rather variable, as it should be.
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m3tan wrote:

I think The Napoleonic Wars (Second Edition) would qualify as a short BoD game system. There are only a few battles per turn and the game can end in ONE turn! You simply add up the factors (battle dice), roll for 5s (retreats) and 6s (kills). The side with the most hits wins. It only goes a 2nd round if there is a tie. But the HUGE variance in combat and completely ahistorical results leave me thinking this is the A&A of Napoleonic Games...


Wellington too. I enjoyed having Wellington with 5 SPs attack Madrid - I had a 1-4 with 9 SPs sitting there - a poor leader with more troops than he can handle on the attack.

You guessed it - I rolled up 1-6 and 5-5s - he rolled up just 2-6s - the resulting rout killed Wellington, and secured Central Spain for France - a near game killer.
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Seth Owen
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Rindis wrote:
wargamer55 wrote:
In theory it slows play down, but only if there are a similar number of combat resolution events.

In reality most bucket of dice style games have relatively fewer combat events than similar scale CRT games. Does it really take more time to throw a bunch of dice for a couple of rounds in one or two big battles than it does to compute the odds and resolve the die rolls for a dozen or more individual battles in a CRT system?

Actually, that sounds like the definition of 'taking longer'. You're just compensating by having fewer of the longer combats to come out to an equal or lesser total time.

Which is a fine way of pointing up the potential limitations of a BoD approach. Though really, the amount of time is a big variable in BoD since it also depends whether the combat can go multiple rounds, and the actual number of dice involved. And both BoD and CRT can take a while to go through if there's a large number of modifiers involved.

About as short as you can get is an old-fashioned single-die odds CRT with minimal modifier adjustments (think The Russian Campaign). About the longest would be a BoD with multiple rounds and other considerations (think Napoleon: The Waterloo Campaign, 1815; battles are practically a game in themselves).

The longest CRT resolution I can think of would be Onward, Christian Soldiers, which has a lot of modifiers to work out, including rolling dice just to get some of the modifiers. I'm not thinking of anything that would qualify as the 'shortest BoD' game I've come across off-hand.

All three examples I give, I consider to be great games.


It's been my experience that the total time involved in BoD games tends to be less than similar CRT-style games, particularly those CRT-style games that reward factor counting, which are the ones at issue here. While the actual resolution of a CRT combat may not take a lot of time, one must also consider the amount of time doing all the factor counting to set it up. There are few less-exciting moments in gaming than sitting there for a half hour while your opponent carefully considers every single possible optimal allocation of his factors across the whole of the Russian front.

Indeed, to the extent that modifiers and untried units and morale checks or artillery/air support and other techniques make it harder to count factors and optimize your attacks they can save more analysis time than they cost in computational time and effort. Buckets of dice or other "to-hit" style combat resolution systems are not the only way to discourage factor counting.
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robbbbbb wrote:
I find that gamers understand means and probabilities pretty well, but they do not understand variance well at all.



I think you make a good point here. As the discussion tends towards the old CRT vs BoD 'debate' to a certain extent, I feel compelled to give an old example.

Let us say, for example, that the offense is 'shooting' (attack only doing damage) with 36 'factors'. With a BoD 'system' each factor represent one six-sided die rolled, with a 1/6 probablity of a 'hit'. The binomial distribution yields an 'expected' result of 6 hits with a variance of 5. Let us say the corresponding CRT has the 36 attack factors rolling (a single six-sided die) on the following 'column', with the possible resulting number of 'hits' given:

DR Result
1____3
2____4
3____5
4____7
5____8
6____9

The expected result is 6, just as with the BoD situation, however, the variance is 4.67 (note, less than with rolling the 36 dice described above). One might also note that the CRT in this case has a min result of 3 and a max of 9, whereas the BoD can return results ranging from 0 to 36. Mind you, the effect of the large number of die rolls is to 'concentrate' the probability for the BoD system around the mean. About 89% of the probability for the BoD resolution described is between 3 and 9. By contrast the CRT example given has a uniform distribution of probability across all possible results.

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One thing I have learned in 5 years of teaching Stats to varsity students, is that very few people (even some Mathematicians!) understand the difference between a one-off event, and repeated sampling. This is ultimately a failure in language, and in what we mean by "probability". Taught at the beginning level, probability is introduced either as an intuitive anticipation of the reliabilty of long-run sampling, ie. the "limiting frequency" paradigm, or as a terribly formal axiomatic system in which all kinds of vague-looking lemmas are proven using some elementary set operations. The first approach suffers from the fatal flaw of requiring some kind of limiting or convergence behaviour in an infinite sequence of trials. The latter just looks like abstract formalism, with no connection to gambling, the weather, or similar events the student is familiar with.

What makes Bowen Simmons's designs so ground-breaking (possibly the most innovative wargames in 30-odd years or so, from a statistical point of view) is that they account for the difference between "randomness" and "uncertainty". This is an important distinction that is gaining traction in statistical research and teaching today.

I respectfully submit that if the game designer can disentangle 'uncertainty' from 'randomness', he/she'd be well on the way to being able to make more informed decisions about what the combat resolution system in a game is trying to show. For instance, in a one-off event, unless you are performing a "random experiment" (problem: define random), you are dealing with uncertainty. That is not the same as randomness. So if I choose a card from a standard deck, and ask you to guess what it is, is this a random event, or something uncertain? You'd figure you have a 1/52 chance to guess correctly. You have used probability theory to model an uncertainty to a high degree of accuracy. However, it can be argued, if I didn't randomly choose the card (did I catch you guys out with tricky language? I said "I choose a card" - I didn't specify how I choose it!) then there is no randomness at all. I picked the Queen of Clubs, because I like clovers for St. Patrick's day, but you've successfully modelled that event using probability.

As things get more and more complicated, we are driven to state "All probability models are wrong. Some are downright bad". Hence, consider a combat results system as a probability model for an uncertain, one-off event. The claims made about the 'BoD' system is that for increasing numbers of dice, the resulting probability histogram is more and more closely normal, or "bell" at least around the mean. One thing to note about the normal distribution, is that it is NEVER, EVER zero! So everything has a positive probability assigned to it! You may not want this over several plays of a single game. How that would translate into a game, is once in a while a game will have taken an hour or more to set up, you've gathered the players, everyone's spent the weeks necessary to really get to know not just the rules, but how they cause the game to happen, and then BANG, your game is ruined in a single dice roll. You bravely play on, trying desparately to be a good sport, but after another turn or so, all can see the game is really over. That is not a good feature in my view, unless the game has a short rulebook, and is a snap to set up again.

Again, this relies on a long-run frequency, and as pur poster has pointed out, very few people understand variance. Highly wacky results are going to crop up far more often the more often you roll a great many dice.

Put it this way - the more dice you roll, the less likely the average becomes!

As a designer you'll need to factor that into your design. Which brings us to the next Big Question:

What is your game attempting to simulate? most people seem to desire a degree of simulating command decisions more realistically. In other words a game can be "realistic" in two ways, as I see it. One, it can realistically replicate historical results. Note I mean replicate, as opposed to duplicate, so you can fight the Battle of Cannae 10 times and have the Romans lose in 8 of them. Now we have slipped into the "repeated sampling" problem. (Quick question: does that mean the probability of a Roman loss is 8/10? Answer: no! The correct answer is that history is not subject to the axioms of probability because (a) it is not reproducible, and (b) we have no idea of what the sample space looks like!).
Two, it can successfully simulate the kinds of decisions a general OF THAT ERA will be required to make. The Commands and Colors: Ancients system does both of these fairly well, but at some cost in another vital area as we'll soon see. So as a designer, two questions to ask yourself are (1) What do I want successful players of my game to be able to do, and how does this ability mesh with historical requirements? and (2) What, if any, probability models will I include to simulate UNCERTAINTY?

(So chess, by way of example, is not random, but has ENORMOUS uncertainty built into it: if I could read my opponent's mind, and never, ever missed a combination, I'd be world champion!)

A third, very important issue in wargame design is what I call "the jip factor". A very clear example of this is those games in which leaders are variably vital to victory, but are subjected to repeated, essentially unavoidable, independent random trials to test their longevity. Their loss was through no direct fault of the owning player, but in some cases his game can suffer greatly because of this. In addition, if this procedure is tedious to boot, that is a high cost. Another is the more unstable BoD games, where more than about 8 dice are involved in battles, and battles are two or more rounds, where performance in round one greatly impacts round two. Wild swings can be OK in these situations, but as a designer, don't be duped into thinking BoD de facto better than CRT. Go back to questions (1) and (2). In the case of CC:A, the jip factor can be very high, but the decisions players are required to make, and the actual outcomes in the scenarios, actually give a good simulation of ancient warfare. If enough randomness is present, many feel the "results smooth out in the long run". This may or may not be true, but I am curious as to whether such games are "decision-sensitive" at all. Meaning that would you be able to consistently win simply by just randomly pushing units about and attacking every chance you got. I am not even clear that CC"A doesn't suffer from this flaw - that the game system at some level just plays itself, regardless of what the player does. Again, what as the designer do you want the successful player of your game to be able to do?

As the gamer, however, you are the final arbiter of the success of the design. Chess is a simply brilliant game. Played by millions and millions, and less than a page and a half of rules. Many wargamers despise chess, or dismiss it as "unrealistic" but the skills demonstrated are solid (guess the enemy's intentions, make optimal use of force, time and space, combined arms ops, etc.) There is no jip factor. You win or lose on your decisions alone, and this makes chess very hard on the ego. However chess has as a fatal flaw, its very strength - it depends absolutely on the skill of the players, and even small differences in skill are often insurmountable. It is thus a socially "difficult" game.

I lean more and more to a compromise. There are many CRTs that do a great job (the PoG one really does work well inside the game system, but not if lifted out and studied absent the pieces, stacking limits, and cards driving the action). At the end of the day, even in a case like CC:A, there are many reasons to dislike the game, and many to like it. I feel as a designer, one needs primarily to justify ones decisions to the gamer, to explain why things were chosen as they were, and most importantly to be able to back up claims you make. If designers (a) were mmore clear themselves in what is being simulated and what is not, and (b) were clear on why they believe there probability model is a good fit for the uncertainties in the game, and (c) effectively communicated that to the public, there'd be alot more informed gaming audience.

Anyhow, please forgive this impromptu dissertation, but this subject is very near and dear to my heart!

Bevan gulp

Edited for clarity, if you can believe thatshake
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Kenny, you provide a good example there. However, what is missing from that is not what the probability of one dice roll is, but what happens under repeated runs of the experiment. In EXCEL fill a cell with the code '=randbetween(1,6)'and drag the results down to row 25 or so, and now across to fill the page. You'll need to cut and "paste special: values" so your data goes nonvolatile. Now you'll have (if you rescale comuns to about 3.2 wide) about 20-30 runs of the 25 dice roll. Draw a histogram and enjoy the chaos!

The other thing that gamers miss often, is that increasing the number of dice isn't automatically getting you closer to the normal, rather there is a shift to one side or the other dependent on what your probability is on any one trial. A general rule for using the normal approximation to the binomial is that n is large, so that np and n(1-p) are both larger than about 10. So 25 dice needing 6's to hit is quite skewed from a normal. The binomial isn't necessarily a symmetric distribution!
 
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Mark Luta
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On the side issue of speed of play which comes up in this thread, I think everyone would agree most 'buckets of dice' games are quicker playing than CRT style (with the notable exception of John Prados Third Reich). But this is not a function of the way the combat is resolved, it is simply because most 'buckets of dice' games are simpler and designed to be played in shorter amount of time.

Of course, complexity and playing length alone do not determine how good a game will be--there are plenty of really bad long and complex games out there! (The original rules of John Prados Third Reich would probably make this criterion, unfortunately!) But, it is certainly true that a game such as Europe Engulfed would be much quicker if CRTs were used for the combat, rather than dice buckets, even though EE is still one of the faster playing WWII in Europe games. Personally, I tend to like the longer and more complex games, but regardless I really do not like time wasted rolling dice, which to me has nothing to do with playing the game. And I would agree the dice rolling is less objectionable in Asia Engulfed, in part because there are a lot fewer dice to roll.

With specific response to the variance issue presented in this thread, I sometimes describe this as skewed results which, while not mathematically pure, seems to be a terminology more people can understand that trying to describe variance and deviation. And I maintain that another reason the dice buckets approach works well for Asia Engulfed is that there should be a high variance (skew!) in the outcomes of naval battles. There is no terrrain to contend with generally speaking, and the naval forces do not remain in place, but go out on missions and come back, or are sunk or damaged. Destroying a high value unit is not only more likely, but can also quickly start to tip the attrition in one direction--while a regiment does not often shatter, and tends to retreat and use terrain to advantage, a ship which is badly damaged is often unable to retreat, but is sunk before escape. And air combat shows the same characteristics, two planes attacking fifty stand a good chance of doing some damage before being shot down, while there were occasions when planes would penetrate the thickest flak relatively unscathed, while another time a handful of shots would bring down a plane. Naval combat over a length of time tends to be either decisive (Trafalgar, Midway), or pretty indecisive (Jutland, or the long attrition of the guerre de course of so many wars). Smaller forces often defeat larger, in terms of both mission accomplishment and damage inflicted.

But in land combat, such skewed results are the exception. Generally the stronger side prevails pretty handily, and if things do not go their way, they simply stop the attack, the weaker side is rarely in a position to harm them much immediately (or suffers drastic losses in an ill-advised counterattack from out of protective terrain, such as at Hastings). Untrained and amateur troops can of course show more unusual results, such as the Iberian Wars of the Napoleonic era. But I would say the majority of our wargames feature trained and reasonably well equipped troops. Even the Battle of Stirling type result referenced above is accounted for in most systems (Agincourt would be an even more extreme result), charging across a bridge (or through muck and mire) tends to nullify the superiour numbers (so we reduce the attacker's strength and increase the defender in such cases). And so these sort of results are still reasonably predictable, even if they are not the most probable outcomes they still can occur in wargame simulations with reasonable frequency (e.g. 10% or 20% of the time) without having to resort to high variance resolution systems that can give inexplicable results (let the heavy cavalry cross the bridge and form up for the charge at Stirling, or hold Agincourt on firm ground, and see how differently the results come out!).
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Rachel Simmons
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Jason Roach wrote:
robbbbbb wrote:
wargamer55 wrote:
For those who might be interested, Bowen Simmons wrote about why he went with a diceless combat system in Bonaparte and Marengo and about chance in wargames generally here: http://www.simmonsgames.com/design/Chance.html


That's a terrific article. Thanks for the pointer!



It is a very good article, was well written, well reasoned, and an enjoyable read. However, although I agree with much of it, I do not agree with the generlization of "the simulation ends when the mechanism for chance is utilized.”

-Jason


That was only an intermediate conclusion, which served as the starting point for a discussion of analytic vs. synthetic simulation. Analytically, I think it is true. Synthetically, I think it is false. I'm sorry if that distinction didn't come through for you as clearly as I wanted it to.
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