Home Forums General Game Design The averaging dice effect myth

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  • #53153
    Jerboa
    Participant

    One of the most popular myths in wargaming is that the more dice you through in a single game the more the stochastic effect (randomness) is minimized. Therefore skill prevails.

    In order to analyze such hypothesis mathematicians usually look for the limit situations. The limit situation here is an infinite number of dice throws. In a d6 the average score for an infinite number or rolls is exactly 3,5 (or 3.5 f you like). Therefore the higher the number of rolls statistically the closer you get to the absolute average.

    The problem is that wargames are often decided by the largest scores difference, the real cutting point. What matters is the actual score distribution within the sequence, not the average.
    Imagine this sequence: 1-3-2-4-6-5… averaging exactly 3,5. In wargames the game will most likely be decided by the 6 moment, therefore the average is meaningless. True average should point to a draw, unless you have a very unbalanced game (not interesting). You must be lucky enough to reach the peak values before your opponent in order to win, therefore the sequence average means very little.

    One example is a mainstream game I played with about 60 bases per side. Tournament and 6h play, countless dice rolls. The game was decided by arguing about a 1mm distance difference and then a single opposed die roll. Not satisfying (also because I conceded 1mm and lost the roll!).
    But on another game I had been outmanoeuvred and was in really bad shape. There was a strict useful time limit of 2h45min. I contacted a General base and rolled like 6-2 and won that game. Great luck, terrible injustice. It did not feel satisfying either.

    The problem is that these types of outcomes happen over and over. My final verdict: boring.

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    #53154
    John D Salt
    Participant

    An interesting point; and you are of course correct.

    It is certainly true that the more dice you roll in a single throw, the greater will be the central tendency of the result if you add them all together. It only takes seven dice to achieve a tolerably good representation of a Gaussian curve (although no number of dice will produce it exactly, as it extends to infinity in both directions).

    This is not at all the same thing as the situation you describe, where lots of separate dice rolls are made over the course of the game. What determines the outcome of the game is not the average score of each roll, but the causual chain of events between each result. And while dice themselves produce random results, it is usually the player’s decision whether the dice will be rolled or not for each specific combat (or other randomised occurrence).

    Of course another argument about “skill” is that it takes more skill to make decisions under uncertainty than under certainty (which is why so many successful Japanese manufacturing methods concentrate on reducing random variation in production processes). This I think was the point of the Duke of Wellington’s remark that Napoleon constructed his campaigns as one might a fine harness; old Nosey constructed his campaigns out of rope, and, when something broke, he simply tied a knot and carried on. If your entire plan of campaign could be defeated by a single bad dice roll, perhaps your plan was based on a gamble, rather than a calculated risk.

    Another point I find interesting is that the contrast between random and relatively predictable processes could perhaps be used to model different approaches to command and control in 20th century armies. Martin van Creveld (“Command in War”) suggests that there is some irreducible amount of uncertainty in any C2 system. Some systems try to concentrate certainty at the top, leaving the blokes at the sharp end to deal with wild variation; others accept a high degree of uncertainty at the top level, in order to make things more predicable low down. Extreme examples would be the Israeli system, which thrives on uncertainty, and regards excessive planning as counter-productive, and the Soviet system, which demands lengthy planning in detail, so that the senior commander has a vast number of planned options. A good game reflecting this difference would, I think, have different levels of randomness in the rules for each side.

    All the best,

    John.

    #53179
    Chris Pringle
    Participant

    Granted that not all die rolls during a game are of equal significance. Granted that an extreme result early on can have disproportionate impact as the early advantage it generates gets magnified over the ensuing turns.

    But Jerboa, perhaps your boredom and frustration could be due to the types of game you play?

    Correct me if I’m wrong, but I’m assuming you’re talking about ancients tournament games. Would I be mischaracterising such games if I suggested that ancient armies are not very resilient? As in, one extreme result somewhere along the line (and it is nearly always a line) is often like a dam being breached and results in catastrophic failure. Loss of a single key element – the general – is similarly catastrophic. So local luck can produce far-reaching effect.

    In later periods, i.e., Napoleonic onwards, I suggest that armies are more resilient and you don’t see the same catastrophic effects. This is because of increased mobility and flexibility of formations, increased weapon ranges, consequent ability to deploy in more depth, more complex non-linear higher-level formations, with distributed mobile reserves and the ability to recover from local setbacks. Thus the armies are better able to survive long enough for the extreme dice to average out.

    Also, the tournament format is necessarily formulaic and therefore potentially boring. I don’t do tournaments. I’m used to historical scenario-based games, which are still contests with explicit victory conditions, but with defined turn limits and where victory typically hinges on possession of multiple geographical objectives related to the historical situation. The norm is that on the last turn there are at least two or three objectives being contested, assaulted and counter-attacked, with all three game results consequently being possible (win/lose/draw). But whereas, in your example of your 6-hour game that you lost on the last dice roll, you felt dissatisfied, my experience is that such last-turn, last-dice nailbiters are tense and exciting and very satisfying indeed – especially if it ends in a draw with honours even and everyone happy.

    I don’t know how much that says about different kinds of game (ancients tournament vs more modern historical scenario-based), and how much it says about our differing personal preferences.

    But to get back to the subject of your post: in the games I’ve been describing, but also in the many tournaments that our club members compete in regularly, my observation is that the more skilful players are the ones who win most of the time, and the best ones lose very rarely indeed. That suggests to me that the dice really do average out enough for the stochastic effect to be mitigated and for skill to predominate. Or have I just been observing a statistically vanishingly improbable conspiracy of coincidence by hundreds of thousands of dice over the years? Are the best players, the ones who routinely top the tournament rankings, just being consistently, game after game after game after game, lucky?

    Chris

    Bloody Big BATTLES!

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    #53183
    Olivero
    Participant

    I read an AAR once where one player seemed to do everything right and everything happening turned out in his favour. While mopping up the last few enemies he send in his vastly superior General, rolled extremely unlucky, General dead, Game lost. Ha ha, I would have gone crazy! Personally, I believe that to be rather bad game design than being the fault of the dice (or fortuna for that matter).

    #53184
    Not Connard Sage
    Participant

    I read an AAR once where one player seemed to do everything right and everything happening turned out in his favour. While mopping up the last few enemies he send in his vastly superior General, rolled extremely unlucky, General dead, Game lost. Ha ha, I would have gone crazy! Personally, I believe that to be rather bad game design than being the fault of the dice (or fortuna for that matter).

     

    I believe it was rashness on the part of the player.

    Perhaps he, and his general, fell victim to the ‘couldn’t hit an elephant’ rule…

    "I'm not signing that"

    #53188
    Norm S
    Participant

    Sort of like Harold getting the arrow in the eye type situation ! (1066) after holding the Normans at bay for 8 hours.

    or

    General John Sedgwick (1864 American Civil War) told his men while trying to motivate them – “They couldn’t hit an elephant at this distance.” – as the words were spoken, a shot hit him below the eye and killed him.

     

    • This reply was modified 4 years, 10 months ago by Norm S.
    #53189
    Jerboa
    Participant

    The fact that dice averaging allowing for skill to become more important is a myth, it is a mathematical and statistical fact.

    D. Salt is right, in that I should not have presented those actual examples.
    I quote ‘What determines the outcome of the game is …. the causual chain of events between each result.’
    I assume ‘causal’.

    The important rolls are those resulting in peak scores – high or low – but obviously also those that are related to key moments in the game. This increases the stochastic level, does not decrease it.
    You may fail a non-key event roll and pass a critical event roll and do well. Whatever decisions led to the actual event, may be more or less relevant, but if their ultimate accomplishment is dependant on a random event, the deterministic component will become secondary, maybe negligible.
    Once a system is partially stochastic, it will remain so. Then you can discuss about the stochastic level for each game, but that’s not important in a generic discussion.

    • This reply was modified 4 years, 10 months ago by Jerboa.

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    #53225
    Chris Pringle
    Participant

    Thanks for the stimulating discussion. Best of luck in finding what you’re looking for.

    Chris

    #53231

    I wonder if I’ve missed something all these years of gaming?

    My “take” on a dice-driven strategy game has always been it involves skill in every aspect short of the situations that need a dice roll to determine an outcome.

    Thus, how I field my army (ie troop types), deploy & manoeuvre the units takes a degree of skill (call it “generalship” if you like: I’d prefer to avoid pretending what I do with mini figs is overly military). The dice rolling covers the imponderables we call “luck”. In the games I play, certainly “luck” is moderated by various factors ie the spread is greater when your Sherdan Guard have better armour than his Arzawa levy. However, I have always expected the “left field” dice roll to occur on occasion &, indeed, would be disappointed if it didn’t ever eventuate. That’s what luck is.

     

    Can I give you a recent example? In a Field of Glory Ancients game, my Gallic warband slowly fought a losing battle against a unit of Polybian Roman legionnaires. The Romans were drilled, of better quality & were wearing better armour, so the dice, as you’d expect, reflected the Gauls were going to lose. To stave off the inevitable, I added a Gallic chieftain to the melee: a tactic that would give me some re-rolling of poor dice. My opponent, blast him, did the same. However, miraculously I threw some great numbers whilst me opponent did the converse. I won that round! However, the rules state leaders in melee must be diced for, to see if they became casualties. As I’d won, I needed an ’11’ or ’12. I threw an ’11’! Dead Roman general!! My opponent needed to throw a ’12’ (I’d won the melee)….& threw the needed’12’. Dead Gallic chieftain. As my army was lead by fewer Leaders than the Romans, this was a far bigger disaster for me & was the event that marked my decent into defeat.

    Did I “deserve” this outcome? Hadn’t I taken the initiative by adding a leader to the fray? Hadn’t I, against the odds, won the melee? Possibly but luck dictated otherwise & the sheer unpredictability is what gives games their spice. Cyrus the Younger can be killed just as Xenophon & his fellow Greeks win the battle for him.

    I probably have missed something in that I don’t often let the calculation of odds interfere too much in my gaming. One die or a bucket of dice: I expect the little cubes to be perverse.

     

     

    donald

     

     

    • This reply was modified 4 years, 10 months ago by Deleted User.
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    #53459
    Phil Dutré
    Participant

    One of the most popular myths in wargaming is that the more dice you through in a single game the more the stochastic effect (randomness) is minimized. Therefore skill prevails.

    I think you are misinterpreting the myth. This statement is usually applied in the context of specific gaming mechanisms, such as buckets of dice to resolve combat.

    Suppose I have a game that works as follows: we both roll a D6. High roller gets a +1. Highest score after 100 opposed die rolls wins. BUT! The 100th roll counts for +500 points … !

    Of course such a game only depends on the last die roll …

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    #53466
    irishserb
    Participant

    I’ve thought about this a bit, since first seeing OP, and come to the conclusion that the game systems that you and I play are quite different.  The over-whelming majority of the games that I have played over the years use percentile dice, where every shot and the result of every hit(where applicable) is rolled separately.  Of the thousands of games that I’ve played, I would be pretty comfortable in saying that less than 10 have used the difference between die rolls to yield a result.

    Additionally, I can’t remember a game where a single die roll decided the result of an entire game, let alone doing so, such that all of the preceding action was rendered pointless.  You may argue that morale rolls for large portions of an army might be such, but those rolls are typically defined by the result of  between dozens and hundreds of shooting rolls (and other rolls for other components of the game), where the opportunity, and effect of each roll are significantly impacted by the skill of the players, and willful risks that they decide to take.

    I’m not arguing that what you are saying about your games is not true, I’m just offering that my rules and experiences are quite different from yours.

     

    #53492
    Jerboa
    Participant

    This not a question of game types.

    Percentile games are in fact a bit different, but not that much. Each roll represent a probability for an event. With d6 it’s 1/6, etc, also a probability.
    But with a range of 1 to 100 you risk letting the stochastic component of the game getting extremely high.

    Overall the principle still applies: you can roll thousands of times, but it will not be true that rolling more will allow for player skill to sand out of randomness.

    I should have not presented actual examples of play in this case, they are mostly casual and irrelevant.

     

    http://dnir.net/JerboaNet/Jindex.htm

    #156782
    Stephen Holmes
    Participant

    Just three observations.

     

    1. Some gamers suffer form “magical thinking” around their dice. I’d expect regular gamers to understand fundamentals like 5,6 on a d6 being one third probability.
    2. Most games have one or two critical rolls: Usually a save, or the break test after a unit takes a drubbing. Even if dice did “even out” (They don’t) these are the rolls that make or break the army.
    3. “Luck” as a proxy for all the random factors in a game, is not the opposite of “Skill” (another nebulous term). Reducing the number of die rolls does not make a more skillful game. Eliminating all randomness makes for an extremely dull deterministic game. Learning to work within the bounds of probability is one of the higher levels skills in wargaming. I’d put it that “Luck” and “Skill” inhabit orthogonal axes.
    #156791
    Tactical Painter
    Participant

    Backgammon is probably one of the best tactical game in existence. A game of skill that is totally driven by luck, but one where the best players are not ‘lucky’ rather they are skilful. Very occasionally an extreme swing of luck may determine a game but in my experience this is very rare. The game is driven by the roll of two D6. The best players know how to play their luck – the good and the bad. They win by making good decisions with the dice they roll. The dice don’t dictate what they will do, they look to the dice to decide how best to do what they want. They will never move more than two pieces in a turn (except when rolling doubles, in which case a maximum of four), the decision is not about the luck of the dice but the selection of pieces to move and how.

    The analogy with a wargame is a good one. The dice represent the current conditions under which a commander is operating. They will not always be optimal, the better commander will make the most of current circumstances. The conditions should not determine what happens, the commander should be determining what is best to do under those conditions. Sometimes you win despite the odds, not because of them. Those conditions are created through 2D6 yet Backgammon has stood the test of time and delivers a balanced, tense game nearly every time. I’m not so sure the number of dice rolled is the critical issue. In fact the number of dice rolled could vary to reflect the scale of an action or a commander’s ability to exercise effective command. I’m convinced good players will make better decisions more often about how to operate under those conditions than poor players. It doesn’t reflect luck so much as tactical skill, ability to read the battlefield, willingness to take risk and how well they prioritise.

     

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    #156797
    Sane Max
    Participant

    I read an AAR once where one player seemed to do everything right and everything happening turned out in his favour. While mopping up the last few enemies he send in his vastly superior General, rolled extremely unlucky, General dead, Game lost. Ha ha, I would have gone crazy! Personally, I believe that to be rather bad game design than being the fault of the dice (or fortuna for that matter).

     

    I am not sure I recounted that here – but that was probably me. It was my Roman General AND Army Standard Bearer in a game of WAB at a tournament, back when I liked tournaments. Rash indeed.

     

    The analogy with a wargame is a good one. The dice represent the current conditions under which a commander is operating. They will not always be optimal, the better commander will make the most of current circumstances.

    Totally. The player doesn’t roll a dice and go ‘Ahah! a 6’.  He thinks ‘I have this game in the bag. One last real combat – I am winning this combat by plus three already, and I have more attacks, and attack first. Shall I send in my Army Standard Bearer and my General in the Rear – Plus Three more…. with an infinitesimal chance that the foe will cause a startling high number of hits and mine will score a startlingly low one? Why no, that would be risky indeed, as I might lose the game in an eye-blink! – they shall, in fact, move away to reduce the chances of Panic…… and then he rolls the dice.

    #156816
    Guy Farrish
    Participant

    The ‘unlucky die roll’ to kill the general thing; excellent modelling of a rare but entirely foreseeable event: Gaston de Foix, boy wonder general of the Italian wars, chasing the defeated Spanish at Ravenna, unseated by horse stumbling, shot and killed.

    I don’t think dice do, or at least shouldn’t, represent the circumstances.

    The circumstances represent the circumstances: General with bodyguard,, enemy army nearly defeated , enemy unit hanging on, weapons, training, formation, ground, weather, supports etc.

    The dice represent the probabilities of the other bits you don’t know about, ‘imponderables’, and the chance, however remote, that running around with pointy sticks and shooty things is sometimes going to result in tears before bedtime.

    The ‘bad’ design bit is if the death of the general automatically loses the battle. De Foix died but won the battle, Gustavus Adolphus likewise (possibly – didn’t lose Lutzen in any event).

    #156823
    Sane Max
    Participant

    The ‘bad’ design bit is if the death of the general automatically loses the battle. De Foix died but won the battle, Gustavus Adolphus likewise (possibly – didn’t lose Lutzen in any event).

    I wouldn’t play a game that did that. There are games where his death can be a serious Blow, again in WAB there’s a chance a lot of your stuff will flee (if you roll bad dice)

    My main argument to show dice average out is that If it was just luck I would win more. But I don’t. I am just a bit rubbish at games, and the dice don’t help or hinder.

     

    #156824
    Patrice
    Participant

    As others have said, the decision to take risks or not can be considered as being part of the skill.

    If you (I mean, your general) are willing to take the risk to enter the melee at the end of the battle, it’s a bet. You take it, or not, depending on the overall situation or on your will to accomplish a great feat of arms. If you are killed… then your glorious death will be remembered (and perhaps more remembered than if you succeed) so it should not be frustrating …and anyway you are dead so you cannot feel frustration any more.

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    #156830
    Mike Headden
    Participant

    The ‘bad’ design bit is if the death of the general automatically loses the battle. De Foix died but won the battle, Gustavus Adolphus likewise (possibly – didn’t lose Lutzen in any event).

    Depends on the period and circumstances.

    In ancient battles the general’s death may not have lost the battle but it would usually lose his faction/ dynasty/ whatever the war. With their death the outcome barely matters.

    As time goes on and states become larger and more resilient this become less and less the case.

    “A horse, a horse! My kingdom for a horse!”

     

     

     

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