“If Only My Dice Were on Average!”

WARNING: STOP READING right now if you do not believe that the average D6 roll result is 3.5!

Dice

Your Dice Are on Average

Put your hand on your heart and answer the following questions: How often have you blamed your dice for a bad turn or a lost game? How often have you groaned loudly about your dice being below or far below average? Once? Twice? During lots or even every game?

During the years I’ve managed to teach myself not to say it loudly (too often). – But well, I’m still getting angry with my dice when they fail miserably although I’d have had a great turn not even needing average dice rolls! Everything had been planned safely – but #$?§%*!

Want some reasons why you shouldn’t cry out loudly (and shouldn’t even think this way)? Here you are:

  1. Your dice are on average. Period. (You’ve probably just forgotten about the 6, 6 to hit or 6, 5, 4 damage roll a turn ago.)
  2. It’s simply bad behaviour: You’re telling your opponent that he didn’t win the game because of his superior strategy or tactics … but dice only.
  3. You’re not learning anything: With a very high probability you’ve lost your turn or game for very different reasons than dice rolls. Try to find your real mistakes and don’t blame the dice (there are very, very few exceptions to this).

Why We Don’t Want “Perfect Averages”

That said, I’d like to get to the more important part of this post finally: We really don’t want to have averages on each and every dice roll! It would be a shame to use dice with a 3.5 on each side!

Have a look at the photo above: 8 dice summing up to 28 perfectly. Lovely! This is what we want, don’t we? But well, I’m mostly rolling attack, damage, and grid dice simultaneously: green to hit and red for damage. And I’ve probably failed to hit with the Uhlans under Hand of Fate. Really annoying.

So why wouldn’t I want perfect averages for each part of my roll? It’s very simple: We’re playing a wargame here, aren’t we? We’re not playing chess or anything else. And if you want to play and to some degree simulate war, you simply have to count in luck. You have to count in emotions, courage, excesses, shock and awe.

You don’t believe me? Here’s Carl von Clausewitz’s famous trinity then. The trinity of forces that drive the course of real-world war in von Clausewitz’s view:

  1. Violent emotion
  2. The interplay of chance and probability
  3. Political calculations driven by reason

When you’re reading Clausewitz’s Vom Kriege, you won’t find one chapter where he’s not talking about general, tactical, or even personal chances and probabilities. One of his main statements: You won’t see too many causalities during a war – if any. Randomness is an integral part of war – and life!

You have to take risks and you still have to stay flexible. … Oh, and don’t blame the dice!

About Kriegsspiele

Kriegsspiele (wargames) talks about tabletop wargaming: Warmachine and Hordes in particular; http://Kriegsspiele.me

16 comments

  1. I disagree, some dice have imperfections or flaws in their design which predisposes them to rolling some numbers rather than others. Since I have departed from rounded edged dice towards square edge dice my dice rolling has – **actually** been about average – or rather what I would expect.

    • Well, there might be some dice with imperfections or flaws, but in general I do believe that even the cheapest standard D6 dice roll a 3.5 on average. And if not: ones troopers are just more excessive or shocked. ;)

  2. Pedant

    ROLL ROLL ROLL

  3. Pingback: Smashdown Saturday Part 1 – 25 points vs Cygnar | Blood Shines Gold And All Coin Spends.

  4. 1. Your dice are on average.
    True… Rolling 2×1 when you need 2 or more on each dice is as much part of “the average” as rolling 2×6 when you need less than 6. Just because the dice are average, doesn’t mean you can’t have bad results caused by the dice. Assuming dice can’t be responsible is assuming they aren’t random. They are random. Bad luck can happen.

    (You’ve probably just forgotten about the 6, 6 to hit or 6, 5, 4 damage role a turn ago.)
    True. It’s called confirmation bias. You remember only that which confirms your theory. It’s a subjective observation. Even so, just because the dice never give you the results you need, doesn’t mean they aren’t average. It just means they’re not giving you what you need.

    2. It’s simply bad behaviour: You’re telling your opponent that he didn’t win the game because of his superior strategy or tactics … but dice only.

    If there’s an element of chance in the game, then it is possible that chance determines the winner, regardless of tactics. A good strategy is to minimize the chance for failure, but if you have nothing to loose, then you can take a risk for greater glory. Dice can decide the outcome of a game. Gosh.. I remember one game where I was almost tabled by round 2 in a game of Warhammer. In my 2 magic phases, I failed every spell but 1 bound spell.. aside from rolling low on winds of magic. In his 2 magic phases he scored well on winds of magic, every spell succeeded, every dispell failed (even when I was tossing in more dice per spell). Is it “superior tactics”?
    How about running a killer unit into chaff, loosing the battle, failing a leadership test, fleeing and being caught in such a manner that his chaff is positioned superbly for the next round? I fail to see the brilliance of my opponent’s tactics.
    It is possible to win the game by dice only. Even if you work out good strategies, in some games you can’t escape the dice factor and it can determine the outcome.

    Never the less… It is bad behavior. A flaw in my character I need to work on myself. But to assume dice can’t be a determining factor in the game is to eliminate that they, in fact, dice.

    3. You’re not learning anything: With a very high probability you’ve lost your turn or game for very different reasons than dice roles.

    I would drop the part of “very high probability” when the subject of the topic is chance. I don’t see any sufficiently founded statistical research to indicate this statement to be correct. :)

    Loosing a battle can be caused by a multitude of reasons. It could be dice, it could be a bad call on your end, it could be clever call on your opponent’s end. When you let emotions take the upper hand, good or bad, it does stop one from analysing a situation objectively. I believe objective analysis is the best teacher. Anger proved a poor teacher for me in the past.. but frustration did prove a good motivator to increase my effort in objective analysis. Contradictory? Not at all.

    When people claim their dice are not “on average”, I believe a smarter analysis would be “what is average?” or “what can you expect?”. A fault I made a lot in the past is to assume the average outcome was the most likely outcome. It’s like thinking that 3.5 as average of your dice will make 3 or 4 more likely as outcome. People work out averages in their tactics, and think that’s the “probable outcome”. When rolling many dice, a binomial distribution will show you that is true in a sense. But it’s a narrow view on the whole spectrum of outcomes. Averages don’t tell you your odds to fail. Averages don’t tell you your odds to succeed. I often made tactics based on averages, and often failed. It wasn’t until I investigated the probabilities more thoroughly that I learned that the chance to get your average is actually quite low and unreliable in many situations. By investigating probability distributions I learned than many of my tactics which were built on “expecting average outcomes” had a low chance of success.

    This changed my perception thoroughly. It helped me accept that part of the error was, indeed, my tactic. But it didn’t improve my sportsmanship in the game. And it didn’t help me accept that.. well.. even if you have a 90% chance to win with a given trick, it can still fail. And in a game of 6 turns, that 90% chance to win trick still has a 47% chance to fail at least once. That means that only 1 game on two is going to work flawlessly but 1 game out of two is likely to have failures and perhaps more than 1 of them.

    So I agree with a few points you make here, but I feel you take a contradictory stance on the role of dice in the game. You start by negating their role in the game, attributing wins to tactics and insight. Then you discuss how randomness enhances the game and improves the experience.

    Dice can loose you the game. Dice can win you the game. That’s the truth of it. But it isn’t the only factor. A good player should focus on minimizing his chance to loose. But to be a good sport in the game… You have to accept that no matter how brilliant or careful your strategy is, it may still all be trashed by the roll of a few dice. Rather than ignoring the factor of dice, I think it’s more important to learn to accept the factor of the dice.

    • Great comment, thanks!

      “If there’s an element of chance in the game, then it is possible that chance determines the winner, regardless of tactics. A good strategy is to minimize the chance for failure, but if you have nothing to loose, then you can take a risk for greater glory. Dice can decide the outcome of a game. … It is possible to win the game by dice only. Even if you work out good strategies, in some games you can’t escape the dice factor and it can determine the outcome.”

      Absolutely. I totally share your assessments. This sums it up pretty nicely:

      “Dice can loose you the game. Dice can win you the game. That’s the truth of it. But it isn’t the only factor. … So I agree with a few points you make here, but I feel you take a contradictory stance on the role of dice in the game. You start by negating their role in the game, attributing wins to tactics and insight. Then you discuss how randomness enhances the game and improves the experience.”

      The two points I’d like to make (and hopefully made): 1. Your dice are on average and indeed, a lot of players overstate the dice factor (by far). It’s just one of a lot of factors determining the outcome of a game – like: knowledge (rules, units), tactics (list building), operations on the tabletop (placements, movements, synergies), the overall execution of your strategy and tactics, your and your opponent’s overall mood etc. pp. Dice are just another factor you’ve got to count in. Nothing more, nothing less. 2. Some other players would probably prefer to play chess or any other game without elements of chance. In my opinion a wargame has to simulate emotions, courage, excesses, shock and awe. It needs to represent these factors (to some degree). Otherwise I wouldn’t call it a wargame. It’s all about balance: and Warmachine and Hordes does it right in my opinion.

      “I would drop the part of ‘very high probability’ when the subject of the topic is chance. I don’t see any sufficiently founded statistical research to indicate this statement to be correct. :)”

      Interesting point. Perhaps someone should start some substantiated work in this field – if it really hasn’t been done already. :)

  5. Reblogged this on Tangible's Day Off and commented:
    This is such a cool post. Very interesting and fun read.

  6. Completely agree. With the number of dice the average gamer throws in a game, the quality of the individual dice makes very little difference. However it is fairly amusing that everyone assumes square edged casino dice are the most random, which is not normally true, because they are designed to be thrown and bounced off a surface rather than rolled.
    For those truly concerned about dice randomness, backgammon dice are the way to go. :-)

    • Personally, I use casino dice because I love how they look like and how they feel like in my hand: they are big and sharp, just like dice should be. ;) – Oh, and I love that everybody can easily recognise the result, even on photos/videos.

  7. “Because it looks good” normally the best reason to use anything! I heartily approve! Thinking about it, I really must obtain some backgammon dice to match my Retribution army…

    • Absolutely! And it’s so sad that Khador can play Scrapjack with Old Witch only: Scrapjack is the best looking Khador jack in my opinion (and has the coolest rules as well – with OW at least thanks to Avatar of Slaughter).

  8. Pingback: The Flying Heavy Gambit: Superiority for the Win! | Kriegsspiele

What do you think?

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 27 other followers

%d bloggers like this: