Dice's dirty secret (how fair are they?)

Boardgames
#19

Found this old thread from May and had to get involved :slight_smile: I love dice as objects (to the point that I bought one made of AMBER. Is it perfectly balanced? Absolutely not!)

I write about Divination a lot, and one of my books is on dice. The ancient Greeks had a dice oracle next to Delphi which they thought was just as important as the Oracle of Delphi.

(Also my favourite part about Delphi was that they had sleeping rooms nearby where you could talk to the gods directly in your dreams and just cut out the middle-man of the Oracle completely. Heh.)

But there’s two types of dice oracle, and one of them feels better than the other. I call them “book” and “hand”. The book version is what the Greeks used: you roll some dice and look up the number generated on a pillar which has paragraphs of text on it, and that gives you your answer. The answer for 534 has nothing to do with 535, so you have no information on what you’ll receive until you find the entry in the book (or on the pillar).

The better way is from the “hand”, where you know what you have as soon as the dice hit the table. This would apply if “2” always means the same thing, so if you see a 2 you know instantly that “love” is part of the reading. Best version is if you can work out the entire answer just from seeing the dice on the table, so you see “Love” and “War” and see that Love is stronger than War in this reading. You don’t have to go anywhere to get extra information before you have at least a summary.

So back to boardgames: that roll and instant hit of success or failure has so much more emotional impact when it comes from something physical that you generated with your hand. You were involved, and the answer was quick. Totally different to a screen telling you some numbers, or you holding numbers in your head until you can look up what their meaning is.

All of which is to say
a) yay dice, I’ll take non-perfect rolling over apps
b) feeling like you accomplished something when you roll the dice, and there being a slight ritual to it, is a feeling that’s been around for literally millennia not even just centuries
c) if you want to inject more immediacy or excitment into your game, have the dice results mean something from the instant they stop rolling, not later when you look it up in a book.

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#20

I think dice pools are good for this: you see that you got a bunch of stabby things and not many monster-clawy things, and that feels good even before you start counting.

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#21

I do get it about the ritual, but OTOH I’ve spent 18 months with roll20 just spitting random numbers at me, and I have to admit I’m also quite happy with not having to scrabble around on the floor when they fall out of the computer.

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#22

Welcome to the site!

There is a convenience offset for virtual dice.

But nothing else in gaming feels quite like shaking a handful of dice and just letting them roll (and then chasing after them…)

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#23

I often have a consistent policy: if I lost badly in a random game (doesn’t have to involved dice), then it’s random. But if I win, then it’s a game of skillzzz

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#24

I don’t disagree with that, but (and you may feel differently) I’m coming increasingly to feel that if my random-number-producer gives bad randomness for the sake of being satisfying to use, that’s a bit like playing 18xx with chocolate coins and eating them now and then.

I appreciate I’m kind of just repeating myself here.

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#25

I think I recall a Knizia quote that stated a good game design is one in which if you lose, you think it was due to bad luck but If you win, you think it was due to skill.

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#26

If they’re dice for a specific game, everyone uses them and any bias becomes part of the game.

If they’re general purpose dice, well, if I genuinely believed that a particular set of 3d6 rolled noticeably other than fair, I wouldn’t use them. Which doesn’t stop me doing the occasional luck ritual, but only because I don’t believe it’ll work.

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#27

I think the trouble with that (although it’s clearly an improvement on American-style everyone bringing their own dice) is that “part of the game” can favour one strategy over another; this is unfair on the player who gets stuffed because a game component was defective.

Likewise, re thinking dice are bogus - but human perception of randomness being what it is, how could I tell in any but the most egregious cases?

(As a teenage boy, and therefore less inclined to be sporting, I was forbidden to use the “famous red dice” after rolling a PPC hit (on an 11) to the head and an LRM hit (on a 12, rolling 12 for number of missiles, first group hit… the head). But those dice had done it before and they were pretty obviously bogus.)

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#28

I think perhaps that my reasons for not being particularly concerned about this are that I’ve never had dice that seemed to have a bias to them (to my unscientific perception or to anyone else’s accusation), and therefore a small bias probably doesn’t do any harm.

On the boardgame side, I tend to play a lot of games a little each, and most of them come with their own dice (custom or not).

On the RPG side I mostly play GURPS, and I mostly use the same set of 3d6 I’ve been using for a while (and occasionally the dice ring I have as my user picture). But I’ve not had a set that seemed to roll particularly well or badly except the explicitly loaded dice I picked up at a GenCon many years ago, light wood with a heavy metal plug in one face, utterly blatant which I presume was the point.

If nobody at the table is feeling unhappy about the randomness, then it’s probably within tolerances. But then I’m very much not a competitive gamer.

Of course one could replace dice with cards, such that one could guarantee that in a long enough term all possible numbers will come up with the right frequency…

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#29

I used to play competitive WarMachine which uses a 2d6-based system (with options to buy additional dice through various mechanics). Gives a relatively stable Gaussian probability curve (ie: you are about 50% likely to roll a 7-or-less, about 90% of rolling a 4-or-less, and so).

If an opponent has a DEF of 12 and you have a MAT of 6, you need to roll a 6 or more to hit (tying or surprising their DEF value). If they have ARM20 and you have POW10, you need to roll an 11 to inflict a wound… unlikely, but not impossible, but you can add a die through Charging, another die if you have Focus to spend, and so on…

Right. All that to say that there was a famous (in the WarMachine community) worlds event where a player needed to roll a 4 or more and had 3 chances to do so. 90% chance three times is mathematically almost 100%… but of course he lost the roll, which meant he lost the game, which meant his team (Australia) lost the tournament.

James has since left WarMachine… and I think he’s come back to it recently (casually). Australia did end up winning the following year, but yeah. Probabilities.

I once played a guy who had sets of dice for specific purposes, all casino cut: yellow for Courage checks (where you want to roll low), red for hit dice (high rolls) and blue for damage (again, high rolls). It bothered me a little, but not enough that it stopped me from stomping him at the tournament.

I tend to get bothered more by systems that hinge on single die rolls, since “buckets of dice” isn’t really an accurate mathematical system. Infinity uses multiple d20s (the worst of all systems), but since I don’t play competitively I can laugh off the ridiculous results more easily. SW Legion uses custom d8s for attacks and custom d6s for defense, and the game often swings very, very heavily on those defense dice. But, again, not attempting to be a balanced system and so it’s more forgivable.

Anyway. Yeah. Gaussian curves are fun.

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#30

I built a system many years ago based on an inverse normal table, to get fine resolution only where it matters at the ends of the scale. Stripped of the fluff, you’d have a standard deviation which defined a table row, then roll a d20. On a 2-19, you’d get the appropriate value (2 = 7.5%, 3 = 12.5%, …, 19 = 92.5%, and then map that to get the appropriate number of standard deviations.) If you got a 20, you’d go to the second table, which mapped 1…19 into the span of 95%≤n<100%, and 20 would go on to the third table. (Similarly if you roll a 1 on the first die, only downwards.) This gets you a resolution of 1/8000 at the ends of the range, but 90% of things can be resolved with a single roll. Of course, it does need a table lookup every time.

This can be summarised as equivalent to “add together an infinite number of infinitely small dice”, giving the true Gaussian curve which adding up finite numbers of dice can only approximate.

In terms of game design I think the right number of die rolls is usually either “none” or “lots”: systems with just a few rolls can be vulnerable to a few unusual random events seeming to drive the course of the game.

Perception may matter more than actuality here. Someone told me that there’s an MMO or similar which quotes you chances of things happening, but lies, because if people are told “95%” they think “that means it will happen” and complain when it doesn’t, even if that event is exactly one time in 20.

Then you get into economics (I really do like economics): requiring small children travelling on aircraft to have their own seats and belts rather than sitting on their parents’ laps increases the total number of children injured. Because it raises the cost of flying with children, so some long-distance trips get made by car instead, and an N-mile road trip is more likely to injure them than an N-mile air trip even if they are unsecured in the aircraft.

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#31

Yes, but for any given roll, it doesn’t matter if you roll a single die or multiple dice. Saying you have to roll 4 or higher on 2d6 is exactly the same as saying you have to roll 2 or higher on a d12.

Where the result distribution curves really matter is how the system is tailored to them, especially modifiers. Using the 2d6 vs. d12 example, shifting the numbers by 2 (6 or higher on 2d6, 4 or higher on d12) shifts the odds differently in each case.

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#32

The idea of having a “+1” on 3d6 makes my statistician’s soul shudder.

#33

And yet, you should be dealing with that all the time with GURPS.

What’s nice about it is that if you’re in the middle of the curve (it could go either way), then a +/-1 means a lot. If you are at the edges (where its pretty much a done deal either way), a +/-1 doesn’t mean a lot and you need a significant modifier to change your odds significantly. To me, this modeling is the true benefit of using 3d6 over d20 (for example).

#34

Perception may matter more than actuality here. Someone told me that there’s an MMO or similar which quotes you chances of things happening, but lies, because if people are told “95%” they think “that means it will happen” and complain when it doesn’t, even if that event is exactly one time in 20.

You may be thinking of X-com here - the apparently obvious percentages caused great frustration in play testing (‘How could a 90% shot miss??’).

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#35

I have this kind of conversation about people being terrible at probabilities with folks about weather forecasting quite frequently. Usually I start with something along the lines of “If it rains on any given day that there was a 20% chance of rain, people get mad at the weather forecast for having been wrong. But if it rains one out of every five times there was a 20% chance of rain, the reality is that particular weather forecast has been 100% accurate.” Some people understand what I’m saying right away and have a sort of lightbulb moment. Some don’t get it no matter how I try to walk them through it.

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#36

no, that’s you keeping them in a jar all these years.

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#37

My understanding of how these percentages are calculated is that the weather service looks at the conditions and compares it to past days with those same conditions. If it rained on 20% of the past days, then the forecast will be 20% chance of rain. (This can also be applied on an hourly basis.)

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#38

There are multiple meanings of possibilities of precipitation. One means “maybe it will rain , maybe it won’t”. The other is “it will rain, but only over x% of the forecast area “. They get combined , too.

The us NWS publish a thing called the “area forecast discussion “ which is a human meteorologist discussing the forecast. It explains why the forecast is what it is , what interactions are driving the weather, and what the uncertainty is. Recommended reading, if you cate about the weather. Google “AFD . “

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