"Why use D10 instead of 2d6?" Topic

Why do some games use one as opposed to the other?

Played a game that uses D10 today. The results seemed to swing wildly. That wouldn't happen as much with 2D6.

The bell curve changes. 2D6 is a 1 in 36 chance of any number coming up. A D10 is 1 in 10 chance.

Depends on what the game designer is after, more events with an equal chance of happening or a range events with a bell curve.

2d6 has a 1 in 36 chance of 2 or 12 coming up but a much higher chance of 7 coming up. There is a 1 in 6 chance of 7 coming up.

D10 doesn't have a bell curve at all.

The chances are all equal so it is a straight line.

I prefer the 2d6 method myself.

However for games with a d10 mechanism, like Fire and Fury, we just roll 2d10 and take the average.

It is not the dice that swing wildly, it is the results chart. If you have a roughy 90% chance for success and 10% for failure, rolling a 1-9 for success on D10 is about the same as rolling 2-10 for success on 2D6. It is how the game designer applies the dice results that may or may not make it seem to swing wildly. If they use the roll as a simple multiplier (e.g. number of hit points lost) then yes, the bell curve of a 2D6 will seem less wild because most rolls will fall between 5 and 9.

The "problem" with 2D6 is with die roll modifiers (DRM). If aiming gives a DRM of +1 and your base chance to hit is 12, that modifier does not represent much of a change (about 6%). But if your base chance to hit is an 8, that same DRM represents about a 17% increase. That is why some designers do not like a bell curve for some mechanics, like shooting or melee.

What Dale Hurtt said.

Plus I like the inherent uncertainty of a D10. War is not fair, and does not play by the bell curve. Small things (which we could never measure or build into a game without overbearing complexity that would doom any sense of a game) make a big difference.

I'm sure that Robert Burns saying that the best laid plans of mice and men "gang aft aleigh" was based on his playing of Fire and Fury when he rolled a 1 and his opponent rolled a 10!

The results seemed to swing wildly.

Results will swing wildly because each number has a 10% of coming up.

Many times I have taken advantage of rules using such linear odds, with people saying you only have a "20%" chance of success. I reply, I have the same chance of rolling any number so why not attack?

d20 is even wilder.

It is also a lot easier to roll 10 d10s instead of 10 pair of d6s.

As a player, and when i have though of designing my own rules, i find 1d10 more intuitive and easy to grasp the chances, as it allows you to think of %

Dale Hurt nails it. Modifiers for 2d6 stack in a bad and non-linear way.

Dice 6 are everywhere even at $1 USD stores in the whole planet.

"Modifiers for 2d6 stack in a bad and non-linear way."

It's not necessarily bad. It depends on what you want.

For example, let's say that you want to show that the Fusiliers are consistently better than the Musketeers… but there should be some remote chance of an upset. With a bell curve, modified, you can achieve things like that.

For instance, the little 45mm AT gun shooting at the Tiger tank. It has the tiniest chance of hurting or killing the Tiger with a lucky shot in some improbable place… but you want that chance to be there.

That's when you want non-linear probabilities.

War is not fair, and does not play by the bell curve.

I'd be very very surprised if measured results of any individual actions followed anything other than a bell curve. Perhaps not a Normal one, but nonetheless some sort of bell distribution (with higher kurtosis in the terminology).

The alternative is that extreme things happen all the time. That may sound right perhaps – until your knights frontally steam-roll pikemen one time in 10 because "war is not fair". In fact the random element in many combats is close to zero (and some wargames even go that far and more or less remove the random element).

I'd want to see some evidence that warfare follows wildly non-normal distributions, not just a wild guess based on intuition.

Small things (which we could never measure or build into a game without overbearing complexity that would doom any sense of a game) make a big difference.

Yes, but lots of small things tend to cancel. Hence a bell distribution is the usual.

It is,I would suggest, an incorrect inference to get from "small things can make a big difference" to "small things usually make a big difference".

Warfare just isn't that random. God is on the side of the big battalions precisely because the random element is overwhelmed by strength. If war was non-bell curved, the weaker side would win a lot more.

The issue isn't the bell curve. The issue is the effect modifiers have on a bell curve. If you have a game that doesn't have any modifiers, it's not an issue. If you have a game that stacks two or three modifier, they don't stack in a linear fashion and each successive plus is worth much more than the previous one.

chriskrum says
The issue isn't the bell curve. The issue is the effect modifiers have on a bell curve. If you have a game that doesn't have any modifiers, it's not an issue. If you have a game that stacks two or three modifier, they don't stack in a linear fashion and each successive plus is worth much more than the previous one.
AND HE IS CORRECT ,,, but modifiers are not always additive and linear. Defending on a hill or behind a wall are each plus 1..but together I'd believe that would be a functional plus 3. Which using a 2D6 system allows for leaving each a plus 1 but the effects are -- intentionally -- non-linear.

Exactly Nashville. The original question is why some games use one instead of the other -- not which is better (which I think is what some people are reading here). Unmodified, both systems let you choose the odds of success and decide what target number needs to be rolled to achieve it. Where they differ is in how modifiers effect them -- that's where a game designer decides what he/she's modeling and what system to use. The answer to the OP's question is because the two systems are functionally different.'

2d10, however, now that's the ticket.

The distribution of outcomes in military operations are generally logarithmic. A bell curve is very poor model of this, particularly with stacked modifiers. A linear result space is better, but you need the effect of the modifiers to decline.

Really, the best solution is a crt as it is a simple way to map logarithmic functions without the aid of a calculator.

Mark Plant,

Well said, and from a larger perspective, I agree with your premise. I wasn't clear that I was thinking about the more tactical fight, not the strategic level. We would probably agree that war on the front line is chaos, with small things making a big difference, just not the difference.

Mike

The other reason to use d10s over 2d6 is that an action might consist of a bunch of independent tests. This is also known as a "bucket o' dice" system.

To make "bucket o' dice" work with 2d6 requires either time or an investment in a bunch of Koplow's double dice.

D10 D20 cool. Everyone at home has D6 in Monopoly, Risk, Parcheesi and many other games. Bucket of D6 is cheap and easy to get.

This is a really interesting subject. As Martin says outcomes can be logarithmic. Which probability distribution that fits best depends on exactly which outcome that we want to approach. For instance total fatalities on all sides of a conflict. Fatalities per battle, over several battles, have been shown to be log-normal or power-law distributed for many conflicts (or parts of conflicts). Power-law meaning that events with few deaths, and events with heavy casualties are more likely than what would be expected if they were bell curve distributed. If a contemporary civil war has an average of 8 deaths per engagement the standard deviation might be as high as 20 due to a few extremely heavy engagements, and a majority of clashes with one fatality.

I haven't seen any data of fatality distributions within a particular battle. I do suspect that if figuring out a way to separate engagements within a battle from eachother, those would probably also be log-normal or power-law distributed.

Who wins a battle (or by how great margin a battle is won) is another type of outcome that may or may not be analogous to the distribution of fatalities.

I have an old post about how I try to reflect log-normal or power-law outcomes within battles by setting up thresholds for when units take casualties. I use the term "squad" but note that the type of mechanism is intended for ancient and medieval engagements. link

First, games should provide the gamer with enjoyment and if a gamer gets enjoyment from various types of dice he should play those rules which use the dice in the manner which satisfies him.

After that, regardless of their facets, color or whatever, dice are tools which enable the rules to reflect the percentage chance for any outcome, historical or not, desired by the designer. Given sufficient rolls, any sided die or multiples of dice can reach any percentage desired.

And that's the thing! The designer owes the gamer a percentage which his research reasonably concludes reflects that which historically occurred. And before we get involved with arguments regarding what reasonably occurred my criteria is method not necessarily numbers (such a percentage of hits at a distance certain) which based on sources tend to vary.

Thus for me the question of dice is a question of efficiency or how much effort it takes to achieve an outcome. For me, most dice, including d6s, are inefficient in arriving at an outcome.

The most efficient are d10s rolled in opposition with the differential providing the result. The differential in two modified d10s rolled in opposition, one by each player, with a maxim of 10 and a minimum of 1 quickly provides the mythical Bell Curve for 100 possible outcomes. Gamers don't have to think about the number or color of dice to be rolled or about the color or the number of saving dice. Additionally, as the non-phasing gamer must also roll he remains involved in the process when not moving and holds his fate in his hands.

Bob Coggins

Less dice to roll off the table.

chriskrum & Nashville address the OP's query most directly. If you want to explore the difference between linear and bell curve randomizers, play BattleTech rolling a d12 to-hit rather than 2d6. (In an optimal BattleTech circumstance, a roll of 4+ is needed to hit with 2d6.) What you'll see are long-ranged weapons, penalized with high modifiers of about 5 to 7 penalties, under the regular rules become considerably more dangerous using the d12 variant. Those penalties allow units to hit each other at long range with 17% chances of success rather than 8% chances under the standard rules. It changes the game.

D10 opposed. Who wins the result of the difference? The phasing player?

vonLoudon,

The highest number. In its simplest form, if you roll a modified "6" and I a modified "5" I would take one casualty. A 6 vs a 2 would be 4 casualties, etc. but governed by other rules, depending on the game.

Bob Coggins

Everyone at home has D6 in Monopoly, Risk, Parcheesi and many other games. Bucket of D6 is cheap and easy to get.

This is still considered a valid argument?

Anyone who is in gaming has access to all sorts of different dice. A D10, D8, D20, … is not really considered a rare object anymore, is it?

I would say it's easier to obtain different types of dice than it is to obtain wargaming figures.

As for logarithmic distributions, there are some dice with the numbers 2, 4, 8, 16 etc… (powers of 2). Probably something can be done with these to model a logarithmic outcome with the roll of a single die ….

There seems to be four questions here:

1. Which dice provide the range of outcomes desired.
2. The kind of dice different gamers like.
3. Which are the easiest to read and understand in play.
4. What range of outcomes and odds of those outcomes are
found in the historical and military situations
portrayed by the wargame.

If the die rolls are supposed to mimic something like the actual/historical chances of different outcomes, that would reverse the order in which each question has to be addressed.

Given sufficient rolls any sided dice can deliver the desired outcomes.

D6s appear to be the most prevelent used by various rules and because of the number and type of outcomes necessary, perhaps the least efficient in delivering an outcome.

Modified opposed d10s require one roll by each player to deliver 100 possible outcomes and when the maximum of 10 and minimum of 1 is imposed a Bell curve which allows for most results to be in the norm but with deviations from the norm.

The range of outcomes and the odds reflecting those outcomes is based on the research of the designer. It is here that it is important to understand that numbers are going to vary depending on the situation and source and because of this method is what is important.

If the designer's interpretation of historical probability is not based on research to determine percentages buttressed by a method then the only thing die rolls can reflect is the designer's unsupported guesses based on his prejudices or perhaps more likely the numbers and percentages regurgitated from previous rules sets.

Bob Coggins

I am suprised that no one has mentioned the outcome provided by the dice roll. Except martin in mentioning the use of a CRT. It doesn't really seem to matter what the number's rolled are provided the designer has taken into account the probability of that number coming up against the probability of an event occurring.

In other words if the designer decides that there is a low probability of an event then he ascribes a low probability dice outcome to having it occur. Essentially a CRT through the back door. It tends to be my preferred system (result of a youth spent playing SPI games I suppose) as it gives me an easy way to tinker with the results in the play test stage of my home brew games.

Really there is no real difference between the two sets of dice. It is just that the numbers become partitioned differently. If you like the 2D6 partitioning, then please use them. But you are limited as to how things can come out and there is difficulty in attaching modifiers to a standard result – that is a result where you think you know how it should come out most of the time. I think that this effect is hard to "understand" on the fly by players, so a mystery remains and players are happy to be ruled by "chance".

Anything you do with 2D6, you can do with 2D10 (e.g. a singles and a tens die). It doesn't work very good going the other way, it is hard to get 2D6 die roll and results table mimic a 2D10 roll.

Here is the breakdown of what you actually have with a 2D6 die roll. Tables don't show up well here in these posts so the below will look a little funny.

Sum of PIPs on the 2 die //// % of time its rolled
2 /// 3%
3 /// 6%
4 /// 8%
5 /// 11%
6 /// 14%
7 /// 17%
8 /// 14%
9 /// 11%
10 /// 8%
11 /// 6%
12 /// 3%

Now die results are used in several ways. One way is to get a specific number rolled, and the chart above gives you the odds of getting that roll. So if you want to test for a single specific event occuring (say it happens 14% of the time) then with 2D6, you say that you have to roll of sum of "6". With 2d10, you have to roll a sum of less the 14%.

A more common way to use the 2D6 is to say that you have to "beat" some target number. (sometimes its be less than or equal or beat,,, here we'll just illustrate "beat" a number).

This leads to a similar set of numbers, which is derived from the chart above. % chances of "beating" a number.

number of pips to be beat /// % chance of success

2 /// 100%
3 /// 91%
4 /// 83%
5 /// 72%
6 /// 58%
7 /// 41%
8 /// 28%
9 /// 16%
10 /// 8%
11 /// 3%
12 /// 0%

So if you lose your D6 die and want to change to 2D10 die, then all you do is look at what the 2D6 target to beat is, go to the above table, take you 2D6 target from the left column and find the % roll needed to beat on the 2D10 roll.

Now a problem with gaming with the 2D6 die is that the intervals between the sum of the number of pips, is not constant when you go up (or down) in the "to beat" number. Since we often game by adding modifiers of +1 or +2 to the "to beat" number, the additional modifiers do not EACH have the same effect because the % change in the odds is different. This leads (as you suspected) to another table, the increase in odds for including an additional +1 modifier on the "to hit" number.

original "to beat" number /// increase in odds for increasing the "to beat" number by one pip

2 /// 9% better
3 /// 8% better
4 /// 9% better
5 /// 4% better
6 /// 7% better
7 /// 13% better
8 /// 12% better
9 /// 8% better
10 /// 5% better

So depending upon where the game designer set his typical result, it may be more powerful to take advantage of a die roll modifier or less important. If they set it a "7" then there is a "magnifying" or reinforcing synergism for hunting up more +1 modifiers to use. I think this occurs to many gamers as a "magic", but it is just simple math and analysis. You can do the same thing with 2D10 die by adding a small % bonus for applying mulitple modifiers.

An advantage of the 2D10 die, is that you can easily transfer what ever you think is, in terms of percent advantage, to the die roll results. With 2D6, I am sure most designers are either blind to these effects or following a tradition of "what has felt good and worked in the past" in the design.

As long as there are no modifiers you can easily switch between 1d10 and 2d6 (or any other dice-combinations). When there are modifiers 2d6 will just get weird and it is very unlikely that they will match any target distribution. Just don't have modifiers and you can make a good CRT that will make sense of any combination of dice.

Also since someone resurrected this thread I'd like to add that Biddle's Military Power book has lots of little graphs showing the effects of various parameters on battles of the last 100 years and the shape of the graphs vary a lot and are almost always a lot more complex than some simple logarithm or such thing will give you, and often there is a maximum to be reached somewhere along the range where the parameter has an optimal value, whereas in typical wargame systems we always assume that more is better and that if you keep adding something it should improve your chances (bucket of dice systems are particularly annoyingly bad).

Part of the problem with choosing dice, has to do with what results are considered average, and how important are your modifiers. If, for example, you want firing to cause on average 6 or 7 hits, you could use a d10, with 1 inflicting 1 hit and 10 inflicting 10 hits. if you roll a lot of combats, the die will average out in the long run, but will swing widely on each roll. Using 2d6, with a 2 doing 2 hits and a 12 doing 12 hits, the swings are less and your average will be more to 6 or 7. More dice (bell curve) lead to more predictable results. Add to that, the size of each die (d6 vs. d10) also influences the value of modifiers. A +4 modifier is huge using a d6, but insignificant using d100. Likewise, when using "opposed" die rolls, the larger the die, the less important the modifiers. Try playing Fire and Fury using a d6 or d8 or 2d6 for melee and see what effect that has on the melee. The closer the possible roll is to the average, the more important modifiers become. The larger the die, and the more linear the result, the modifiers become less important. I guess my point is, the fewer die rolls that the game contains, if you feel die roll modifiers are important, and the closer you want each roll to be to the norm, use multiple dice to achieve a bell curve. The more times you are rolling for results, and you believe that the wide range of results are acceptable, use a single die. You could also vary the number of dice based on situation, ie in F&F use 1d10 for firing, use 2d6 for melee.

If you have to roll for multiple shots, you can roll all of the D10's together. If you are using 2D6, you have to roll for each result one at a time.