A Very Interesting Email: Part 2

Here's the second half of that email that Ryjak sent me, and my responses. This one's going to be quite interesting, as I compare the result ranges of D6 and D10 dice rolled in series, and why D10 isn't as much of a better choice for a wargame as people tend to think it is.

Ryjak said:

4) Rolling Low vs. Rolling High/Low

I really liked Eriochrome’s take on the game’s rolling mechanics. It had also never occurred to me my dice were biased. BTW, I did a lot of research on this. It is not well known that Chessex dice roll twice as many ones as sixes. What has been determined is that any given Chessex dice, and any dice sharing the same manufacturing technique, will have a bias to rolling certain numbers and not other numbers, and each dice has its own unique bias. For example, a Chessex d6 could have a preference for 6 (say 25% instead of 16.6%) and an aversion to 3 (10%) while the 1 still has a 16.6% chance of turning up.

For game simplicity, I like the idea of having one method across the board, no matter what you’re doing. With the comparison mechanic, I think the best way to go is below, instead of the current chart. With this system, the lower you roll, the better. It’s like The Price Is Right; spin the wheel, but you lose if you go over $1.00.Take your base stat, add a d6, and try to roll under the comparison stat.
For shooting, take a Ballistic Skill of 5 shooting at an Evasion of 7 with a terrain modifier of +2. To hit, you need 5+X=7+2, or 9-5=X… so 4+ to hit. Since people can’t do algebra in their head, the Rules would be written in this fashion.

Determine the Target Stat (Evasion) and subtract the Base Stat (Balistic Skill) to determine what you need to roll for the Pass Test Roll (To Hit).

SandWyrm:

That would work (it's an inversion of the Flames armor penetration roll), but would players like it? I get enough scratched heads with the roll-low toughness test as it is. :)

Besides which, the comparative system works well already. Plus, players are used to something similar in 40K for strength/toughness tests. The only thing they have to remember is that 1 doesn't always fail, and there aren't 2 levels of pass-on-a-six on that chart. But it's an easy transition to make. Certainly easier than a completely new (to them) mechanic.

And... I haven't worked it out, but I think that doing it your way would reduce our available stat range compared to a comparative system. Or at least require our stats to go above 10 for common units. That's not ideal I think. Simple system, but a more complicated and unfamiliar chart.

While the rules could be written to apply modifiers to the Base Stat and Target Stat, it might be simpler to write all the rules as modifiers to the Pass Test Roll. The same could be applied to your awesome Skill Tests (Pass One Rolls, Pass All Rolls) as well.

I only see one down side to this system, though. Because it is so easy for a player to bring weighted dice (intentionally or unintentionally) the game system needs to have an equal number of rolls requiring high values and low values to succeed. So while I prefer the elegance of having one across-board system, any competitive game system must mix it up.

So, since the most basic game mechanic is Rolling to Hit, then Rolling Armor Penetration, it would be best to make one of these a Rolling N+ mechanic, and the other a Rolling N- mechanic.

This was one of the reasons for going with roll-low for toughness. Switch up the needed roll to foil those with loaded dice. Roll high for To-Hit, roll low for killing after they fail their saves. Most folks don't seem to care so much about that though. We would have to explicitly explain the reasons for it in the rules, and even then... well. We're fighting folks's natural inclinations.

5) Using d6 Dice

I understand all the reasons for using a d6 system: it’s the most commonly used die and it’s the mostly widely available die. However, with some of the recent changes in gaming, d10s are becoming more widely available, and companies/websites like AwesomeDice and Versivus are selling 10d10 sets… mostly for Vampire: The Masquerade. Or go to Shapeways, where people with 3D printers sell their designs and products, and order some beautiful 10d10 Steampunk dice. As 3D Printing takes off, it will be easier to get d10 dice… or any type of die.

I won't dispute that D10's are becoming more popular.

But here's the reality:

1) Most 40K players don't play anything other than GW games.
2) Most 40K players (myself included) have gobs of D6 dice. But few of other types.
3) You can't buy large packs of D10 dice at most game stores. Just expensive singles.

There was a time when Fantasy used D4, D8, & D10 in addition to D6. But that was a long time ago. Right now, if someone hears about us, what are they going to have handy? They're sure to have D6 dice. But only 1-5% of the 40K playerbase is going to have more than a couple of D10 dice. Which they'd have to dig out of their old D&D box, because 40K & Fantasy don't use them anymore.

So either we go with D6 and anyone who hears about us can try the game within a few minutes of downloading the PDF, or they have to put off trying us out while they figure out how to get 20-40 D10 dice. Do they have the money? Do they have the time? Do they like ordering online? Will they remember to buy some the next time they visit the store? Once getting there, will something more exciting than a pack of dice catch their eye instead?

The more barriers that we put in the way of 40K players trying us out, the more likely they are not to try us out at all. Even if they're interested in us. So we use what they have. They have the standard GW templates. They have GW Scatter Dice. They have D6 dice to track suppression. They probably have some beads for nerve markers. They'll also have coins for marking GtG/Firing status. So we work within those constraints.

From a game system design point, d10s give you more statistical variance. For example, with a simple d6 N+/- roll, the values vary by 16.6%, versus 10%. This makes it harder to playtest, since your mind isn’t trained to work with 16.6%, but 10% is natural. For your other rolls (Pass One Rolls, Pass All Rolls, 6+d6) the math is also much easier, so it’s easier to see how modifiers for a Pass One Roll impact the statistics. I would need to use a spreadsheet and complex formulas to see how Leadership/Nerve tests for LGuard verse Knights work out statistically… a d10 system I can do in my head.

Just something I thought you should consider.

I actually have considered this at length, and the results may not be what you expect.

Here's a chart that I worked up once to demonstrate the useful range of results from both types of dice. Just because a die has more possible combinations, doesn't mean that it's range of usable results is just as high.

Rolling 2D6 in series (to-hit, to-wound) has 36 possible combinations, but only 18 unique results if plotted on a scale from 0-100% success.

Rolling 3D6 in series has (to-hit, to-wound, save) has 216 possible combinations, but only 42 unique results.

Rolling 2D10 in series (to-hit, to-wound) has 100 possible combinations, but only 40 unique results.

So while a 2-roll D10 system would have almost 3x the number of die combinations as a 2-roll D6 system, it really only adds a bit more than twice the actual useful range of results. While a 3-roll D6 system has more than twice the number of combinations of a 2-roll D10 system. But only a 5% higher useful range of results.

Look at the distribution of those results too. Rolling multiple dice in series always biases the results towards the failure end of the scale. Do we need that many gradations of failure? Past a certain point, does it even matter all that much?

The advantage of a D10 system would be at the top end, where it would have 4 levels above 80% to the 2 levels of the 2D6 & 3D6 systems.  But two of those results (80% & 81%) are so close together that they really don't have much meaning as separate values. So going to a D10 would gain us only 1 more effective result at the high end than we do now. While as you go down the scale, there's really only another small range (60%, 63%, 64%) where where a D10 would offer something that 2D6 with a conditional 3rd die (infrequent armor or toughness rolls) would not.

Also, look at the 40K plotline above for their 3-roll D6 system. Why are the curves different? Why are there 2 more usable results above the 70% line, and one more just below it?

Easy. We don't auto-fail on rolls of 1. Ones auto-pass instead. That one change to 40K's roll system gives a 2D6/3D6 system most of the advantages of a 2D10 system without the need for players to buy new dice.

Here's more food for thought: What if we switched to a D10 system and used an auto-fail on 1 mechanic, just like GW? What would that do to the D10 curve?

Easy. It would top out at 81%. 9/10 * 9/10 = 81/100 = 81%.

That would chop off the 2 highest results. Making our 2D6/3D6 system superior to it as well.

So when I look at D10 versus D6, I don't really care about the ranges so much. That's not the most important thing. Instead, I'm more concerned with being able to add more modifiers, easier in-game calculation of odds, and the little point on each number's face that gives you a built in scatter-die.

But there's a limit to the 'fun' number of modifiers. Which tops out at a D6 friendly 3 or so for wargames. Experienced 40K players are used to knowing D6 odds, and we're not using scatter as a mechanic anyway. It causes too many arguments and slows down play.

So net advantages: 

1) Easier odds calculation for less mathhammer-minded players.
2) A slightly more granular range of useful results at the middle and high end.
3) No need for a conditional 3rd die for some troop types.

That's not enough of a reason to switch IMO.

Plus, and this is important too, D10 dice are harder to read quickly, and tend to 'cock' more. Most I've seen also tend to be of the 'gem' type, as they're usually used for roll playing games where mass readability isn't as much of a concern. You really have to look around for opaque, high-contrast versions.

Thoughts?