The Sixes System Pt 4: Doing Things 2
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0. Fundamentals (repeated for all posts:)
— The Sixes System has been used in my Dr Who campaign since September 2014, and has just come to a successful conclusion.
— Characters are constructed using a point-buy methodology with NPCs generatable using die rolls for speed.
— Success or Failure on tasks is determined by adding dice to a pool based on ability and circumstances which are then rolled against a target number determined by the GM.
6. Setting Targets
It wasn’t until I started laying out the tables that will be found a little later in this article that I realized just how much this section was the heart of the entire game system. Everything to date feeds into this section, one way or another. All of section 5 (‘Doing Things, Part 1’) can be viewed as an interface between the rest of the game system and this section, which underpins everything. Accordingly, this is the material that it is most important for the GM to master.
The good news for GMs is that even if you never use the Sixes System for one of your games, mastering the content in this section will still be beneficial, because at the end of it, you will understand dice and die rolls more clearly than you did before. Unless you’re some kind of expert already, of course!
Setting a target would be really tricky without a simple process to follow that takes all the complexity and submerges it someplace where it won’t bother anyone. I’ll explain why, and discuss the difficulties involved, a little later. For now, let’s detail that process. There are six simple steps:
- Difficulty Factor
- Eligible Dice
- Target Average
- Base Target
- Number Of Sixes
- Amended Target
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6.1 Difficulty Factor
Circumstances are generally either for or against the character doing what he has described; it’s very rare for all the factors involved to cancel out, leaving a base roll.
If the circumstances make life easier for the character, they are described by a negative Difficulty Factor; if they make life more difficult, they are described by a positive Difficulty Factor.
Difficulty Factors are either “0” (i.e. nothing noteworthy), “1” (slight), “2” (significantly beneficial/adverse), or “3” (extremely beneficial/adverse).
In the most extreme of circumstances, the GM might contemplate a “4” but this is NOT recommended.
If the character is especially skilled or competent, these numbers (except 0, of course) may be increased by 1 or even 2.
6.2 Eligible Dice
Adding 1/2 the value of Stat that the character is using to the value of the Purpose with which he is using the Stat and subtracting the Difficulty Factor gives the number of Eligible Dice.
Note that this is not the full count of the die pool available to the character when the action is attempted, a fact that will become significant later in the process.
6.3 Target Average
The third step is to select an appropriate target average, based on the difficulty of the task under typical circumstances (remember that the specific circumstances involved in this specific attempt have already been taken into account).
The average for any d6 is 3.5, or 7/2, so that’s the base line. It takes an astonishingly small deviation from that average to significantly alter the likelihood of success. There is perpetually a knife-edge between “too easy” and “too hard”, a fact that has greatly influenced the system design. Quite literally, a range of ±1 normally covers the full gamut from 95% chance of success to 95% chance of failure – or more.
There are tables later in the rules to assist you in selecting an appropriate Target Average. But there’s a simpler way, and it’s this that I use when playing the system.
1. Average 3
Three is the average recommended for easy tasks, so if that description matches the difficulty of the task, then that’s it, you’re done.
2. The ED Range
Subtracting 1/2 the ED from the product of 3 and ED gives a Target Average of 2.5. Adding 1/2 the ED from the product of 3 gives a Target Average of 3.5.
Adding the ED from the product of 3 gives a Target Average of 4.
Adding 1.5 times the ED from the product of 3 gives a Target Average of 4.5.
Those two numbers – ED and 3 – and a determination of the relative ease of the task – is all that you need to know in order to set the Base Target.
3. The Difficulty Modifier
So, decide the relative ease, and rate it on a scale of 0 to 2×ED. Then subtract 1/2 of ED. This is called the Difficulty Modifier (not to be confused with the Difficulty Factor already determined).
6.5 Base Target
Multiply the ED by 3.
Add the Difficulty Modifier.
That’s your Base Target.
Image by Steve Bidmead from Pixabay
6.4 Number Of Sixes
The next question, is how many Sixes are you going to require in the roll? This isn’t quite as simple as it sounds, because the law of averages states that 1/6th of the ED will come up sixes, and that needs to be taken into account.
The most accurate answer is to take the Difficulty Factor and add ED/6. But that’s too complicated to do in your head.
The next most accurate answer is to take the Difficulty Factor and add 1 for every 6 dice after the first three – so +1 (cumulative) at ED 3, 9, 15, 21, and 27. (You’re unlikely to ever see an ED higher than that). But that’s too much work when you’re bust with other things, too.
So, the simplest solution is to further compromise with practicality: Difficulty Factor +1 for every 6 ED. And that’s good enough.
6.6 Amended Target
Multiply the number of 6’s that you determined in the previous step by 6, and add the Base Target. The result is the Amended Target that you announce to the player.
An example:
1) Stat: 10. Purpose: 4.
2) Difficulty Factor -1 (fairly beneficial circumstances).
3) ED = 10/2+4-(-1) = 5+4+1=10.
4) Difficulty Modifier range: 0-20.
5) Difficult task, so a Difficulty Modifier of 17-ED/2 = 17-5 = 12.
6) Base Target = 3 × ED + 12 = 30 + 12 = 42.
7) Number of Sixes = -1 (Difficulty Factor) +1 (for ED 10) = 0.
8) Amended Target = 0 + 42 = 42.
Same example, more adverse conditions:
1) Stat: 10. Purpose: 4.
2) Difficulty Factor +2 (challenging circumstances).
3) ED = 10/2+4-2 = 5+4-2 = 7.
4) Difficulty Modifier range: 0-14.
5) Difficult task, so a Difficulty Modifier of 10-ED/2 = 10-3.5 = 6.5 – round up to 7.
6) Base Target = 3 × ED + 7 = 24 + 7 = 31.
7) Number of Sixes = +2 (Difficulty Factor) +1 (for ED 7) = 3.
8) Amended Target = 3 × 6 + 31 = 18 + 31 = 49.
Example 3: Same Character, Different Stat & Purpose, Very Difficult task, even more adverse conditions:
1) Stat: 12. Purpose: 3.
2) Difficulty Factor +3 (very adverse circumstances).
3) ED = 12/2+3-3 = 6+3-3 = 6.
4) Difficulty Modifier range: 0-12.
5) Very Difficult task, so a Difficulty Modifier of 11-ED/2 = 11-3 = 8.
6) Base Target = 3 × ED + 8 = 18 + 8 = 26.
7) Number of Sixes = +3 (Difficulty Factor) +1 (for ED 6) = 4.
8) Amended Target = 4 × 6 + 26 = 24 + 26 = 50.
Analysis: What’s Actually Happening Here?
- Step 1 notes the characteristic and purpose, and the number of dice resulting from them.
- Step 2 determines the base number of sixes required for a success.
- Steps 3-6 work out what average is required on the rest of the dice, given the difficulty of the task:
- Step 3 works out how many dice are left after the sixes are excluded.
- Step 4 works out how big a variation the difficulty can cause in the subtotal.
- Step 5 determines a number within that range to reflect the difficulty of the task.
- Step 6 bypasses working out the average by skipping straight to (effectively) calculating # of dice multiplied by that average. This is something that would have to be done anyway, so this simply cuts out a number of intermediate calculations.
- Step 7 adjusts the number of sixes for the size of the die pool.
- Step 8 adjusts the target number to include the value of the required sixes.
6.6 The Scale Of Activity: The Impact of Skill and Equipment
Note that the Character gets more dice in his pool to use to reach the target from Skills and Equipment. So there is room for the GM to err a little on the high side when it comes to setting targets.
The tables given in the System Introduction show just how potent adding just one or two dice can be. Potentially, the character can be adding ten to the die pool as it stands for the above calculation – but 2, 3, or 4 are far more common values.
Even that’s significant. How significant? Two dice is an average of +7 to the total rolled. Three dice is an average of +10.5 to the total rolled. Four dice gives an average +14 to the total!
Equally important, these add significantly to the number of opportunities to roll a 6 – and sixes are worth their weight in gold in this game system.
To demonstrate this, let’s assume that the character from the third example above has a Skill of 2 and Equipment worth +1, for a total dice pool of 6+3+2+1=12 dice. Without the extras, he is faced with rolling 50 or better on 9d6 – an average of Five and Five-Ninths!, an almost impossible target. Which is only fair enough given the difficulty of the task and the adverse circumstances. Now, put those three extra dice back in – the required average drops to 50/12, or four and one-sixth. What was an almost impossible roll is now merely very difficult – the chances have improved from 0.01% to 10.36%, a more than 1000-fold increase!
Every extra die is like gold – if the character can get two additional dice from related skills, his chances rise still further, to 46.91%. Throw in a convincing line of argument about partial successes and a second chance, and you would almost start to feel confident about getting there in the end – which is what justifies trying to do something so difficult even under these adverse conditions. Even throwing in an extra 6 requirement because the character is extremely competent would only raise the target to maybe 52, maybe 53 – which, with 14 dice is 34.92% and 29.37%, respectively. Call it one chance in three. Given the subsystems that can bolster attempts to achieve success, you’d take those odds – if you had to.
Reference Tables: Target Numbers
What follows are six tables, the last of which is presented in three parts. Between them, they tell you everything you need to know to set a target – only simple addition required. But they also reveal patterns that will be both compelling and fascinating to anyone with a mathematical bent. Each will be followed by some notes and the occasional side observation. It’s important to remember that none of these values has been selected at random; they are all an outgrowth of basic probability theory and the fundamental concept of six-sided dice. Which means that those patterns are also not coincidental, but are part of the usually-hidden structure of the universe – and would be shared by any universe in which d6 could exist.
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The first table lets you take a certain number of dice and a selected average result, and gives you the relevant target. The averages selected range from one less than the normal average result on a d6 to one more, i.e. from 2.5 to 4.5, in 0.25 intervals. These are the smallest intervals at which each table entry for a given number of dice is unique; smaller divisions and rounding would mean that the same target would appear under multiple columns. Since the system mechanics relies, in part, on the concept of a higher average translating to a higher target, that is an unacceptable outcome.
If the die pool (excluding required sixes) is 14 dice, for example, an average roll (ave=3.5) gives a target of 49; a target average of 3 gives a target of 42, of 4 gives 56. Just pick the average that you want and find the entry that matches the die pool to get the target.
I find that this is also useful for analyzing the impact of requiring a certain number of sixes in combination with a given target. Take the average of 3 and the target of 42. One six in addition would result in a total of 48, which on the 15-dice line (14+1) is just short of a 3.25 average; since this is below the normal average on a rolled d6 of 3.5, it’s still a fairly easy roll. Two sixes gives a total of 54 and on the 16-dice line, that’s mid-way between 3.25 and 3.5 – still fairly easy. Three sixes is a total of 60, and the 17-dice line, which is exactly on the 3.5 average target – so there is basically a 50-50 chance of success.
You can also track the impact of additional dice from skills and equipment to get some idea of the effect, but that is better handled as part of the next table.
A number of observations are possible concerning the data in this table. The first is that tiny differences in the average translate into significant differences in target numbers. The second is that there are obvious patterns down the columns, because each entry is the addition of another ‘average’ amount. The columns for 3 and 4 averages show this most clearly.
It’s the progressions at an inclination that are most interesting, even though there are less of these. For example, start with the 10-dice and 4.5 average, a target of 45. Now track the targets shifting one column left and down each time, to get the pattern 45, 47, 48, 49, 49, 49, 48, 47, 45. Fascinating.
You may also note the color coding. The darker-colored values at the extremes are not recommended; they tend to be too easy or too hard. The effective range of usable averages (under normal circumstances) is the inner set of values.
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Table 2 contains the same data as table one – but translates the target into a percentage chance of success.
Take the target from the example used in describing the previous table – an average of 3 and 14d6. The resulting target works out to an 87.85% chance of success, as you can see by finding the intersection of these two values.
We then looked at adding one mandatory six – equivalent to an average of just under 3.25 on the 15d6 line. That’s a chance just a little better than 72.56%, according to this table.
Two sixes was exactly midway between 3.25 and 3.5 on the 16d6 line – so somewhere in between 52.89% and 74.33%. It’s hard to be more precise because these are non-linear curves. But it’s a fair bet to be 63%-plus-or-minus something.
Three sixes was exactly 3.5 on 17d6 (a target of 60) – and, not surprisingly, that gives a 50% chance of success.
What happens if the actual dice pool gets 4 additional dice from skills and equipment? Well, we need to use table 1, and find the equivalent average on 17+4=21 dice. Sixty, on the 21d6 line, is midway between an average of 2.75 and 3. Looking those up on table two gives a probability of 91.97-to-97.99% – so that’s about 95%, give-or-take, or the equivalent of 1-19 (or 2-20) on a d20.
You can’t really come to grips with what this table is telling you until you relate it back to table one, which provides the context. But you don’t have to track very many of the rows across to realize that a small linear change in target yields a huge difference in the probability of success, and the more dice in the target pool, the sharper that difference. Look at the 23-dice row for example – +1/4 over the basic average of 3.5 more than halves the chance of success. In other words, the more dice in the pool, the more important small changes in the target become – an outcome some people find counter-intuitive.
This also means that the more dice in a pool, the less significant any given number of sixes becomes. You can also observe this trend by considering the averages described in the example above.
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Table 3 is exactly the same as table 1 – but it uses a tighter and non-linear grouping of results: ±1/6, ±1/3, and ±2/3.
And yet, despite this non-linearity, the targets look surprisingly linear. Take the 9d6 row (and ignore the extreme results) – 29-30-32-33-35. Or the 21d6 row: 67-70-74-77-81. Just another peculiarity of mathematics.
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Just as table three is the same as table one (but with different divisions), so the above is the same as table two – but with divisions as per table three.
These are harder values to calculate in your head – but that doesn’t matter, because I’ve done all the calculation for you. That’s the whole point of these tables.
But I should probably remind everyone at this point that I don’t personally use these, because there’s such a simple way of doing it all directly. At most, these will be used for confirmation, or to give me a clearer idea of the range of targets within which I should be operating.
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You may or may not have realized that Table 2 started off being part of Table 1, just as Table 4 started out being part of what is now Table 3. They were split because the Theme used by Campaign Mastery permits only about 550 pixels of content on a line, and the tables would have spilled out of the ‘contents’ area into the navigation panel to the right.
Why, then, has this table not received the same treatment? Primarily because the four columns to the right of the “5” column are analysis of the 9 columns to the left (including the “5” column, and the value of this analysis would be almost completely wiped out by breaking the table up. Secondarily, by the time the article reaches this table, I would hope that the RHS Nav would have ended – and I’ll pad the article with illustrations, if necessary, to achieve this. That left only one objection – that it might not render properly on a mobile phone, or when printed. Well, the first is a risk that is always present – Campaign Mastery wasn’t designed to be viewed on such devices – and the second has been solved by providing the tables in separate, downloadable form.
But I thought it important to explain this to readers in order to place the content description below in context.
If you can determine a percentage chance of success (as shown in tables 2 and 4), then you can construct a table in which nominated percentage chances are the headings, and the table content provides the target numbers that yield that %chance of success (or better). It was this thought that led to the creation of table 5.
The columns that read “95”, “88” and so on are the % chance of success. You’ll notice that the extremes are color coded as “not recommended”.
There’s a subtle element of game psychology that explains why this is the case.
Even on very likely actions, there should be a reasonable risk of failure (given that there are so many ways in which the chance of success is improved – additional dice, virtual sixes, more time, and cooperative actions being the major ones). Similarly, even on very unlikely-to-succeed actions, there should be a measurable chance of success, perhaps one far in excess of what is reasonable.
All RPGs are Adventure Games of various flavors. That means that you can’t remove the thrill of uncertainty. But, at the same time, the PCs are the stars of the show, and should succeed in doing the near-impossible on a reasonably-regular basis.
Structurally, then, this can be thought of as combining tables 1, 2, 3, and 4. Except that the whole “averages” concept has been embedded and submerged in favor of selecting a given chance of success – which is then modified by the requirement of sixes, the inclusion of extra dice for skills and equipment, and the litany of chance-enhancing game mechanics features mentioned in the panel above.
What comes across quite starkly in the table, even from the first row, is how small a change in target is needed to have a significant chance in the chance of reaching that target.
The “Spread” column is the first of the analysis features. It subtracts the lowest target number – the one in the “95%” column – from the highest target number – the one in the “5” column. This is the maximum range of results that you have to play with in setting a target. You can actually halve the spread and write the range of useful values as 50%-target plus-or-minus (spread / 2).
Outside of this range, the chances of success or failure are so high that you normally not even have to roll.
The “Narrow Spread” deals only in the more useful range, defined as the lighter-colored entries. Once again, the low-chance value (in the “25%” column) is subtracted from the high-chance value (in the “75%” column).
Finally, the “Plateau” represents the range between a 60% chance of success and a 40% chance. When you look at the shape of a statistical bell curve, which all rolls of Nd6 are if N>1, you find that there is a slow rise, a rapid rise, a leveling off, a rapid decline, and then a slow decline. The plateau is defined, for the purposes of this analysis, as the range described.
You quickly reach the conclusion that the size of the plateau includes a 0.5, which rounds down unless paired with another the same. The plateau for 6d6 is not actually 2, under this theory, it’s 2.5 wide. Rounded, that becomes an alternating pattern of 2’s and 3’s for even numbers of dice and odd, respectively.
You then congratulate yourself on the insight, and are so busy doing so that you never actually absorb the fact that you’re wrong.
If you look more closely at the table, you find that it’s the even numbers of dice that have the twos, the ’round downs’, and the odd numbers that have the “round ups”. At best, you’re half-right – the pattern is the result of a rounding error, but it’s caused by the definition of the target numbers as “the first target number which has the indicated % success rate or better”. This is the same phenomenon that caused every second row in the middle column (the “3.5 average” column) to have values greater than 50% on tables 2 and 4.
Having discerned this pattern, I noticed a pattern within the pattern, and that is described by the “plateau group” column, which is color-coded for easy reference. From 6d6 to 11d6, the plateau is 2-3 target numbers wide; from 12d6 to 21d6, it’s from 3-4; from 22d6, it’s 4-5. Or maybe the ranges are 6-11, 12-22, and 23-?. Or 6-10, 11-21, 22+. It’s hard to decide exactly where the border lies.
Anyway, the point of all this is that it quickly lets you zone in on the range of possible target numbers that are appropriate for the challenge facing the character.
It’s a tool, in other words.
Which brings me to the three-part table six. I wanted to present the basic information in as many formats as possible so that the most useful one could always be employed. Tables 6-1, 6-2, and 6-3 exchange the two axes of tables 2 and 4, putting the number of dice across the top, and listing every possible target for any of the dice indicated. There are a number of possible entries – in order, high to low:
- 100 (red background) = 100% certain, guaranteed to succeed.
- ~100 = 99.9% or better chance of success.
- >99 = between about 99.1 and 99.9 % chance of success.
- ~99 = between 89.9 and 99.1 but not 99.0 % chance of success.
- Number between 99 and 1 without a symbol: the number % chance of success.
- ~1 = between 1.1 and 0.9% chance.
- <1 = between 0.1 and 0.899% chance.
- ~0 = between 0.1 and 0 % chance, i.e. 1 in a thousand rolls or worse.
- — = 100% certain failure (unless additional dice are brought in.)
This table isn’t about the patterns across a row, it’s about the specific chances of success for any given target and number of dice. They show just how compressed the information in tables 1-5 actually were. But more than that, because I was able to extend these up to 30d6, larger than any reasonable die pool should ever be expected to get.
Wherever possible, I have ‘collapsed’ rows which had exactly the same results – this can be seen for target numbers 57 and 58 on table 6-1, where two rows had exactly the same content; they have been conflated to make the table a little smaller. That means that there is no difference between the two target numbers within the given range of numbers of dice,
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This trio of tables contain the raw data from which all the other tables were derived. There are five ways to use them.
- The most obvious one – find the right column for the dice pool, track down to the row that contains your target and read off the percentage chance.
- Almost as obvious – find the right column for the dice pool and track down that column until you find the base chance of success that you think is right, then left to get the target number that will deliver your chosen percentage.
- You can estimate what the required number of sixes involved does to the chance of success. Remember that each is essentially +6 to the target and +1 to the number of dice.
- You can quickly determine the impact that skill and equipment has on the chance of success – these add (or in some cases, subtract) from the dice pool without changing the target.
- Having no skill reduces the size of the dice pool by two without changing the target. So it’s very easy to see what effect that has on the chances of success, and whether a roll is even necessary, or if the nominated task is beyond someone without the appropriate skills – just go left two columns and read off the chance of success. Note that equipment can replace some or all of those lost dice.
I have to admit that if I had these tables available, I might have used them now and then, even with the quick and easy method given earlier; so I gave some thought as to how to make them accessible. The downloads I am providing are the solution I came up with.
I don’t think they should take the place of the system of calculation that I use, but use for verification, for estimating the impact of a sixes requirement, and for estimating the capabilities conferred by a given number of skill ranks for a particular PC or NPC* cannot be underestimated.
* It has to be for an individual, because no one else is likely to have exactly the same combination of Stats and Purposes, and this is especially true in light of the self-defined stat.
Image by Parker_West from Pixabay
Designer’s Notes & Discussions: Doing Things
I’ve been a little lazy in this article in terms of separating notes and observations from the rules. I thought I should start what remains in this section by explaining why. The purpose of these posts is to communicate how this game system works, and I have set a structure in place that, in general, promises to do that with minimal distraction and side-issues – but I am perfectly willing to set that structure aside if that seems to me to be more effective in achieving that purpose.
That being said, I do still have a few points to discuss, mostly related to the probabilities involved, and hence applicable to any system that uses multiple d6 to determine damage – and indirectly relevant to any system using multiples of some other die size..
Observations of Results Distribution
The more dice there are in a roll, the more room for small drifts from even distribution because that only needs one or two of them to roll higher than averages would dictate.
At the same time, the more dice there are in a roll, the smaller the room for large deviations from the mean outcome, because that requires an increasing number of dice rolling significantly higher or lower than the average.
The entire action resolution system rests on these two effects.
These phenomena mean that characters with high stats & purposes can perform moderately-difficult tasks under normal circumstances with greater reliability, in addition to being able to attempt more challenging actions with some chance of success. The influence of skill ranks and equipment on these probabilities are even over both, as are the circumstantial difficulties that need to be overcome, whereas the stat/purpose effect is more relevant to the reliability question.
In other words, you can have low Stats and Purpose, but if you have enough skill and equipment bonus, you can still attempt difficult tasks and will, every now and then, succeed.
Another way to look at the results distribution is that the probability curves become increasingly narrow with flat trails to either side. I have seen some who describe the difference between a 3d6 roll (which does not display this curve shape) and higher die rolls (which do) as being a “pinch” in the probability curve.
For these higher dice populations, a probability curve consists of four features distributed amongst 7 regions on the curve:
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- A pair of regions of low-probability extreme results which grows rapidly in range with additional dice and is very flat in terms of the probability of a specific die roll. One of these will exist for high rolls and one for low.
- A pair of regions of rapid increase in probability of results, the probability rising in almost a straight line.
- A pair of regions of transition between these regions, often quite small, perhaps even only a single result.
- In addition, there is a pair of regions at which the high-rising probability joins the “ballistic” motion. Interestingly, if you scale the probability curves of multiple different die rolls and superimpose them, you will find that these points are very closely the same, in relative terms, regardless of the number of dice (Ndn with N greater than 3). Larger numbers of dice show that there is actually a curve formed by these points.
A central region in which the probability looks like ballistic motion, rising to a peak and then declining. An increasing share of the total number of possible results will be found within this region.
Below are a number of probability curves for your consideration.
The first shows the true results of 9d6, 15d6, 21d6, and 27d6 (increases of 6d6 each time)- values chosen to make the features described above more readily visible. They are a series of steadily-flattening patterns, which is exactly what you would expect with results being distributed over a greater range of results. Note the red line showing the trend in maximum single-result probability.
The second graph aligns the minimum possible result of these die rolls and also scales them so that the maximum possible results are also aligned. This naturally means that the points of maximum probability are also aligned. The curves were all scaled so that the maximum probabilities were the same for each of the die rolls, enabling a more direct comparison of the shapes of the curves. Finally, each result was raised to permit each of the curves to be seen. All of which sounds more complicated than it was. The patterns of probability that I describe are made quite clear by the direct comparison this set of graphs provides.
The third graph is, I admit, an afterthought. Similarly to the second graph, it shows “ridiculous” numbers of dice, scaled to fit: 25d6, 50d6, 100d6, 200d6, and 400d6. Given that the area under each is going to be the same (100%, in total), it clearly shows how the “effective” range of results continues to narrow as the number of dice increases.
Implications: Number Of Sixes
The average number of sixes in any given die roll are equal to the number of d6 divided by six. If you get a remainder, that indicates a chance at one more than the integer result, which you can guesstimate as 100 sixths of the remainder (%), (roughly, multiply by 17). So,
Remainder 1 = 17% of +1;
Remainder 2 = 34% of +1;
Remainder 3 = 51% of +1;
Remainder 4 = 68% of +1;
Remainder 5 = 85% of +1.
The environmental and circumstantial difficulties to be overcome are represented by requiring more dice to come up sixes, or ‘virtual’ sixes, on top of this minimum expectation.
It is only logical that the more dice you are rolling, the more opportunity you have for some of those dice that aren’t expected to roll high to do so. In other words, with increasing dice in the pool, you have more opportunities to get the additional dice imposed by circumstantial difficulties – and those are dice from any source, including skill levels and equipment.
In game terms, then, the system naturally makes characters able to routinely overcome adverse conditions, regardless of whether that’s through native talent (Stats + Purpose) or acquired expertise (Skill + Equipment).
In fact, if Skill+Expertise totals 6, you can reasonably expect one of the them to be a “bonus” six, completely on top of whatever can be achieved through ‘natural ability’. But 1/6th of the time, one rank is all that you need.
All this makes perfect sense, but it’s a reassuring reality check to observe that the game system conforms with the logical reality that it’s trying to simulate. The great news is that it does all this with no additional workload imposed on the GM.
Implications for Game Mechanics
In general, then, small die pools tend to be either spectacular successes or failures and will less often be routine expectations. As die pools grow, the probability of a result at or near the average increases.
These are facts that the GM should take into account when setting targets. The smaller the die pool, the lower the target should be if the character is to have a reasonable chance of success, in relative terms. As die pools increase, it gets harder to achieve even a modest increase in the average result, but easier to achieve that average result.
Whereas with a die pool of only 6-10 dice (on the low end), I might expect an average of 4 or more for an inherently difficult task, with a die pool of 11-14 dice (fairly common) an average of 3.75 might represent the same task, and a die pool of 15-18 dice (quite high) might require an average of three-and-two-thirds.
Why the Virtual Sixes?
Originally, there were no Virtual Sixes in the rules, as I have explained elsewhere, and the demand for additional sixes was far more critical than the target (which represented the inherent difficulty of the task. In favorable conditions, it was too easy to work miracles; in unfavorable conditions, it was too hard to achieve even modest successes. What’s more, the need to stop and actually count the number of sixes rolled was slowing the game system down quite noticeably. Bringing in the ‘Virtual Sixes’ system enabled me to determine a target at the same time as the player was rolling and totaling his dice – as close to 100% efficiency as you’re going to get.
The Limitations Of Virtual Sixes
The problem is that this devalues the rolling of an actual six. That was something that I addressed with the critical success mechanics. It follows that even though they are described as an optional rule, I strongly advise in favor of them.
What’s more, I found that the player organizing his die roll into tens for easy counting made it easier for me to – at a glance – determine whether or not the number of sixes were greater than required, or if there was a significant population of ones (in the event of a failure). It represents virtually no overhead to the GM, in other words. That starts to change with pools of more than 18 dice, when the maximum number you need to count to with that glance becomes (for a very difficult task) 6 or more – even under ideal circumstances.
But, what I discovered was that the length of time it took to sort and total more dice increased faster then the increase in overhead caused by this problem. I still had more than enough time to determine a target AND count the number of sixes or ones – and I could tell with that initial glance which one of those options might be relevant. The Critical-Hits-and-Fumbles rules remained an option with no overhead cost – for me.
I’m not everyone – others might not find it so easy (though they will improve with practice). So I’ve provided the simplification of playing without the criticals – but don’t recommend it unless you are forced into it by a total inability to do simple math, AND don’t have the game tables to hand.
Recommendation: Critical Hits and Fumbles
I strongly recommend playing up the drama of critical hits and fumbles. That often means that the former should be led up to in the narrative by narrowly escaping failure until ‘the stars align’ and the character does something spectacularly well – all of it part of the ONE die roll. PAD if you have to.
Similarly, a fumble shouldn’t be a simple “you drop your sword”, it should be more in the nature of a train-wreck or farce with the character in the starring role. I try to avoid dues-ex-machina when doing this (unless I’ve set the stage for them already) but that’s the only censor. So, unless combat is taking place in a region known to be extremely volcanicly active, I generally won’t have a fissure open beneath the character’s feet – but I’m quite happy for them to lose their grip on their weapon in mid-swing, propelling it into the ceiling or high up a wall, cutting the cords holding a chandelier along the way, which crashes to the ground right next to the character, showering him with shards of glass or crystal.
Part 6 of the Sixes system will deal with doing more things – like combat – but there are a few quick pieces of infrastructure that I should put in place first. So Part 5 will deal with them: Base Values (how many character points a character should be built on), Disadvantages and what they can be used for, Character Penalties, Experience, and What you can do with it (i.e. Improving Characters).
- Introducing The Sixes System: A Minimalist Universal RPG
- The Sixes System Pt 1: Fundamentals
- The Sixes System Pt 2: Education, Abilities, and Tools
- The Sixes System Pt 3: Doing Things 1
- The Sixes System Pt 4: Doing Things 2
- The Sixes System Pt 5: Campaign Infrastructure
- The Sixes System Pt 6: Doing More Things
- The Sixes System Pt 7: Characters
- The Sixes System Pt 8: Genres
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