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Resilience to Upscaling: Statistical constraints for the design of roleplaying games (RPGs) and campaigns

Bild von Drak

Hurricane 1 A game for average roleplaying groups must (1) be able to cope with people who miss out on sessions and (2) be playable with either 2-7 or 3-9 participants.

Alternative title: "Why it ruines most groups, when players miss every 4th session. And what can we do about it."

If you want to know the science behind that quite daring claim, please read on.

Let's start with (1) to build the statistical foundation for (2).

(1): Every game and every campaign must be able to cope with missing people


It is well known that statistics often go against common sense2, and that hits us when playing tabletop roleplaying games: For the question of whether enough players come to a given session to play, and for assessing the effects of players who cannot make it now and then.

I show here that the constraints arising from these effects are almost unavoidable (even with fairly reliable players), so that all roleplaying systems and RPG groups should take measures to mitigate the problems due to the constraints.

(Directly to Conclusion 1 with solutions)

Statistics in RPG sessions

Let's start with an assumption (we’ll generalize this later). We play on the weekend and each of us has to skip 4 random weekends, Christmas and other regular holidays excluded.3 Examples of those skipped weekends are one's own birthday, the birthday of the spouse or a close friend and the birthdays of their parents. For families, we need to add two further birthdays for the children.

This brings us to a participation probability for a given player and a given evening of (50-4) / 50 = 92%; for parents only (50-6) / 50 = 88% due to the children’s birthdays. All of that under the assumption that we are never sick (alternatively assume 4 sick times instead of 4 birthday celebrations). The real figures are probably somewhat higher, but we can ignore that: we only need to find a lower bound. Effectively we assume that the players skip a session only once every 3 or 2 months. Later in this article we’ll consider games with higher skip-rates, too, but let’s keep this simple for starters.

Now we can start with ignoring all special cases4, and assume that the probability of skipping is the same for all players. When two people meet, the probability that one of us has to skip is 1-0.92² = 15.36%; for parents 1-0.88² = 22.56%. So every 4-7 weeks one of us misses the session (instead of once every 2 to 3 months, when we look at just one person).

This effect gets stronger with every additional person in your group.

NOTE: The following part is still the mostly raw output of Google translate. Only read on, if you can tolerate Yoda and C3PO trying to translate what R2D2 says about roleplaying ;)

If you can cope with that, and additionally want to help improving the text, please register and send us a message, so I can give you the rights to edit it like a wiki. The text is free licensed like most of the site (GPL).

Probability that all are present

TeilnehmerJeder fehlt 1× pro Jahr 98%2×/J 96%4×/J 92%6×/J 88%1×/Monat 75%

The table shows for 2 to 9 participants, the probability that a randomly selected game night are all there, if only every 1 ×, 2 ×, 4 ×, 6 × or 12 × in the year is missing. It clearly shows that more than 2 days off per year and more than 3 players, the probability drops very quickly that everyone is there. Bold marked just the meaningful groups (limit).

In addition the table are values ​​for most reliable players who are missing only once or twice a year, and a value for people who lack even a month. The numbers are all rounded.

According to Survey Tanelorn would get ⅔ of the people if a game more often than every 4th Meeting fails, the round will take place with a past that is less than 75% probability.

If the games always have to be all there, it means that only rounds in which the individual people are missing a maximum of twice a year with more than 3 participants are playable. Even at 4 absences per year and 4 participants (eg a SL players and 3) the round is more often than every 4 Time out.

Larger groups in which all must always be there, will only work in an extremely structured environments, eg as a school-AG, or if the parties are extremely reliable. Could only 2 days off per year for example a group of 5 people to play 4 of 5 nights. Then there are really only two days off per * person *.

Can we play on the other hand, if all are up to there, then the picture changes significantly:

Probability that at most one missing

TeilnehmerJeder fehlt 1× pro Jahr 98%2×/J 96%4×/J 92%6×/J 88%1×/Monat 75%
3 (≥2 da)99,9%99,5%98%96%84%
4 (≥3 da)99,8%99% 97%93%74%
5 (≥4 da)99,6%98,5%95%89%63%
6 (≥5 da)99,4%98% 92%84%53%
7 (≥6 da)99,2%97% 90%80%44%
8 (≥7 da)99% 96% 87%75%37%
9 (≥8 da)99% 95% 84%70%30%

The table shows for 3 to 9 participants, the probability that a randomly selected game is missing one night at most parties, if only every 1 ×, 2 ×, 4 ×, 6 × or 12 × in failure. It clearly shows that even here at 6 days off in groups of up to 7 people are still able to play. With a day off work per month but still nothing is done. Bold marked just the meaningful groups (limit).

As long as people are missing more than 6 × year (ie every 2 months), and is also played, if one is missing, falls into a group of up to 8 participants (≥ 7 there) more than every 4th Lap. Even in normal people who give the role-play a very important role, so are a round up and SL feasible to 6 players (if SL can change, so does the rounds even if SL is not the usual).

If we lack even 2 to match the skill itself is then given to 7 participants, if any once per month goes down, and people with more reliable, it is almost certain:

Probability that more than two missing

99.9 percent will be written here as 99%, so as not to create the false impression that the game ability is 100% secure.

TeilnehmerJeder fehlt 1× pro Jahr 98%2×/J 96%4×/J 92%6×/J 88%1×/Monat 75%
4 (≥2 da)99%99%99%99%94%
5 (≥3 da)99%99%99%97%90%
6 (≥4 da)99%99%99%96%83%
7 (≥5 da)99%99%99%94%76%
8 (≥6 da)99%99%99%92%68%
9 (≥7 da)99%99%99%89%60%

This table now shows for 4 to 9 participants, the probability that a randomly selected game is missing in the evening at most two, if only every 1 ×, 2 ×, 4 ×, 6 × or 12 × in the year is missing. Here, even with a day off work rounds per player per month to 7 participants often play again. Bold marked just the meaningful groups (limit).

So if we as ⅔ of Tanelorn users hold a round with more than a dropout time per 4 nights for prohibitive, even a round of work with three parties, which always must all be there only when all most 4 missing dates in the year have, therefore, fail more than once every 3 months, including any sick time - or even without individual meetings with regularity. Even with 4 rounds of parties need extremely disciplined player, if they want to play with full occupancy.

If they are actually five people who are not 6 × year and can play as soon have 4 time, is only one out of 10 rounds. Even with only 3 players accept and SL, as a minimum, the round so that every now and missing someone - and this really needs 5 participants. And so is (1) have already shown: Even with only 3 participants (SL + 2 players), a round of more than 4 incorrect dates in the year did not work every weekend, without causing stress, because a game goes down once a month. Actually, each system must be so, and each campaign are so clear, when players are missing.

Therefore, we are preparing now for only data point (2): If we want more than one failure of 8 rounds, we have to tolerate the loss of players, our round must then be correspondingly larger: The corresponding probabilities are:

Maximum Frustration free group size

(Min group /. Present) does not exceed the failure of one round per month (75%) or every 2 months (88%) or 2 per year (96%). Fat is in each group with the fewest missing, but at least three participants.

Spielwahr­scheinlich­keitJeder fehlt 1×/J 98%2×/J 96%4×/J 92%6×/J 88%1×/Monat 75%
75% (1/Monat fällt aus)>12/>12 7/7, >12/>113/3, 12/11 8/7, >12/>103/2, 7/5, 10/7
88% (1 pro 2M) 6/6, >12/>113/3, >12/>117/6, >12/>105/4, 10/8 5/3, 8/5, 11/7
96% (2/Jahr fällt aus) 2/2, >12/>118/7, >12/>104/3, 9/7 3/2, 6/4, 11/8 6/3, 8/4

Note: For a day off work per month are groups of 9 people only able to play more than 75% (more precisely, 83%), if they accept up to 3 missing.

Conclusion of (1)

The consequence of (1) is thus in a nutshell: Every campaign and every system should be so designed that players can easily suspend for one round.

In technophobes, we have realized through order structure in the style of Shadowrun and with a single headquarters, we start to go to "dream the other" on a planet that our smuggle goods and then return to "dream the other" back to look at Kjeol another order is placed.

In several rounds we had Kryokapseln who like to have time malfunction, making them the only occupants were out on the next game night.

We come then to (2): (directly to Conclusion 2 with solutions)

(2): Each game must be playable with either 2-7 or 3-9 people

This thesis may sound radical in itself, just because you have hardly enough an RPG, but it follows directly from the statistics - and, I believe is one of the main reasons that role-playing have not spread much further.

Why is

The reason for this is what happens when a game is too big, so if many people begin to play role games and are looking for existing rounds.

When new players to join a round, grows on the round until she has so many people that it is confusing. Then there's no more to be larger for the round. If more people come to have to share the round to accommodate them.

The condition for a successful pitch is that the round of play again both before and after the partition is 5.

Case study: 3-6 participants

If the system or the campaign now e.g. for SL and 3-6 players work well (ie for 4-7 participants), the round will be divided if the next one to do so. Then we have the best of worlds, two groups of 4, but only to 60 - are 72% complete. Because the sample system here needs at least 4 people, every third to every 4th Evening turn out - what is intolerable in itself alone.

Additionally, there are probably players who want to not be separated, so that a round is larger than the other or will some players in both groups, which can then be but not on the same evening.

More realistic than the best of worlds, ie the assumption that from a 8-person group is a 3-5-he and a group he is - what can only work if the system with a SL and * two * players work well. Even then, the group of 3 is capable of playing only 68-78%. If parents have named are (missing at least 6 × year), it does not reach the 75% that ⅔ of the players in the survey of Tanelorn as a minimum criterion for the playing ability.


Thus both the large and small groups play again, the output group thus have 9 people, so that small groups get 4 and 5 participants, or the small groups must play again with two participants, ie with SL and * * player.

In other words, if we do not play with 9 people, then we have to design the games so that they can also be fun if there are only 2. If it makes us no pleasure, we have to make the big rounds played.

The initial group will play each evening after 8 to 10 attendees, 7-9 characters.

There are only about ⅓ of the Round 9 players be there (32 to 47%), 8 but there are already 2 of 3 rounds. Games must therefore be possible and fun to play with all stakeholders. The greatest difficulty is probably that the SL keeps track and stay on the ball and the players do not block each other.

An example of problems in large groups

As an example, how does it not, I fondly remember a Gurps-fight with 8 players. We have thrown only 2 hours to cover here at 3 second fight, then I realized that this does not work and simply offered that we omit the dice and I describe just what happens. The struggle has made it even then (much) fun.

It would play out with the full rules against it simply boring, because so many of us most of the time would have to wait. The rules were not suitable for 9 participants.

We had it here but managed to keep reasonably track lasted (with some exceptions), but individual actions so long that the duration of the war passed, can think with focus on people at a time.

Conclusion of (2)

If we want to role play can spread more easily and that there are groups of a subdivision, each system must be either 2-6 or 3-9 participants playable, * so * with 1-5 or 2-8 players.

Since the date is usually difficult, we need ways to make this easier.

Scale Up

To make this better to scale better then the system up, can sketch or battle maps and a simple initiative rules help to keep things clear (we use in non-critical situations like the simple rule: "First it's your turn, then the opponent, in the order in which we sit at the table, "or" one of you, then be (e) opponents, then the next one of you "- complex only when it seems really important to us ).

A further advantage is clear with few skills or modifiers Standardmodifikatoren (I am happy "if there is a clear advantage: +3"), so that will not have long sought, which will now be rolled exactly.

In general, the rapid treatment of individual actions is important, so players often go through and all can be active (the waiting period may be sufficient to plan the next step, but not to get bored).

Regardless of the rules can use the SL cutting techniques to shorten a long time, but unimportant actions, "she clarifies the formalities. After two stressful hours, you finally come out of the Community Office. Do you want to do something else important in the afternoon, or we can immediately jump to the evening news? "

Plus it's useful, what the SL decreases labor, eg a co-SL, the rule clarifies questions or NPC takes over and can also easily lead to a part of the group when the characters split up.

Just as it is one of them that players even for a short time or permanently for her lead interesting NPCs - perhaps with the SL previously clarified (simple) instructions.

Or, what is described in Laivindil Tanelorn, actually two rounds to the one taking place only when the first would be too large, and otherwise play all in the first round (so that the second round provides a buffer).

Scale down

To work with very small circles, the preparation time should be reduced for the SL, because one or two players can burn in 15 minutes through a plot that takes several hours to larger groups. Dice tables facilities would be to couple directly to the back-story (n) of the characters.

A plot needs a job, a role for the SCs, NPCs, and a place.

For example, the SL choose an adventure just a background character - thanks to speaking qualities and skills suited to the 1d6 system, almost every character value - and throw it on 3 lists, in order to obtain a framework for an adventure: mediator role of mediator and place. Then they could roll the dice on a table for tasks: verb (what to do) and object (what).

In technophobes might look something like this (rough draft): 6


Character value as a starting point: simply dial a value of the character - if in doubt of a cube. From him, everything. Then cube, what happens to it, by whom and where.

union mediator role of mediator scene
6 smuggler chance Trading Post
5 Raumpatroullie threat pirate station
4 rebels / anarchists Legend / Sponsors Technophobenplanet with Spaceport
3 Pirates Completely incapable Technophobenplanet without Spaceport
2 innocent citizens same ideas dream the other
1 petty criminals reverse asteroid habitat

Technophobes planetary

union Company Form utopia / dystopia
6 utopia / dystopia Ökoparadies
5 Ancient Rome (bread and games) Group dictatorship
4 Wild West entertainment world
3 Middle Ages Church State
2 Modern Democracy Communism
1 colonial times Surveillance State


Look at the previous results of dice. What would be your wake-SL malicious grin? Perfect!

And KISS: Keep it simple. The players then make it even already complicated.

Task: 2 × roll:

union Action thing
6 Acquire / save object
5 destroy / defeat person / group / enemies (roll a die to roll up)
4 Seeking / smuggling / protect Planet / Town / City / transport
3 investigating understand / Crime / situation
2 organize / joints Company / action
1 stand on / escape threat / alien

Reward: Pass it on your lap, roll 2 ×

These are examples of the group of technophobes adapted: Kass, Lomo nan tar, and Chessos Nayres. They write about on your own lap. Two means of throwing the same time "right much".

  • 6: Making Money (Lomo nan Tar Chessos)
  • 5: Saving Lives (Lomo nan Tar)
  • 4: New Equipment (Chessos, Kass)
  • 3: contacts (Nayres)
  • 2: improve learning abilities / (Nayres)
  • 1: to uncover secrets (Kass)

Names and NPC

You'll also need a list of names for which you are, for example Create random names from the Onomasticon can and with create them as a basis NPCs using the minimum necessary data: name, two words, quote, an external feature and essential for the scene. That too could be packed into a simple table.7

Indie and PiHalbe

There is also now a number of indie RPGs, which are aimed at very small rounds. After PiHalbe on 30/08/2011 a podcast (PiCast Episode 30: number of players) has, in which he says he would rather like small rounds, we may be lucky that he is the next time this topic takes and deep insights into the art of conducting with small rounds of offers (* wink *).


To dynamically growing RPG rounds and thus allow a better distribution of role-playing games, role-playing system and have campaigns with rounds of SL and 1-6 or 2-8 players to be playable.

  1. The picture “Hurricane” was drawn by Philip Barber for Battle for Wesnoth. As almost everything else on this site, it is licensed under the GPL. 

  2. The most common evidence that we cannot deal well with statistics is the probability that two people among a group of 23 have the same birthday-date. Each person must be compared with every other person, so that the probability is over 50%

  3. We only make this assumption for getting a more convenient description. It can easily be transferred to any other game frequency: simply extend the periods accordingly. Christmas, etc. are irrelevant because (almost) all have to skip them, so they are not considered as potential roleplaying sessions and thus an absence is irrelevant. 

  4. Special cases: (a) One reliable player: Just take the numbers of a smaller round. (B) One unreliable player: Take a group with one less person and then multiply by the probability that the unreliable player will come. (c) *Correlated skipping (partners?): Just use a group with one person less when you only play when all are available, or with 2 less people when you play when one is missing and multiply by the probability of the two people to find out whether you are enough to play. Statistically both together are treated as one person. 

  5. This should also be clear why I am so harped on the grounds of playing ability. 

  6. the effective use of the creative constraint for easier and faster design of plots so that the design of plots for the SL is less stressful. 

  7. A quick way to create a memorial worthy NPC, just use Interesting characters represent part 2.5: What NPCs need at least

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„Das Regelwerk meiner Träume zu diesem Zweck [eigene Rollenspielwelten] sollte… auf verschiedene Hintergründe und Welten anwendbar sein… einfache und überschaubare Regeln bieten… [und] frei sein… Und wer hätte das gedacht, das 1W6-System erfüllt alle diese Anforderungen.“
— RowC
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