Monday, February 17, 2020

5d6 but only count straights and matching

On 7 Feb 2020, diregrizzlybear on the GLOG channel of the OSR Discord asked1:

5d6 but only count straights and matching.

One solution might be to list all the rolls and score each one. This is probably feasible with a script. Instead, I enumerated the “hands”, and then found the probabilities of each of those.

Hands with No Degrees of Freedom

Run of Five

There are only two runs of five: ⚀⚁⚂⚃⚄ and ⚁⚂⚃⚄⚅. There is only one way to “make” each of these hands (“Count”), but because each die has a different face, there are 5!=120 possible orderings of each hand (Permutations).



There are six possible quintuples, and again, there is only one way to construct each one. While there are 5! possible orderings of five dice, because five of them are interchangeable, there is only one possible ordering of a quintuple (5!/5!=1), which makes a quintuple much less likely than a run of five.

If this seems counter-intuitive, consider rolling one die five times in order. If your first roll is a ⚀, to eventually score quintuples, the next roll must also be a ⚀ (1/6 odds). To eventually score a run of five, the next roll must only be not ⚅ or ⚀ (4/6 odds).


Run of Three + Double

There are 24 ways to score a run of three + double: 4 runs of three and 6 doubles. Depending on the doubled number, it may be possible to score this as other hands (run of four, triple), but this is never advantageous.

Because of the doubled number, there will be fewer ways to order this hand than a run of five, but more than a quintuple. If the doubled number is in the run, there are 5!/3!=20 possible orderings, and if it is not, then there are 5!2!=60.


Triple + Double

There are 30 ways to score a triple + double: 6 ways to score one and then 5 remaining ways to score the other (to exclude quintuples, which are already accounted for). As with run of three + double, we must account for duplicated numbers when counting orderings. There are then 5!/(3!*2!)=10 permutations of each.


Hands with One Degree of Freedom

Run of Four

There are three possible runs of four: ⚀⚁⚂⚃x, ⚁⚂⚃⚄x, ⚂⚃⚄⚅x, where x is our "unfixed" die (our degree of freedom). If x is equal to either the highest or lowest element of the run, then we instead have a run of three + double. If it is equal to a number after either end of the run, then we instead have a run of five. So for ⚀⚁⚂⚃x and ⚂⚃⚄⚅x, x has three possible values, and for ⚁⚂⚃⚄x, x has two possible values. We will also consider the cases where x is “inside” the run and “outside” the run separately, as the number of permutations is different.



There are 6 possible quadruples, with 5 ways to construct each one (again, to exclude quintuples). There are 5!/4!=5 permutations of a quadruple.


Two Doubles

There are 15 ways to score two doubles (half as many as triple + double, because it doesn't matter which number is the first multiple and which number is the second). The unfixed die (x) can take any of the four remaining values2. A hand of two doubles has 120!/(2!*2!)=30 permutations.


Hands with Two Degrees of Freedom

Run of Three

There are 4 runs of three: ⚀⚁⚂xy, ⚁⚂⚃xy, ⚂⚃⚄xy, ⚃⚄⚅xy. However, x cannot equal y (else we have run of three + doubles), x and y cannot both equal numbers in the run (else we have two doubles), and neither of x and y can equal a fourth part in the run (else we have a run of four).

For a run of three with no duplicates (for example, ⚀⚁⚂⚄⚅), there are 5!=120 permutations. For a run of three with one duplicate, there are 5!/2!=60 permutations.



There are six possible triples, each with two degrees of freedom (x,y). x cannot equal y, neither of x and y can equal the tripled number, and x and y cannot form a run of three with the tripled number. There are then (52-5)/2-R=10-R ways to make each triple, where R is the number of runs of three containing the tripled number.


Hands with Three Degrees of Freedom


There are six possible doubles, each with three degrees of freedom (x,y,z). None of x, y, and z can equal each other, none of x, y, and z can equal the doubled number, and x, y, and z cannot form a run with the tripled number. There are then 5!/(3!*(5-3)!)-R1-R2 =10-R1-R2 ways to make each double, where R1 is the number of runs of three (4) and R2 is the number of runs of four containing the doubled number.


Other Hands

Other hands are not possible with 5 dice, but I did not bother to prove this more formally. Instead, I can show that all hands are accounted for: there are 6^5=7776 possible rolls (in order), and the sum of all the “Odds” of the above hands is 7776.


Now we can sum the odds by score (instead of by hand) and normalize them. This gives us the following distribution.


The minimum score is 2, maximum 30, mean ~12.4, median 11, and mode 6. My spreadsheet is a bit messy, but you can see it here. Let me know if anything here seems off.

1 “Asked” is a strong word. Nobody asked for this.back

2 In the case of ⚀⚀⚁⚁⚂, both run of three and two doubles would score 6. For convenience, we will consider it as two doubles, because restrictions to exclude it are already part of the math for a run of three.back

Thursday, December 26, 2019

Crisis on Christmas

The problem with Troika! is that it’s written in a bunch of encapsulated little thought-forms. And they’re infectious ideas, like the way you start counting every word’s syllables after you first learn about haiku. What started as an entry in my running note of bad ideas blossomed into a week-long distraction from work, and now this thing.

I wanted to get this out on Christmas day, but I didn't want to take myself away from the festivities to write this post. So happy Boxing Day! It wouldn't be a proper gift if I'd given myself time to finish it, but I may go back and finish it later.

Tuesday, December 17, 2019

Secret Santicorn 2019

Sky Seeker asked:
Dear Santicorn,
Please bring me

New ways to mess with time/space/fate, be it mechanics, spells, worldbuilding or beyond. If pokemon can reboot the universe to patch in a baby god we can do better:

The Slipsoul – a Character Option

Infinite parallel universes teem around us, multitudes branching out with every decision and movement. Normally, these worlds are inaccessible and inhospitable. But when you die, your mind does not go gently into the night, but casts about wildly to find purchase on any reality that will take it. When you’re lucky, it’s relatively close to the world your remember.

These rules assume a D&D-ish game, but could be easily adapted to others. Mechanical effects, if any, are left as an exercise for the referee and the effects of further re-rolls are left open to negotiation.

Whenever you fail a death save, roll on the slide table and appear stabilized, but in a different reality. That this reality is different is apparent only to you. For example, if you roll “No eyes” the wound is old, and your companions may remember how you lost them. If you later re-roll the same number, you find yourself instead in the universe the next column over, as your mind reaches for further and further branches of reality. For example, if you roll a “1” a second time, then you still have no eyes, but find yourself able to see spirits.

The Slide Table

d12 First Second Third Fourth
1 No eyes. See spirits. See the past. Something else sees what you see.
2 Covered in tattoos. Know and can cast random spell. Spell casts itself when you take damage. No one else can cast the spell.
3 Dave loyally follows you everywhere. Davinia also follows you everywhere. Dave & Davinia are retired in the city. Nobody has ever heard of Dave or Davinia.
4 Pockets full of money. Warrant for your arrest. Owe a criminal favor. Run a small gang.
5 Forsaken by religions. Resting grants no benefit. There are no stars. Free from the wheel of death and rebirth.
6 No fingers on off hand. Off-arm is a tentacle. +d6 tentacles. You are an octopus.
7 Lycanthropy. Contacts despise you. Covered in scars. +d6 wolf companions.
8 Slide on any failed save. Slide instead of save. Optionally, slide instead of skill check. Roll twice when sliding.
9 Super nice clothes. Parents look for you. Assassin targets you. Inherit a small estate.
10 Require double rations. Do not need sleep when you rest. Cannot heal naturally. Begin to rot.
11 Very short. Darkvision. Stonecunning. Ancestors will aid you.
12 False leg. Key hidden in leg. Compartments in limbs. Need regular maintenance.


I also made this printout of the table, so that you might have the satisfaction of striking the universes you've already rolled.

Licking the Bowl

Taking the prompt as "petty uses of cosmic power", I also sketched out two other ideas.

Fold Self – a GLOG Spell

When you rest to heal, you can choose not to heal any number of HP, instead leaving part of yourself (astrally) in that location. When casting the spell, roll [dice] over (max HP - HP at that location) to transport yourself and your carried objects to that location. This isn't really teleportation, it's more like squeezing a four-dimensional water wiggly.

Johnny Luckturner – an NPC Outline

Recently broke off from a larger organization and they're not happy about it. All their best people have returned broken or not at all. Maybe a bunch of bumbling patsies could get the job done?

Whenever multiple dice are rolled against Johnny, only the worst value is used (even if they would normally sum). Sneak attacks, advantages, fireballs, etc. all fall flat before his absurd luck. He doesn't know how this works though, and he's a pretty average combatant.

Saturday, November 30, 2019

Podcasts (Fiction)

Following Dan at Throne of Salt, I decided to review some of the podcasts I listen to. Because "Oh God I Listen to So Many" is a sentiment I can share. I found his post very useful, as it finally convinced me to listen to the Magnus Archives, so I hope that someone else may find some gems here.

To keep the list manageable, I'm only listing fiction podcasts for now (not actual play, history, etc.), and I've broken it into "Abandoned", "Caught Up", "Underway", and "On My Radar". "Serialized" means you should probably start at the beginning, and "episodic" means you can probably start anywhere. "Nondiagetic" here means that the people doing the recording know there's an audience, but I've probably applied it inconsistently. "Explicit" means you'll want headphones, at least.


I started these, but have no intention of finishing or catching up right now.

Archive 81

  • serialized (?)
  • horror
  • nondiagetic

If the act of producing The Magnus Archives was itself a ritual of some kind. I just didn't have the time to get a feel for it.

The Signal

  • serialized
  • sci-fi

I remember listening to this, but nothing else about it.

Steal the Stars

  • serialized
  • sci-fi

A para-military organization guards a UFO. Too tense for me. I can do horror, but I can't do suspense generated by human decisions. I imagine this is like how some people just cannot handle cringe comedy.

The Black Tapes

  • episodic
  • horror
  • nondiagetic

A podcaster follows an experienced paranormal investigator looking into his "black tapes"—the tapes he could never explain away. I liked individual episodes well enough, but they felt "unfinished". I didn't care at all for the metaplot, which from what I understand dominates later episodes.

It Makes A Sound

  • serialized

An obsessive fan of an obscure musician searches for an early tape. I think? It wasn't what I was expecting, so I left quickly.

The Other Stories

  • episodic
  • horror

Short horror stories. Seemed workmanlike, but I may revisit it. There is a different podcast also called The Other Stories, which is unrelated.


  • serialized
  • comedy

I was only in it for the first miniseries (5 episodes), starring Ben Partridge of Beef & Dairy Network. If you like Beef & Dairy Network, you'll like that, but the rest is wildly different from what I can tell.

Mission to Zyxx

  • episodic (?)
  • comedy
  • sci-fi

A space-diplomat gets sent to the sticks. It's not bad, but there are too many podcasts. I do enjoy the episodes that crop up on the Max Fun bonus episode feed.

Caught Up

I've listened to all of these that there is to listen to.

Adventures in New America

  • serialized
  • horror
  • comedy

Satire in future America with space vampires. Very camp. I probably would have bounced off it, but I had a lot of time on my hands.

Beef and Dairy Network

  • episodic
  • comedy

Absolutely one of my favorite podcasts, but very difficult to explain. When I try to explain it to friends I just get weird looks. I recommend starting with the first episode ("Dr. David Pin") or episode 52 ("Tusk Henderson", guest starring Nick Offerman).

The Bridge

  • serialized
  • horror

Traffic reports broadcast from a watchtower along the (abandoned) trans-Atlantic bridge. I think I'm a sucker for both alternate history settings and horror about people with boring jobs.


  • serialized
  • comedy
  • sci-fi

Inside the bubble is a city of relative safety, and outside is wasteland with devils in it. The devils occasionally break through and fighting them is subcontracted through a ride-share style app. A weird premise, but well-executed.

Deadly Manners

  • serialized
  • comedy
  • crime

Basically the Clue movie but with different famous people (LeVar Burton, Kristen Bell, Michelle Visage) and a good dose of cold war paranoia.


  • serialized
  • horror
  • explicit

Weird things happening to a horny gay musician spending a winter as a zookeeper in Cleveland Ohio. It's a mood.

Getting On with James Urbaniak

  • episodic
  • comedy

Comedian James Urbaniak, whose voice you know, adopts a variety of personas to deliver deranged self-centered monologues. A true gem, but sadly dead.

In Darkness Vast

  • serialized
  • horror
  • sci-fi

Season 1 is "when Star Trek goes wrong". Season 2 is a about identity and celebrity, but more about survival on a hostile planet. I really enjoyed these, and hope for more.


  • episodic
  • horror (?)

Aims for Doctor Who with Ghosts, but sometimes ends up a little on the "community theater" side of things. Charming though, enough to compensate.

The Orbiting Human Circus

  • serialized

Julian Koster of Neutral Milk Hotel tells surreal Christmas tales for children. If it had actually been broadcast in the 20th century, I expect that listening to it would be a family Christmas tradition, like a sharp-edged Rankin-Bass film.

Pounded in the Butt by My Own Podcast

  • episodic
  • comedy
  • explicit

Podcasting celebrities read the works of Chuck Tingle aloud, sometimes with friends, rarely sober, and apparently with very little preparation.


  • serialized

What if the engine behind the newest voice assistant was actually just a secret warehouse of people with access to all of your personal information? Despite that setup, this is not a satire or sci-fi show. It hit the same "tension comes from people's decisions" note that I found very stressful in Steal the Stars, but I made it through.


  • serialized
  • sci-fi

A scientist is trapped on the surface of a strange planet, with only intermittent communication. A weirdly meditative experience.

A Very Fatal Murder

  • serialized
  • crime
  • comedy

The Onion does Serial. If you're the type of person to read a whole Onion article, you'll get a kick out of this. If you're the type of person to laugh at the headline and then move on, you'll probably be content to know that it exists. The ads are memorable.

Your Attention Please

  • episodic
  • comedy

Monologues delivered without context. Dead at two episodes, but I was laughing out loud at both of them (well, giggling madly).


I have listened to some of these and either finished, or intend to finish.

Alice Isn't Dead

  • serialized
  • horror

Season one, a trucker makes odd deliveries around the US while searching for her wife (Alice) and running from things. Season two is all conspiracies and paranoia. It's really good.

The Cryptonaturalist

  • episodic

Each episode describes an encounter with a fantastical cryptid, and also has some poetry and other ramblings. Took me a couple episodes to get into, but I think it was just me.

The Ghastly Tales Podcast

  • episodic
  • horror

Scottish people read short stories.

Hello From the Magic Tavern

  • serialized
  • fantasy
  • nondiagetic

A podcaster fell through a gap in reality to the mystical land of Foon and this podcast is his lifeline. Every episode he and his friends interview a different resident of Foon. It's like an improv game, where the only rule is that anything anyone says is canon. It's hilarious, and I understand there's a great second season and a spinoff podcast, but there's just so much of it.

Lake Clarity

  • serialized
  • horror

Strange goings-on around Lake Clarity. A pastiche of classic campground horror.

LeVar Burton Reads

  • episodic

LeVar Burton Reads things to you. It's good.

Lightspeed Magazine - Science Fiction and Fantasy

  • episodic

A small stable of narrators read stories from recent issues of Lightspeed Magazine. I'd recommend a lot of them.


  • serialized
  • horror
  • crime (?)

A radio host looks into the historical disappearance of a secluded research facility. Really good tension, satisfyingly banal evil. I haven't listened to season two yet, and I understand there's a show on "Facebook Watch", which I unfortunately do not care enough to learn how to use.

The Lost Cat Podcast

  • serialized (seasons 2 & 4)
  • episodic (seasons 1 & 4)
  • horror

Nominally, the host looks for his lost cat. Each episode in any season is a well-crafted horror story, and in the first three seasons, each one has a brief musical interlude. I really love the worldbuilding.

The Magnus Archives

  • episodic
  • horror

I'm listening to this as I write these reviews, and it occurs to me how many other podcasts must have been aiming for this, and how skillfully it avoids all of their pitfalls. An archivist inherits a backlog of supernatural witness statements, and sets about recording them on tape and sometimes taking new statements. It's a very clean premise: every episode, of necessity, has something supernatural, and then the host is allowed to poke at it after. I appreciate that this poking is usually disbelief, but not always because it might be more likely within the world of the Archives.

Old Gods of Appalachia

  • episodic (?)
  • horror

The Appalachain chain was a prison for unspeakable things, and also there's witches. It's pretty good so far.

The Orphans

  • serialized
  • sci-fi

A bunch of crash-landed amnesiacs try to survive on a weird planet. I'm not far into it yet.

The Thrilling Adventure Hour

  • episodic
  • comedy

Different titles recall different types of show from classic old-time radio, but with modern comedians doing the voice acting. I particularly enjoy "Beyond Belief" (what if Nick and Nora saw ghosts) and "Sparks Nevada: Marshall on Mars" (self-explanatory).

The Truth

  • episodic

Each episode is a fully-produced, sharply-written, short drama. There's a lot of them, and a lot of them walk that same uneasy line as Limetown and Sandra.

Welcome to Night Vale

  • episodic
  • horror
  • comedy

"Community radio from the Twilight Zone". Justified and ancient. Sometimes gets a bit caught up in its mythology, but when it's good it's really good.

Within the Wire

  • serialized
  • horror
  • sci-fi
  • nondiagetic
  • second person

A series of guided meditation tapes help you escape from some kind of dystopian institution. Immersive experience.

Wolf 359

  • serialized
  • sci-fi
  • horror
  • comedy

Comms officer on a remote monitoring station broadcasts his logs into the void. There's a lot of Red Dwarf in the DNA, but also some alternate history world-building and some banal corporate evil.

On My Radar

I haven't even started these yet.

  • Darkest Night
  • DUST
  • Empty
  • Twilight Histories
  • The Walk
  • The White Vault
  • Wooden Overcoats

Monday, November 11, 2019

Discourse & Discord

“The Discourse”

I can't keep up with The Discourse. There's always something happening, and I mostly don't care. But I try to be a good person and also to not support shitty people, so I have to care a little.

I stopped using the "OSR" tag on this blog, because it has been associated with a lot of terrible people, and also it seemed unnecessary1. This was an imperfect solution because "OSR" has a defined sensibility that it was useful to have a name for. (*DREAM is a cool group, but I think it's turning into something different—compare a game like Songbirds V2 with a game like Bastionland.)

Then Zedeck had a thread and pointed out that it was selfish to continue playing in the space but to disown the label. I still respect people who used to be "OSR" and then decided that it didn't actually describe the games they enjoy, or that it wasn't worth dealing with the people. But I'll try to use the "OSR" tag for my stuff where it seems relevant, and also to be a decent person.


Where is the OSR community now? As far as I engage with it: mostly Discord. Many Discord servers are runaway reactors of creativity. Unfortunately, they're also transient, and brief conversations get lost. Here's some things to come of them that I hope others might find useful.

Troika! Backgrounds Jam

I may never play Troika! proper, but it's an infectious idea. Similarly, I don't know if I'll ever sell my games, but seems to be where the cool games are these days. The Troika! Backgrounds Jam was apparently the push I needed to throw something together and put it on itch2. The jam is over, but this clip of how-to seems worth keeping:

(Instructions from Jared Sinclair, used by permission.)

And here is my entry, loosely inspired by Dial H:

I went ahead and put Bloodring up there too:

Alternate Beholders

Something about a beholder demands an answer. "Dungeons and Dragons" is nominally about dragons, but you know you're really playing D&D when you see a beholder. The 5e Monster Manual has three or four variant beholders. The AD&D Monstrous Manual has twelve. Everyone wants to do their own take3.

So the OSR Discord server was brainstorming alternative "beholders": burning wheels of eyes, disco-laser robots, etc. And I had what I thought was a pretty good idea, and now a bona fide meme: An Octopus with Too Many Wands. Now that we've survived one in Spwack's game, I thought I'd take the opportunity to share the idea here for posterity. It's a great monster: it's weird, it's dangerous, it's intuitive, and it makes its own treasure.

(Art from Nate Treme, used by permission.)

1 I call all the games I play "D&D" in speech, even things like Mothership. It's just easier sometimes.back

2 Looking back at my blogging, I find I am unexpectedly motivated by challenges and competitions, even though I am not a competitive person by nature.back

3 What I can find on short notice includes:

But there are many many more, I'm sure.back

Wednesday, October 30, 2019

The City of Emination, a Newer Crobuzon

Following Anne at DIY & Dragons, I've made a city out of some monsters (three "humanoid" minorities and three "bizarre" creatures).



Recent refugees of distant war, they are not trusted. Good merchants, negotiators, tour guides. Some rumors about doppelgangers:

  • They bleed a different color (true, but so do some Aasimar).
  • They can read minds (true).
  • They can't stand garlic (false).
  • They'll replace the recent dead (sometimes: they consider dead people's identities "unclaimed").
  • They'll leave you to raise their children for them (false).
  • They'll steal your stuff (rarely: they have different ideas about property).
  • They can't drink alcohol (true, or at least, they can't keep it down).


Unable to enter the inner city (which is hallowed ground) sprawl has forced the ghouls to integrate. Well-fed, they work as laborers. Otherwise they don't think so good and eventually go dormant. Those that let hunger drive their actions are swiftly dealt with.


Aristocratic upper-class, descended from celestials that followed Wormwood (they claim). The original celestials have long since moved on, leaving their progeny to manage the city.



In the city square, a mound of unrotting flesh. It spasms in the rain, and it's good luck if it twitches when you spit on it. It's unknown how it got there, as Emination is landlocked.

The Angel Wormwood (Solar)

Millenia ago the angel Wormwood came to the mountains and there made itself a throne. It never speaks. It has not moved. Ancient pilgrims cut paths through the mountains from all sides, making Emination into an important crossroads.

Earth Elementals

Before the city were the mountains, and the elementals there. Taking the forms of rams and bears, they cut swathes through the outer city until they smash on the inner city walls, raining down charged earth. They always travel in a North-South direction and are more active around geomagnetic reversals.

Other New New Crobuza

There are also some entries from 2009 collected at The Book of Judd. Sphinxcorland (Sea of Stars) was a late addition (2010).

Sunday, October 27, 2019

Other Palaces

I entered the 200 word RPG challenge! I nitpick and revise constantly, so you can see the final version here, and past versions here (I am bad at GitHub). I wanted a widget to see my revisions side-by-side, so there's also this:


(Art from Evlyn Moreau, used by permission.)


  • In the swapper, I did not mark the changes when lists were re-ordered. Between versions 0.4 and 0.5, I made all the lists alphabetical, because I worry about limiting my imagination by consistently "matching" e.g. "kitchen" and "food". I also think it's more presentable. (In longer lists I do this to catch duplicates.)
  • Due to my personal refereeing style, CHECKs are very rare in practice, so I had a hard time deciding a good value for STAT. The expected damage of an attack that causes a CHECK is 4, occurring on 5 in 6 attacks. Therefore, if STAT=18, there is a 1 in 4 chance of failing a CHECK as a result of the first attack. At STAT=16 this is 1 in 3, and at STAT=12 this is 1 in 2.

The Future

I've been working on the set-up of a specific palace, "The Palace Semi-Infinite". I had some wonderful playtesters who were willing to just mess-up a a palace, but I think something with more direction might have better staying power. I'm keeping the palace generation parts, but I may end up scrapping the game system for Into the Odd or something.

That said, the system is a svelte 61 words in the official word-counter, so it may make a reasonable base for future entries. I'm eager to see what other people have cooked up when I have a chance to sift through them.