GNU Terry Pratchett

Oliver Brown
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The phrase “GNU Terry Pratchett” originates from one of the Discworld novels, “Going Postal,” where it is used as a code or message passed between characters to remember the deceased.

Specifically, there is a communication system known as “the clacks”, and there part of the way that system works involves additional metadata messages being sent (known as “the overhead”).

I only recently discovered that people have been embedding that message in all sorts of things as a way to memorialize Terry. One of the places they do this in the headers of websites.

So, you will now see an additional header in all the HTTP responses on this site:

X-Clacks-Overhead: GNU Terry Pratchett

Star Trek episode title word miscellany

Oliver Brown
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After investigating Star Trek episode titles with interesting characters, lets look at ones with interesting words.

Numbers

I already included this as a side note in the previous post, but many episodes have numbers as words, with each series having at least one.

Title Series Episode
The Galileo Seven TOS 1x13
One of Our Planets Is Missing TAS 1x03
Angel One TNG 1x15
One Little Ship DS9 6x14
One VOY 4x25
Thirty Days VOY 5x09
One Small Step VOY 6x08
The Haunting of Deck Twelve VOY 6x25
Friendship One VOY 7x21
Shuttlepod One ENT 1x16
Two Days and Two Nights ENT 1x25
First Flight ENT 2x24
Babel One ENT 4x12

Ordinals

Title Series Episode
First Contact TNG 4x15
The Nth Degree TNG 4x19
The First Duty TNG 5x19
Second Chances TNG 6x24
Second Sight DS9 2x09
Second Skin DS9 3x05
The Seventh ENT 2x07
First Flight ENT 2x24

Non-English words

This is probably the collection that caused me the most difficulty in deciding what should be included.

I settled on:

  • Actual words (no 11:59 or E²)
  • Real word languages
  • Not proper nouns (especially names of characters)

Considering all that, there are in fact only two non-English languages used in the titles of Star Trek episodes:

French

Title Series Episode
The Menagerie TOS 1x15
Ménage à Troi TNG 3x24
Vis à Vis VOY 4x20

Latin

Title Series Episode
Sub Rosa TNG 7x14
Dramatis Personae DS9 1x18
Inter Arma Enim Silent Leges DS9 7x16
Non Sequitur VOY 2x05
Terra Nova ENT 1x06
Vox Sola ENT 1x22
Terra Prime ENT 4x21

Honorable mentions

One Klingon word, and one Vulcan word that is only probably a proper noun.

Title Series Episode
Looking for par’Mach in All the Wrong Places DS9 5x03
Kir’Shara ENT 4x09

Character names

Who has the privilege of being named in an episode title? Again, there are surprising edge cases so I’ve split it up into several groups.

  • Q appears in the most titles.
  • Two titles mention two characters: Datalore and Ménage à Troi (which I assumed, in the spirit of the episode, is a reference to both Deanna Troi and Lwaxana Troi).

Direct character references

Definite direct references to characters in Star Trek.

Title Series Episode Character
Mudd’s Women TOS 1x03 Harry Mudd
Charlie X TOS 1x07 Charles Evans
Miri TOS 1x11 Miri
I, Mudd TOS 2x12 Harry Mudd
Elaan of Troyius TOS 2x02 Elaan
Spock’s Brain TOS 3x06 Spock
Plato’s Stepchildren TOS 3x12 Plato
Mudd’s Passion TAS 1x10 Harry Mudd
Bem TAS 2x02 Bem
Hide and Q TNG 1x11 Q
Elementary, Dear Data TNG 2x03 Data
The Outrageous Okona TNG 2x04 Thadiun Okona
Q Who? TNG 2x16 Q
Deja Q TNG 3x13 Q
Sarek TNG 3x23 Sarek
Ménage à Troi TNG 3x24 Deanna Troi
Ménage à Troi TNG 3x24 Lwaxana Troi
Data’s Day TNG 4x11 Data
Darmok TNG 5x02 Darmok
Ensign Ro TNG 5x03 Ro Laren
True Q TNG 6x06 Q
A Fistful of Datas TNG 6x08 Data
Aquiel TNG 6x13 Aquiel Uhnari
Dax DS9 1x08 Dax
Melora DS9 2x06 Melora Pazlar
The House of Quark DS9 3x03 Quark
Shakaar DS9 3x24 Shakaar Edon
Our Man Bashir DS9 4x10 Julian Bashir
Sons of Mogh DS9 4x15 Mogh
Caretaker VOY 1x01 The Caretaker
Jetrel VOY 1x15 Ma’Bor Jetrel
Tuvix VOY 2x24 Tuvix
The Q and the Grey VOY 3x11 Q
One VOY 4x25 One
Alice VOY 6x05 Alice
Rajiin ENT 3x04 Rajiin

Other characters

References to people, either fictional or real that were not actually characters in Star Trek.

Title Series Episode Character
The Galileo Seven TOS 1x13 Galileo Galilei
The Mark of Gideon TOS 3x17 Gideon
Requiem for Methuselah TOS 3x21 Methuselah
The Icarus Factor TNG 2x14 Icarus
Daedalus ENT 4x10 Daedalus

Indirect

Indirect references to characters that are awkward in some way.

Title Series Episode Character
Datalore TNG 1x14 Data
Datalore TNG 1x14 Lore
Qpid TNG 4x20 Q
Q-Less DS9 1x07 Q
Tinker Tenor Doctor Spy VOY 6x04 The Doctor

Accidental

Character names that are not intended to be references to Star Trek characters. Mainly The Doctor from Voyager, but also Q2 which was the script name for the member of the Q Continuum in the TNG episode Deja Q.

Title Series Episode Character
We’ll Always Have Paris TNG 1x24 Thomas Paris
Doctor Bashir, I Presume DS9 5x16 The Doctor
Q2 VOY 7x19 Q2
Dear Doctor ENT 1x13 The Doctor
Doctor’s Orders ENT 3x16 The Doctor

One

There is one special character name that is clearly not intended to be a reference, but comes up a lot - One from Voyager.

Title Series Episode Character
One of Our Planets Is Missing TAS 1x03 One
Where No One Has Gone Before TNG 1x06 One
Angel One TNG 1x15 One
One Little Ship DS9 6x14 One
One Small Step VOY 6x08 One
Friendship One VOY 7x21 One
Shuttlepod One ENT 1x16 One
Babel One ENT 4x12 One

Q

And finally, the letter Q appears a few times while clearly not being a reference to Q.

Title Series Episode Character
The Squire of Gothos TOS 1x18 Q
Requiem for Methuselah TOS 3x21 Q
Time Squared TNG 2x13 Q
Quality of Life TNG 6x09 Q
Aquiel TNG 6x13 Q
Rules of Acquisition DS9 2x07 Q
The Maquis DS9 2x19 Q
The House of Quark DS9 3x03 Q
Equilibrium DS9 3x04 Q
The Quickening DS9 4x24 Q
Inquisition DS9 6x18 Q
Non Sequitur VOY 2x05 Q
Equinox VOY 5x26 Q
Q2 VOY 7x19 Q
Acquisition ENT 1x19 Q

Just the character

One bonus list considering all the above - titles that are just a character name.

Title Series Episode Character
Miri TOS 1x11 Miri
Bem TAS 2x02 Bem
Sarek TNG 3x23 Sarek
Darmok TNG 5x02 Darmok
Aquiel TNG 6x13 Aquiel
Dax DS9 1x08 Dax
Melora DS9 2x06 Melora Pazlar
Shakaar DS9 3x24 Shakaar Edon
Caretaker VOY 1x01 The Caretaker
Jetrel VOY 1x15 Jetrel
Tuvix VOY 2x24 Tuvix
One VOY 4x25 One
Alice VOY 6x05 Alice
Q2 VOY 7x19 Q
Rajiin ENT 3x04 Rajiin
Daedalus ENT 4x10 Daedalus

Sortable Discworld audiobook release date list

Oliver Brown
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As an Amazon Associate I earn from qualifying purchases. See here for more information.

New audio versions of all* of the Discworld books are being produced. I’ve made a few posts tracking the release dates. Since then I’ve updated the blog to support nice sortable tables.

So here are the the books listed on Audible as of 21st May, 2023 in a single table (now with primary narrator). All columns should be usefully sortable.

If you don’t already have an Audible membership, you can get a 30-day free trial (UK).

New Discworld audiobook release dates

Title Series Release date Narrator
Hogfather Death 20 2021-12-09 Sian Clifford
Equal Rites Witches 3 2022-04-28 Indira Varma
Wyrd Sisters Witches 6 2022-04-28 Indira Varma
Witches Abroad Witches 12 2022-04-28 Indira Varma
Lords and Ladies Witches 14 2022-04-28 Indira Varma
Maskerade Witches 18 2022-04-28 Indira Varma
Carpe Jugulum Witches 23 2022-04-28 Indira Varma
Small Gods Standalone 13 2022-04-28 Andy Serkis
The Colour of Magic Wizards 1 2022-07-07 Colin Morgan
The Light Fantastic Wizards 2 2022-07-07 Colin Morgan
Sourcery Wizards 5 2022-07-07 Colin Morgan
Eric Wizards 9 2022-07-07 Colin Morgan
Interesting Times Wizards 17 2022-07-07 Colin Morgan
The Last Continent Wizards 22 2022-07-07 Colin Morgan
Unseen Academicals Wizards 37 2022-07-07 Colin Morgan
The Amazing Maurice and His Educated Rodents Standalone 28 2022-10-06 Ariyon Bakare
Mort Death 4 2022-10-27 Sian Clifford
Reaper Man Death 11 2022-10-27 Sian Clifford
Soul Music Death 16 2022-10-27 Sian Clifford
Thief of Time Death 26 2022-10-27 Sian Clifford
Pyramids Standalone 7 2023-03-30 Alfred Enoch
The Truth Standalone 25 2023-02-23 Mathew Baynton
Monstrous Regiment Standalone 31 2023-02-23 Katherine Parkinson
Going Postal Moist von Lipwig 33 2023-02-23 Richard Coyle
Making Money Moist von Lipwig 36 2023-02-23 Richard Coyle
Raising Steam Moist von Lipwig 40 2023-02-23 Richard Coyle
Moving Pictures Standalone 10 2023-05-18 Jason Isaacs
Guards! Guards! The Watch 8 2023-05-25 Jon Culshaw
Men at Arms The Watch 15 2023-05-25 Jon Culshaw
Feet of Clay The Watch 19 2023-05-25 Jon Culshaw
Jingo The Watch 21 2023-05-25 Jon Culshaw
The Fifth Elephant The Watch 24 2023-05-25 Jon Culshaw
Night Watch The Watch 29 2023-05-25 Jon Culshaw
Thud! The Watch 34 2023-05-25 Jon Culshaw
Snuff The Watch 39 2023-05-25 Jon Culshaw
The Wee Free Men Tiffany Aching 30 2023-06-15 Indira Varma
A Hat Full of Sky Tiffany Aching 32 2023-06-15 Indira Varma
Wintersmith Tiffany Aching 35 2023-06-15 Indira Varma
I Shall Wear Midnight Tiffany Aching 38 2023-06-15 Indira Varma
The Sheperd's Crown Tiffany Aching 41 2023-06-15 Indira Varma

* There are 41 Discworld books. The website says “40 magnificent new recordings”. The one that seems to be missing is “The Last Hero”.

Star Trek episode title character miscellany

Oliver Brown
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While doing other more systematic investigations of Star Trek episode titles, I made notes of interesting things I spotted.

Here are some collections of episode titles with interesting characters.

Q puns

Most episodes featuring Q had a pun in the title:

Title Series Episode
Hide and Q TNG 1x11
Q Who? TNG 2x16
Deja Q TNG 3x13
Qpid TNG 4x20
True Q TNG 6x06
Q-Less DS9 1x07
The Q and the Grey VOY 3x11
Q2 VOY 7x19
See the ones that did not
Title Series Episode
Encounter at Farpoint TNG 1x01
Tapestry TNG 6x15
All Good Things… TNG 7x25
Death Wish VOY 2x18

Interestingly, Q has so far made a further appearance in Lower Decks and nine in Star Trek Picard, and none of them had puns in the title.

Digits

Title Series Episode
11001001 TNG 1x16
The Siege of AR-558 DS9 7x08
The 37’s VOY 2x01
11:59 VOY 5x23
Q2 VOY 7x19
ENT 4x05
Cold Station 12 ENT 3x21
See titles containing numbers as words

Numbers

Title Series Episode
The Galileo Seven TOS 1x13
One of Our Planets Is Missing TAS 1x03
Angel One TNG 1x15
First Contact TNG 4x15
The Nth Degree TNG 4x19
The First Duty TNG 5x19
Second Chances TNG 6x24
Second Sight DS9 2x09
Second Skin DS9 3x05
One Little Ship DS9 6x14
One VOY 4x25
Thirty Days VOY 5x09
One Small Step VOY 6x08
The Haunting of Deck Twelve VOY 6x25
Friendship One VOY 7x21
Shuttlepod One ENT 1x16
Two Days and Two Nights ENT 1x25
The Seventh ENT 2x07
First Flight ENT 2x24
Babel One ENT 4x12

Punctuation and other interesting characters

Containing '

There are so many titles with apostrophes I decided to break it down by use:

Possessive

Title Series Episode
Mudd’s Women TOS 1x03
Friday’s Child TOS 1x03
Spock’s Brain TOS 3x06
Plato’s Stepchildren TOS 3x12
Mudd’s Passion TAS 1x10
How Sharper Than a Serpent’s Tooth TAS 2x05
Yesterday’s Enterprise TNG 3x15
Captain’s Holiday TNG 3x19
Data’s Day TNG 4x11
Devil’s Due TNG 4x13
Galaxy’s Child TNG 4x16
The Mind’s Eye TNG 4x24
Time’s Arrow TNG 5x26
Journey’s End TNG 7x20
In Purgatory’s Shadow DS9 5x14
By Inferno’s Light DS9 5x15
Time’s Orphan DS9 6x24
The Emperor’s New Cloak DS9 7x12
Future’s End VOY 3x08
Dragon’s Teeth VOY 6x07
Child’s Play VOY 6x19
Doctor’s Orders ENT 3x16

Part of an alien word

Title Series Episode
The Jem’Hadar DS9 2x26
Looking for par’Mach in All the Wrong Places DS9 5x03
Shadows of P’Jem ENT 1x15
Kir’Shara ENT 4x09

Contraction

Title Series Episode
We’ll Always Have Paris TNG 1x24
It’s Only a Paper Moon DS9 7x10

Clarifying a plural

Title Series Episode
The 37’s VOY 2x01
See the full list in order
Title Series Episode
Mudd’s Women TOS 1x03
Friday’s Child TOS 1x03
Spock’s Brain TOS 3x06
Plato’s Stepchildren TOS 3x12
Mudd’s Passion TAS 1x10
How Sharper Than a Serpent’s Tooth TAS 2x05
We’ll Always Have Paris TNG 1x24
Yesterday’s Enterprise TNG 3x15
Captain’s Holiday TNG 3x19
Data’s Day TNG 4x11
Devil’s Due TNG 4x13
Galaxy’s Child TNG 4x16
The Mind’s Eye TNG 4x24
Time’s Arrow TNG 5x26
Journey’s End TNG 7x20
The Jem’Hadar DS9 2x26
Looking for par’Mach in All the Wrong Places DS9 5x03
In Purgatory’s Shadow DS9 5x14
By Inferno’s Light DS9 5x15
Time’s Orphan DS9 6x24
It’s Only a Paper Moon DS9 7x10
The Emperor’s New Cloak DS9 7x12
The 37’s VOY 2x01
Future’s End VOY 3x08
Dragon’s Teeth VOY 6x07
Child’s Play VOY 6x19
Shadows of P’Jem ENT 1x15
Doctor’s Orders ENT 3x16
Kir’Shara ENT 4x09

Containing -

Several episode titles contain a hyphen. One episode contains two. The producers and/or writers probably intended an em dash or similar but were likely limited to hyphens for technical reasons.

Title Series Episode
Operation -‌- Annihilate! TOS 1x29
The Magicks of Megas-Tu TAS 1x08
The Counter-Clock Incident TAS 2x06
Q-Less DS9 1x07
Trials and Tribble-ations DS9 5x06
The Siege of AR-558 DS9 7x08
Badda-Bing, Badda-Bang DS9 7x15

Containing ,

Several episode titles contain commas. One had the option to include two with an Oxford comma.

Title Series Episode
Mirror, Mirror TOS 2x10
I, Mudd TOS 2x12
More Tribbles, More Troubles TAS 1x05
Elementary, Dear Data TNG 2x03
I, Borg TNG 5x23
Doctor Bashir, I Presume DS9 5x16
Treachery, Faith and the Great River DS9 7x06
Badda-Bing, Badda-Bang DS9 7x15
Author, Author VOY 7x20
In a Mirror, Darkly ENT 4x18

Containing ?

Title Series Episode
What Are Little Girls Made Of? TOS 1x09
Who Mourns for Adonais? TOS 1x04
Is There in Truth No Beauty? TOS 3x07
Q Who? TNG 2x16
Who Watches the Watchers? TNG 3x04
Who Mourns for Morn? DS9 6x12

Containing

Title Series Episode
All Good Things… TNG 7x25
Let He Who Is Without Sin… DS9 5x07
When It Rains… DS9 7x21
These Are the Voyages… ENT 4x22

Containing :

Title Series Episode
Assignment: Earth TOS 2x26
Course: Oblivion VOY 5x18
11:59 VOY 5x23

Containing !

Title Series Episode
Operation -‌- Annihilate! TOS 1x29
Bride of Chaotica! VOY 5x12

Containing à (and é)

There are a pair of episodes with accented characters (which have recently been joined by Võx from Picard).

Title Series Episode
Ménage à Troi TNG 3x24
Vis à Vis VOY 4x20

Containing ²

Title Series Episode
ENT 3x21

An aside for the titles of Picard

Oliver Brown
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Star Trek Picard logo

Star Trek Picard season three has just completed. It was not perfect but was probably the best live action Star Trek since Enterprise.

In honor of this, here is a quick analysis of the episode titles.

I’m not including Picard in the main analysis for consistency for now. There is also a small chance there may be more episodes (or possibly something else #StarTrekLegacy).

Title length

Picard does not challenge for overall shortest or longest title.

Shortest

Title Length Episode
Võx 3 letters 3x09

Like other series, it has several single word titles:

Title Length Episode
Remembrance 11 letters 1x01
Nepenthe 8 letters 1x07
Penance 7 letters 2x02
Assimilation 12 letters 2x03
Watcher 7 letters 2x04
Monsters 8 letters 2x07
Mercy 5 letters 2x08
Farewell 8 letters 2x10
Disengage 9 letters 3x02
Imposters 9 letters 3x05
Dominion 8 letters 3x07
Surrender 9 letters 3x08
Võx 3 letters 3x09

Longest

Title Length Episode
The End is the Beginning 24 letters 1x03
Title Length Episode
The End is the Beginning 5 words 1x03
Fly me to the Moon 5 words 2x05

Single word titles

The overall single word title stats are very similar to Enterprise.

Series Enterprise Picard
Total 42 13
Percentage 44.68 % 44.83 %
Shortest 2 3
Longest 12 12
Average 7.79 8
See comparison with other series'
Series TOS TAS TNG DS9 VOY ENT PIC
Total 5 3 50 42 77 42 13
Percentage 6.33 % 13.64 % 29.76 % 24.71 % 48.13 % 44.68 % 44.83 %
Shortest 4 3 4 3 2 2 3
Longest 13 10 16 12 14 12 12
Average 7.6 7.33 7.92 8.1 7.81 7.79 8

When split by season there is a lot variation though. I expect this to be true of most Star Trek series after Enterprise - the seasons are generally shorter and the serial nature means there are more likely to be patterns within seasons that don’t hold between them.

Season 1 2 3
Total 2 6 5
Percentage 22.22 % 60.00 % 50.00 %
Shortest 8 5 3
Longest 11 12 9
Average 9.5 7.83 7.6

Ionic episodes

Two new “ion” titles (but no “ions”):

Title Length Episode
Assimilation 12 letters 2x03
Dominion 8 letters 3x07

Image copyright © Paramount Global and used under fair use.

Similar Star Trek episode titles

Oliver Brown
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With nearly 700 episodes, there were bound to be some that are similar to each other. But which are most similar? And what do we mean by similar?

Summary

Before I go into the more technical analysis, I shall begin with some headlines.

Not technically part of this analysis but there are two Star Trek movies that share a title with an episode (if you ignore the “Star Trek” part of the title):

Title Series Episode Title
First Contact TNG 4x15 Star Trek: First Contact
Nemesis VOY 4x04 Star Trek Nemesis

There are three pairs of titles that differ by only one character. Two of them are just a final “s” as part of a plural:

Title Series Episode Title Series Episode
The Survivor TAS 1x06 The Survivors TNG 3x03
Facets DS9 3x25 Faces VOY 1x14
Demon VOY 4x24 Demons ENT 4x20

There are three pairs of titles that differ only by a leading “the”:

Title Series Episode Title Series Episode
The Eye of the Beholder TAS 1x15 Eye of the Beholder TNG 7x18
The Emissary TNG 2x20 Emissary DS9 1x01
The Muse DS9 4x21 Muse VOY 6x22

One of the more significant lines in Star Trek has both its variations appear as titles:

Title Series Episode Title Series Episode
Where No Man Has Gone Before TOS 1x01 Where No One Has Gone Before TNG 1x06

There is also a TNG episode that is specifically a sequel of sorts to an earlier episode with a similar title:

Title Series Episode Title Series Episode
The Naked Time TOS 1x06 The Naked Now TNG 1x03

A pair of episodes with weirdly similar titles, but in a way that isn’t easy to define:

Title Series Episode Title Series Episode
Beyond the Farthest Star TAS 1x01 Far Beyond the Stars DS9 6x13

There is an interesting prefix that appears three times in TNG, and only in TNG:

Title Series Episode
A Matter of Honor TNG 2x08
A Matter of Perspective TNG 3x14
A Matter of Time TNG 5x09

Four incidents worthy of naming:

Title Series Episode
The Terratin Incident TAS 1x11
The Counter-Clock Incident TAS 2x06
The Enterprise Incident TOS 3x04
The Andorian Incident ENT 1x07

Technical details

Below I present the top 10 pairs of similar episodes, with four different measures of similarity:

  • Levenshtein distance - Informally, the number of single character edits needed to change one title into another.
  • Prefix - The number of characters at the start of the titles that are in common (ignoring case).
  • Suffix - The number of characters at the end of the titles that are in common (ignoring case).
  • Contains - If one title is contained entirely within another (possibly at the start or end), then the length of the contained title (0 otherwise).

Additionally each one is presented with an absolute version, and another normalized to the length of the longest title.

Most similar titles

Levenshtein (absolute)

Title Series Episode Distance Title Series Episode
The Survivor TAS 1x06 1 The Survivors TNG 3x03
Facets DS9 3x25 1 Faces VOY 1x14
Demon VOY 4x24 1 Demons ENT 4x20
The Cage TOS 0x01 2 The Game TNG 5x06
The Cage TOS 0x01 2 The Chase TNG 6x20
Wink of an Eye TOS 3x13 2 Blink of an Eye VOY 6x12
The Loss TNG 4x10 2 The Host TNG 4x23
The Chase TNG 6x20 2 The Chute VOY 3x03
Masks TNG 7x17 2 Oasis ENT 1x20
Genesis TNG 7x19 2 Nemesis VOY 4x04

Levenshtein (normalized)

Title Series Episode Similarity Title Series Episode
The Survivor TAS 1x06 92.3% The Survivors TNG 3x03
Where No Man Has Gone Before TOS 1x01 89.3% Where No One Has Gone Before TNG 1x06
Wink of an Eye TOS 3x13 86.7% Blink of an Eye VOY 6x12
Facets DS9 3x25 83.3% Faces VOY 1x14
Demon VOY 4x24 83.3% Demons ENT 4x20
The Eye of the Beholder TAS 1x15 82.6% Eye of the Beholder TNG 7x18
Inquisition DS9 6x18 81.8% Acquisition ENT 1x19
Profit and Loss DS9 2x17 80.0% Profit and Lace DS9 6x23
The Cage TOS 0x01 77.8% The Chase TNG 6x20
The Chase TNG 6x20 77.8% The Chute VOY 3x03

Prefix (absolute)

Title Series Episode Similarity Title Series Episode
Who Mourns for Adonais? TOS 1x04 15 Who Mourns for Morn? DS9 6x12
The Alternative Factor TOS 1x20 12 The Alternate DS9 2x12
The Survivor TAS 1x06 12 The Survivors TNG 3x03
Once Upon a Planet TAS 1x09 12 Once Upon a Time VOY 5x05
A Matter of Honor TNG 2x08 12 A Matter of Perspective TNG 3x14
A Matter of Honor TNG 2x08 12 A Matter of Time TNG 5x09
A Matter of Perspective TNG 3x14 12 A Matter of Time TNG 5x09
Profit and Loss DS9 2x17 12 Profit and Lace DS9 6x23
Eye of the Beholder TNG 7x18 11 Eye of the Needle VOY 1x07
The Naked Time TOS 1x06 10 The Naked Now TNG 1x03

Prefix (normalized)

Title Series Episode Similarity Title Series Episode
The Survivor TAS 1x06 92.3% The Survivors TNG 3x03
Demon VOY 4x24 83.3% Demons ENT 4x20
Profit and Loss DS9 2x17 80.0% Profit and Lace DS9 6x23
Remember Me TNG 4x05 72.7% Remember VOY 3x06
The Naked Time TOS 1x06 71.4% The Naked Now TNG 1x03
A Matter of Honor TNG 2x08 70.6% A Matter of Time TNG 5x09
Starship Mine TNG 6x18 69.2% Starship Down DS9 4x07
Once Upon a Planet TAS 1x09 66.7% Once Upon a Time VOY 5x05
The Child TNG 2x01 66.7% The Chase TNG 6x20
The Child TNG 2x01 66.7% The Chute VOY 3x03

Suffix (absolute)

Title Series Episode Similarity Title Series Episode
The Eye of the Beholder TAS 1x15 19 Eye of the Beholder TNG 7x18
In the Hands of the Prophets DS9 1x20 17 Tears of the Prophets DS9 6x26
Where No Man Has Gone Before TOS 1x01 16 Where No One Has Gone Before TNG 1x06
Wink of an Eye TOS 3x13 13 Blink of an Eye VOY 6x12
Ship in a Bottle TNG 6x12 12 Message in a Bottle VOY 4x14
The Ensigns of Command TNG 3x02 11 Chain of Command TNG 6x10
Rules of Acquisition DS9 2x07 11 Acquisition ENT 1x19
The Terratin Incident TAS 1x11 10 The Andorian Incident ENT 1x07
Conspiracy TNG 1x25 10 The Voyager Conspiracy VOY 6x09
Once More Unto the Breach DS9 7x07 10 The Breach ENT 2x21

Suffix (normalized)

Title Series Episode Similarity Title Series Episode
Wink of an Eye TOS 3x13 86.7% Blink of an Eye VOY 6x12
The Eye of the Beholder TAS 1x15 82.6% Eye of the Beholder TNG 7x18
Inquisition DS9 6x18 81.8% Acquisition ENT 1x19
Emergence TNG 7x23 70.0% Divergence ENT 4x16
Code of Honor TNG 1x04 69.2% Day of Honor VOY 4x03
Obsession TOS 2x18 66.7% Accession DS9 4x17
Angel One TNG 1x15 66.7% Babel One ENT 4x12
The Emissary TNG 2x20 66.7% Emissary DS9 1x01
Friday’s Child TOS 1x03 64.3% Galaxy’s Child TNG 4x16
Heart of Glory TNG 1x20 64.3% Blaze of Glory DS9 5x23

Contains (absolute)

Title Series Episode Similarity Title Series Episode
The Eye of the Beholder TAS 1x15 19 Eye of the Beholder TNG 7x18
The Survivor TAS 1x06 12 The Survivors TNG 3x03
Rules of Acquisition DS9 2x07 11 Acquisition ENT 1x19
Conspiracy TNG 1x25 10 The Voyager Conspiracy VOY 6x09
Once More Unto the Breach DS9 7x07 10 The Breach ENT 2x21
The Enemy Within TOS 1x04 9 The Enemy TNG 3x07
And the Children Shall Lead TOS 2x05 9 The Child TNG 2x01
The Cloud Minders TOS 3x19 9 The Cloud VOY 1x06
The Enemy TNG 3x07 9 Face of the Enemy TNG 6x14
The Siege DS9 2x03 9 The Siege of AR-558 DS9 7x08

Contains (normalized)

Title Series Episode Similarity Title Series Episode
The Survivor TAS 1x06 92.3% The Survivors TNG 3x03
Demon VOY 4x24 83.3% Demons ENT 4x20
The Eye of the Beholder TAS 1x15 82.6% Eye of the Beholder TNG 7x18
Remember Me TNG 4x05 72.7% Remember VOY 3x06
The Emissary TNG 2x20 66.7% Emissary DS9 1x01
The Ship DS9 5x02 66.7% The Shipment ENT 3x07
Paradise DS9 2x14 61.5% Paradise Lost DS9 4x12
One VOY 4x25 60.0% Drone VOY 5x02
The Enemy Within TOS 1x04 56.2% The Enemy TNG 3x07
Shattered Mirror DS9 4x20 56.2% Shattered VOY 7x11

Most similar titles without leading “the”

Levenshtein (absolute)

Title Series Episode Distance Title Series Episode
The Eye of the Beholder TAS 1x15 0 Eye of the Beholder TNG 7x18
The Emissary TNG 2x20 0 Emissary DS9 1x01
The Muse DS9 4x21 0 Muse VOY 6x22
The Survivor TAS 1x06 1 The Survivors TNG 3x03
Haven TNG 1x05 1 The Raven VOY 4x06
Facets DS9 3x25 1 Faces VOY 1x14
Demon VOY 4x24 1 Demons ENT 4x20
Night VOY 5x01 1 The Fight VOY 5x19
The Cage TOS 0x01 2 The Game TNG 5x06
The Cage TOS 0x01 2 The Chase TNG 6x20

Levenshtein (normalized)

Title Series Episode Similarity Title Series Episode
The Eye of the Beholder TAS 1x15 100.0% Eye of the Beholder TNG 7x18
The Emissary TNG 2x20 100.0% Emissary DS9 1x01
The Muse DS9 4x21 100.0% Muse VOY 6x22
Where No Man Has Gone Before TOS 1x01 89.3% Where No One Has Gone Before TNG 1x06
The Survivor TAS 1x06 88.9% The Survivors TNG 3x03
Wink of an Eye TOS 3x13 86.7% Blink of an Eye VOY 6x12
Facets DS9 3x25 83.3% Faces VOY 1x14
Demon VOY 4x24 83.3% Demons ENT 4x20
Inquisition DS9 6x18 81.8% Acquisition ENT 1x19
Haven TNG 1x05 80.0% The Raven VOY 4x06

Prefix (absolute)

Title Series Episode Similarity Title Series Episode
The Eye of the Beholder TAS 1x15 19 Eye of the Beholder TNG 7x18
Who Mourns for Adonais? TOS 1x04 15 Who Mourns for Morn? DS9 6x12
Once Upon a Planet TAS 1x09 12 Once Upon a Time VOY 5x05
A Matter of Honor TNG 2x08 12 A Matter of Perspective TNG 3x14
A Matter of Honor TNG 2x08 12 A Matter of Time TNG 5x09
A Matter of Perspective TNG 3x14 12 A Matter of Time TNG 5x09
Profit and Loss DS9 2x17 12 Profit and Lace DS9 6x23
The Eye of the Beholder TAS 1x15 11 Eye of the Needle VOY 1x07
Eye of the Beholder TNG 7x18 11 Eye of the Needle VOY 1x07
Return to Tomorrow TOS 2x22 10 Return to Grace DS9 4x14

Prefix (normalized)

Title Series Episode Similarity Title Series Episode
The Eye of the Beholder TAS 1x15 100.0% Eye of the Beholder TNG 7x18
The Emissary TNG 2x20 100.0% Emissary DS9 1x01
The Muse DS9 4x21 100.0% Muse VOY 6x22
The Survivor TAS 1x06 88.9% The Survivors TNG 3x03
Demon VOY 4x24 83.3% Demons ENT 4x20
Profit and Loss DS9 2x17 80.0% Profit and Lace DS9 6x23
Remember Me TNG 4x05 72.7% Remember VOY 3x06
The Hunted TNG 3x11 71.4% Hunters VOY 4x15
A Matter of Honor TNG 2x08 70.6% A Matter of Time TNG 5x09
Starship Mine TNG 6x18 69.2% Starship Down DS9 4x07

Suffix (absolute)

Title Series Episode Similarity Title Series Episode
The Eye of the Beholder TAS 1x15 19 Eye of the Beholder TNG 7x18
In the Hands of the Prophets DS9 1x20 17 Tears of the Prophets DS9 6x26
Where No Man Has Gone Before TOS 1x01 16 Where No One Has Gone Before TNG 1x06
Wink of an Eye TOS 3x13 13 Blink of an Eye VOY 6x12
Ship in a Bottle TNG 6x12 12 Message in a Bottle VOY 4x14
The Ensigns of Command TNG 3x02 11 Chain of Command TNG 6x10
Rules of Acquisition DS9 2x07 11 Acquisition ENT 1x19
The Terratin Incident TAS 1x11 10 The Andorian Incident ENT 1x07
Conspiracy TNG 1x25 10 The Voyager Conspiracy VOY 6x09
Friday’s Child TOS 1x03 9 Galaxy’s Child TNG 4x16

Suffix (normalized)

Title Series Episode Similarity Title Series Episode
The Eye of the Beholder TAS 1x15 100.0% Eye of the Beholder TNG 7x18
The Emissary TNG 2x20 100.0% Emissary DS9 1x01
The Muse DS9 4x21 100.0% Muse VOY 6x22
Wink of an Eye TOS 3x13 86.7% Blink of an Eye VOY 6x12
Inquisition DS9 6x18 81.8% Acquisition ENT 1x19
Haven TNG 1x05 80.0% The Raven VOY 4x06
Night VOY 5x01 80.0% The Fight VOY 5x19
Descent TNG 6x26 71.4% The Ascent DS9 5x09
Emergence TNG 7x23 70.0% Divergence ENT 4x16
Code of Honor TNG 1x04 69.2% Day of Honor VOY 4x03

Contains (absolute)

Title Series Episode Similarity Title Series Episode
The Eye of the Beholder TAS 1x15 19 Eye of the Beholder TNG 7x18
Rules of Acquisition DS9 2x07 11 Acquisition ENT 1x19
Assignment: Earth TOS 2x26 10 The Assignment DS9 5x05
Conspiracy TNG 1x25 10 The Voyager Conspiracy VOY 6x09
Shattered Mirror DS9 4x20 9 Shattered VOY 7x11
This Side of Paradise TOS 1x25 8 Paradise DS9 2x14
The Paradise Syndrome TOS 2x03 8 Paradise DS9 2x14
The Survivor TAS 1x06 8 The Survivors TNG 3x03
The Emissary TNG 2x20 8 Emissary DS9 1x01
Remember Me TNG 4x05 8 Remember VOY 3x06

Contains (normalized)

Title Series Episode Similarity Title Series Episode
The Eye of the Beholder TAS 1x15 100.0% Eye of the Beholder TNG 7x18
The Emissary TNG 2x20 100.0% Emissary DS9 1x01
The Muse DS9 4x21 100.0% Muse VOY 6x22
The Survivor TAS 1x06 88.9% The Survivors TNG 3x03
Demon VOY 4x24 83.3% Demons ENT 4x20
Remember Me TNG 4x05 72.7% Remember VOY 3x06
Paradise DS9 2x14 61.5% Paradise Lost DS9 4x12
One VOY 4x25 60.0% Drone VOY 5x02
Assignment: Earth TOS 2x26 58.8% The Assignment DS9 5x05
The Game TNG 5x06 57.1% Endgame VOY 7x25

Elo rating for unfair games

Oliver Brown
— This upcoming video may not be available to view yet.

In my previous post, I described an extension to Elo that could handle multiple players. The next restriction to overcome is that Elo assumed players of equal skill have an equal chance of winning.

In most games, players don’t actually have an equal chance of winning a single game. Chess overcomes this by having a match consist of several individual games with players switching who goes first. This is a good solution for two player games but gets awkward for multiplayer games. It is also inconvenient if having a multi-game match is undesirable for any reason.

Adjusted rating

Elo is fundamentally designed to handle players of different skill levels and produce a probability of them winning. The approach is therefore to determine an adjusted rating for someone such that the probability of winning is as desired.

The formula to work out an Elo expected score is:

E = 1 1 + 10 R 400

In our case we have an expected score (the win probability) and want to work out a rating difference, so we can just rearrange to get:

R = 400 × log 10 1 E - 1

We then subtract this adjustment from the player’s actual rating to get their effective rating to use in the rest of the Elo calculations.

The reason we subtract it is that for players A and B, the rating difference is calculated as RB - RA which is the opposite way round to what we want.

Here are the rating adjustments for some sample win probabilities:

Win probability Rating adjustment
0.01 -798
0.10 -382
0.25 -191
0.49 -7
0.50 0
0.51 +7
0.75 +191
0.90 +382
0.99 +798

If you try to calculate the adjustment for a win probability of 0 or 1, you get -∞ and +∞ respectively.

This means, for example, if you beat someone of an equal rating at a game you only have a 10% chance of winning, it’s the same as beating someone rated 382 points higher at a fair game.

Putting it all together

After explaining the theory of how to expand an Elo rating to support all the variations in Tic-tac-toe Collection, it’s time to put it into practice.

While writing this I’ve also been working on an implementation.

As well as adding it to Tic-tac-toe Collection, I’m planning on creating some kind of site and/or app just to work out Elo ratings for various results (and hopefully even to maintain ratings for players in any kind of competition you might want to run).

Single-word Star Trek episode titles

Oliver Brown
— This upcoming video may not be available to view yet.

My earlier post included a list of all single-word episode titles. That list is long enough that it could be analyzed in isolation and still produce some interesting results. Firstly, here is a summary:

Series TOS TAS TNG DS9 VOY ENT
Total 5 3 49 42 77 42
Percentage 6.33 % 13.64 % 29.17 % 24.71 % 48.13 % 44.68 %
Shortest 4 3 4 3 2 2
Longest 13 10 16 12 14 12
Average 7.6 7.33 7.96 8.1 7.81 7.79

Single-word titles by Series

It seems the number of single-word episode titles started low and increased over time, peaking with Voyager (although Enterprise was very close behind by percentage of total episodes).

The Original Series

The original Star Trek is the only series to have a season with no single-word titles at all (and it has two if you follow the convention that the original pilot, “The Cage” is part of its own “Season 0”).

Many titles from the original series were intentionally unusual, in the hope it would generate interest from people browsing TV listings (as explained more by Bruce Bennett). This generally led to longer titles and is part of the reason there are so few with just one word.

Season 0 1 2 3
Total 0 4 1 0
Percentage 0.00 % 12.50 % 3.70 % 0.00 %
Shortest - 4 9 -
Longest - 13 9 -
Average - 7.25 9 -
See all
Title Length Episode
Miri 4 letters 1x11
Arena 5 letters 1x19
Catspaw 7 letters 1x01
Metamorphosis 13 letters 1x02
Obsession 9 letters 2x18

The Animated Series

The animated series followed a similar naming style to the original, although in this case even the single world titles are pretty odd.

Season 1 2
Total 1 2
Percentage 6.25 % 33.33 %
Shortest 10 3
Longest 10 9
Average 10 6
See all
Title Length Episode
Yesteryear 10 letters 1x02
Bem 3 letters 2x02
Albatross 9 letters 2x04

The Next Generation

TNG was clearly a transition point in the history of Star Trek. It was obviously more modern and naturally led into the later series with most of the new production staff staying with Star Trek.

It was also still led by Gene Roddenberry early on, along with some of the original writers. This meant that although there were a plenty of long and unusual titles, the preference for simpler ones was becoming established.

Looking at the list of titles we can see TNG has the first that might stretch the definition of “single word”, and that maybe 11001001 is not even be a word. By my established definition though, it counts.

Season 1 2 3 4 5 6 7
Total 7 2 4 7 6 10 13
Percentage 28.00 % 9.09 % 15.38 % 28.00 % 25.00 % 43.48 % 56.52 %
Shortest 5 7 5 4 6 6 5
Longest 10 9 16 10 11 10 11
Average 7.57 8 10 6.57 8.33 7.7 8.31
See all
Title Length Episode
Haven 5 letters 1x05
Justice 7 letters 1x09
Battle 6 letters 1x10
Datalore 8 letters 1x14
11001001 8 letters 1x16
Symbiosis 9 letters 1x22
Conspiracy 10 letters 1x25
Contagion 9 letters 2x11
Manhunt 7 letters 2x19
Evolution 9 letters 3x01
Allegiance 10 letters 3x18
Sarek 5 letters 3x23
Transfigurations 16 letters 3x25
Family 6 letters 4x02
Brothers 8 letters 4x03
Legacy 6 letters 4x06
Reunion 7 letters 4x07
Clues 5 letters 4x14
Qpid 4 letters 4x20
Redemption 10 letters 4x26
Darmok 6 letters 5x02
Disaster 8 letters 5x05
Unification 11 letters 5x07
Violations 10 letters 5x12
Conundrum 9 letters 5x14
Ethics 6 letters 5x16
Relics 6 letters 6x04
Schisms 7 letters 6x05
Rascals 7 letters 6x07
Aquiel 6 letters 6x13
Tapestry 8 letters 6x15
Birthright 10 letters 6x16
Lessons 7 letters 6x19
Suspicions 10 letters 6x22
Timescape 9 letters 6x25
Descent 7 letters 6x26
Liaisons 8 letters 7x02
Interface 9 letters 7x03
Gambit 6 letters 7x04
Phantasms 9 letters 7x06
Attached 8 letters 7x08
Inheritance 11 letters 7x10
Parallels 9 letters 7x11
Homeward 8 letters 7x13
Masks 5 letters 7x17
Genesis 7 letters 7x19
Firstborn 9 letters 7x21
Bloodlines 10 letters 7x22
Emergence 9 letters 7x23

Deep Space Nine

DS9 followed a similar pattern to TNG. Many single-word titles, but plenty of longer ones too.

It also has another title that is questionable as a single word (that is yet another Q pun) in Q-Less.

Season 1 2 3 4 5 6 7
Total 9 9 9 5 1 4 5
Percentage 42.86 % 37.50 % 37.50 % 20.00 % 3.85 % 15.38 % 20.00 %
Shortest 3 6 6 8 7 5 7
Longest 11 11 11 12 7 12 10
Average 6.56 8.33 8.33 9.4 7 8.75 8.4
See all
Title Length Episode
Emissary 8 letters 1x01
Babel 5 letters 1x05
Q-Less 6 letters 1x07
Dax 3 letters 1x08
Vortex 6 letters 1x12
Storyteller 11 letters 1x14
Progress 8 letters 1x15
Forsaken 8 letters 1x17
Duet 4 letters 1x19
Cardassians 11 letters 2x05
Melora 6 letters 2x06
Sanctuary 9 letters 2x10
Rivals 6 letters 2x11
Whispers 8 letters 2x13
Paradise 8 letters 2x14
Shadowplay 10 letters 2x15
Crossover 9 letters 2x23
Tribunal 8 letters 2x25
Equilibrium 11 letters 3x04
Meridian 8 letters 3x08
Defiant 7 letters 3x09
Fascination 11 letters 3x10
Destiny 7 letters 3x15
Visionary 9 letters 3x17
Explorers 9 letters 3x22
Shakaar 7 letters 3x24
Facets 6 letters 3x25
Indiscretion 12 letters 4x05
Rejoined 8 letters 4x06
Homefront 9 letters 4x11
Crossfire 9 letters 4x13
Accession 9 letters 4x17
Rapture 7 letters 5x10
Resurrection 12 letters 6x08
Waltz 5 letters 6x11
Inquisition 11 letters 6x18
Valiant 7 letters 6x22
Afterimage 10 letters 7x03
Chrysalis 9 letters 7x05
Covenant 8 letters 7x09
Chimera 7 letters 7x14
Penumbra 8 letters 7x17

Voyager

By the time Voyager was written, the preference for single-word titles is well established, peaking in season 2 in which 20 out of 26 have only one word, and includes two separate runs of seven consecutive episodes with single-word titles.

There is another Q pun with Q2 and a bit of controversy with 11:59.

Season 1 2 3 4 5 6 7
Total 7 20 10 8 11 9 12
Percentage 46.67 % 76.92 % 41.67 % 34.78 % 44.00 % 36.00 % 54.55 %
Shortest 5 4 4 3 5 4 2
Longest 10 14 9 13 12 10 12
Average 7.29 8.8 7.1 7.25 7.36 7.22 8.25
See all
Title Length Episode
Caretaker 9 letters 1x01
Parallax 8 letters 1x03
Phage 5 letters 1x05
Emanations 10 letters 1x09
Cathexis 8 letters 1x13
Faces 5 letters 1x14
Jetrel 6 letters 1x15
Initiations 11 letters 2x02
Projections 11 letters 2x03
Elogium 7 letters 2x04
Twisted 7 letters 2x06
Parturition 11 letters 2x07
Tattoo 6 letters 2x09
Maneuvers 9 letters 2x11
Resistance 10 letters 2x12
Prototype 9 letters 2x13
Alliances 9 letters 2x14
Threshold 9 letters 2x15
Meld 4 letters 2x16
Dreadnought 11 letters 2x17
Lifesigns 9 letters 2x19
Investigations 14 letters 2x20
Deadlock 8 letters 2x21
Innocence 9 letters 2x22
Tuvix 5 letters 2x24
Resolutions 11 letters 2x25
Basics 6 letters 2x26
Flashback 9 letters 3x02
Remember 8 letters 3x06
Warlord 7 letters 3x10
Macrocosm 9 letters 3x12
Coda 4 letters 3x15
Unity 5 letters 3x17
Darkling 8 letters 3x18
Rise 4 letters 3x19
Displaced 9 letters 3x24
Scorpion 8 letters 3x26
Nemesis 7 letters 4x04
Revulsion 9 letters 4x05
Hunters 7 letters 4x15
Prey 4 letters 4x16
Retrospect 10 letters 4x17
Unforgettable 13 letters 4x22
Demon 5 letters 4x24
One 3 letters 4x25
Night 5 letters 5x01
Drone 5 letters 5x02
Timeless 8 letters 5x06
Counterpoint 12 letters 5x10
Gravity 7 letters 5x13
Bliss 5 letters 5x14
Juggernaut 10 letters 5x21
11:59 5 letters 5x23
Relativity 10 letters 5x24
Warhead 7 letters 5x25
Equinox 7 letters 5x26
Alice 5 letters 6x05
Riddles 7 letters 6x06
Pathfinder 10 letters 6x10
Virtuoso 8 letters 6x13
Memorial 8 letters 6x14
Tsunkatse 9 letters 6x15
Collective 10 letters 6x16
Muse 4 letters 6x22
Fury 4 letters 6x23
Imperfection 12 letters 7x02
Drive 5 letters 7x03
Repression 10 letters 7x04
Nightingale 11 letters 7x08
Shattered 9 letters 7x11
Lineage 7 letters 7x12
Repentance 10 letters 7x13
Prophecy 8 letters 7x14
Workforce 9 letters 7x16
Q2 2 letters 7x19
Homestead 9 letters 7x23
Endgame 7 letters 7x25

Enterprise

Enterprise titles continue the trend set in Voyager, despite dipping slightly.

If you wanted to be picky you might question the single-word status of Kir’Shara since not only does it contain an apsotrophe, but also a capital letter in the middle.

Season 1 2 3 4
Total 7 11 13 11
Percentage 28.00 % 44.00 % 54.17 % 55.00 %
Shortest 5 4 2 4
Longest 12 12 10 10
Average 8.71 8 7.38 7.45
See all
Title Length Episode
Unexpected 10 letters 1x05
Civilization 12 letters 1x09
Fusion 6 letters 1x17
Acquisition 11 letters 1x19
Oasis 5 letters 1x20
Detained 8 letters 1x21
Shockwave 9 letters 1x26
Minefield 9 letters 2x03
Marauders 9 letters 2x06
Singularity 11 letters 2x09
Dawn 4 letters 2x13
Stigma 6 letters 2x14
Canamar 7 letters 2x17
Judgment 8 letters 2x19
Horizon 7 letters 2x20
Cogenitor 9 letters 2x22
Regeneration 12 letters 2x23
Bounty 6 letters 2x25
Anomaly 7 letters 3x02
Extinction 10 letters 3x03
Rajiin 6 letters 3x04
Impulse 7 letters 3x05
Exile 5 letters 3x06
Twilight 8 letters 3x08
Similitude 10 letters 3x10
Stratagem 9 letters 3x14
Harbinger 9 letters 3x15
Hatchery 8 letters 3x17
Damage 6 letters 3x19
2 letters 3x21
Countdown 9 letters 3x23
Home 4 letters 4x03
Borderland 10 letters 4x04
Forge 5 letters 4x07
Awakening 9 letters 4x08
Kir’Shara 9 letters 4x09
Daedalus 8 letters 4x10
United 6 letters 4x13
Affliction 10 letters 4x15
Divergence 10 letters 4x16
Bound 5 letters 4x17
Demons 6 letters 4x20

What about “the”

My anlysis has so far treated a leading “the” as a word. Repeating this while ignoring “the” may produce interesting results, and at the very least will increase the count in Voyager season 2.

Ions

Finally, while browsing the list one interesting pattern stood out. There are 8 episode titles ending in “ions”, including the longest Transfigurations, and a further 22 ending in “ion”.

Sadly, there are none from the animated series.

See all "ions" episodes
Title Length Series Episode
Transfigurations 16 letters TNG 3x25
Violations 10 letters TNG 5x12
Suspicions 10 letters TNG 6x22
Emanations 10 letters VOY 1x09
Initiations 11 letters VOY 2x02
Projections 11 letters VOY 2x03
Investigations 14 letters VOY 2x20
Resolutions 11 letters VOY 2x25
See all "ion" episodes
Title Length Series Episode
Obsession 9 letters TOS 2x18
Contagion 9 letters TNG 2x11
Evolution 9 letters TNG 3x01
Reunion 7 letters TNG 4x07
Redemption 10 letters TNG 4x26
Unification 11 letters TNG 5x07
Fascination 11 letters DS9 3x10
Indiscretion 12 letters DS9 4x05
Accession 9 letters DS9 4x17
Resurrection 12 letters DS9 6x08
Inquisition 11 letters DS9 6x18
Parturition 11 letters VOY 2x07
Scorpion 8 letters VOY 3x26
Revulsion 9 letters VOY 4x05
Imperfection 12 letters VOY 7x02
Repression 10 letters VOY 7x04
Civilization 12 letters ENT 1x09
Fusion 6 letters ENT 1x17
Acquisition 11 letters ENT 1x19
Regeneration 12 letters ENT 2x23
Extinction 10 letters ENT 3x03
Affliction 10 letters ENT 4x15

Expanding the Elo rating system

Oliver Brown
— This upcoming video may not be available to view yet.

One of the features I have planned for Tic-tac-toe Collection is a player rating system.

One such common rating system is the Elo rating system, most famously used in chess. There is a lot of discussion about how good it is, but for my purposes it seems fine - at least as a starting point.

There are two fundamental restrictions on Elo that I would have to overcome though:

  • It is limited to two players.
  • It assumes each player has an equal chance of winning if they have equal skill.

Elo

First an introduction into how Elo rating works. There are two parts:

Given two player ratings, calculate an expected result.

The expected result is essentially the chance of winning, given as a decimal between 0 and 1, in which 0 represents a guaranteed loss and 1 a guaranteed win.

Given a player rating, an expected result, and an actual result, calculate how much the rating should change.

If you do better than expected then your score will go up. If you do worse then your score will go down. With a bigger difference there will be a bigger change.

Multiplayer

Simple Multiplayer Elo

I found an existing implementation of Elo for more than two players by Tom Kerrigan called Simple Multiplayer Elo.

In SME, players are ordered by performance, and then a simulated match is played between pairs of consecutive players, with the players’ ratings updated using the normal Elo method for two players.

This is certainly acceptable, and Tom includes some tests to show it works well. One oddity is if you get a victory over someone with a much higher rating than you, but also beat them by more than one place, you essentially don’t get the benefit for it. For example, consider the following result:

Position Player Initial rating vs player above vs player below Total
1st A 1000 +24 +24
2nd B 1200 −24 +27 +3
3rd C 1500 −27 −27

Here, Player A with a rating of 1000 has beaten Player C with a rating of 1500, but essentially hasn’t gotten the credit for it.

My unnamed Elo

My solution is to conceptually run the algorithm on every pair of players (in this case there would be A v B, B v C and A v C). There is a straightforward optimization so that the estimating part of the operation does not directly depend on the other players, just the difference between a single player’s expected and actual scores. So the algorithm is actually:

  1. Calculate the expected scores for each pair of players.
  2. Sum the expected score for each player.
  3. Divide each score by the number of players to normalize back to the range 0 to 1.
  4. Calculate the rating change for each player using their actual score and the combined expected score.

The details

With the same data as above, the results are as follows:

Player Initial rating Expected score
A 1000 0.097
B 1200 0.304
C 1500 0.599

Which is made up of the following score pairs:

Pair A B C
A v B 0.24 0.26
B v C 0.15 0.85
A v C 0.05 0.95

This results in rating changes of:

Position Player Initial rating Change
1st A 1000 +29
2nd B 1200 −9
3rd C 1500 −19
  • Player A has gained more which is good. That was basically the goal of the change.
  • Player B has now changed a small gain into a moderate loss. That’s a little odd and probably not desired, after all the victory against C should be more significant than the loss against A
  • Player C has changed a big loss into a slightly smaller (but still big) loss. After some thought, that is probably reasonable. Although C is expected to win just having more players should generally reduce your expectation of winning and therefore how much you are penalized for failing.

Improvements

So why did these results happen? It might be better to look at a table also including expected and actual results, which reveals a choice that has to be made that I have not yet mentioned:

Position Player Initial rating Expected score Actual score Change
1st A 1000 0.097 1 +29
2nd B 1200 0.304 0 −9
3rd C 1500 0.599 0 −19

Notice the actual scores used. Player A has a score of 1 indicating a win. Players B and C have a score of 0, which indicates a loss, but an equal loss.

If we instead use different values for the actual score we get a more sensible result

Position Player Initial rating Actual score Change
1st A 1000 0.67 +18
2nd B 1200 0.33 +1
3rd C 1500 0 −19

In this case, the “actual score” for a player placed Nth out of C is:

2 N C × C - 1
Explain this formula

This formula is conceptually simple, but a bit opaque when simplified.

Think of it as each player getting a number of shares of the total score. The person in last gets 0 shares, the person second from last gets 1 share, then next player gets 2 shares, and so on. The person in first place gets C−1 shares.

That means each player gets N shares and the total number of shares is equal to the C−1th Triangular number.

The formula for a triangular number is:

T x = x × x + 1 2

Substituting C-1:

T C - 1 = C - 1 × C - 1 + 1 2

This simplifies to: T C - 1 = C × C - 1 2

Therefore each player gets:

N / C × C - 1 2

which simplifies to:

2 N C × C - 1

Handling ties

To be as general as possible (and because it actually happens in some of my multiplayer Tic-tac-toe variants) we need to handle arbitrary ties.

The simplest way is to evenly distribute the score to all the players that are tied. So if the top two players in a three-player game tie, their scores of 0.67 and 0.33 are summed and split between them (0.5 each).

As a more complex example, consider:

Position “Raw” score Actual score
1st 0.286 0.262
1st 0.238 0.262
3rd 0.190 0.143
3rd 0.143 0.143
3rd 0.095 0.143
6th 0.048 0.048
7th 0 0

Final thoughts

I’ve addressed the first restriction of Elo, only supporting two players. As for unfair games, that will have to wait as this post is long enough as it is.

When is Easter?

Oliver Brown
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I wrote a post about calendar reuse that included an offhand comment about Easter. The common definition of when Easter is, is:

the first Sunday after the first full moon that falls on or after the vernal equinox

That isn’t quite right, and I made a vague mention of the correct definition.

Since then, someone has made a video explaining the the correct definition in depth with details about the history and why it is this way.

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