[sticky entry] Sticky: My OCs!!

Sep. 26th, 2024 01:21 pm
fennaixelphox: (Default)
These are my OCs! (Collectively referred to as the "Phox Gang" by most)












I'm also accepting asks towards them!!

[sticky entry] Sticky: My Social Links!!

Sep. 22nd, 2024 01:42 pm
fennaixelphox: (Default)
In addition to being on here, you can also find me at the following sites.

Cohost (soon to be defunct)
Neocities
My Discord Server (Phox's Zodiac)
Twitter (bruh)
Tumblr
Ask-blog Tumblr
Bluesky
Steam
Mastodon
Telegram
Signal
Twitch
YouTube
Windows Live Messenger
(my username here is [email protected])

fennaixelphox: (Default)

Around this time last year, I got really into The Ouroboros King, and it made me want to try making a chess RPG of my own. So here's my idea for one: Caissa's Crusaders!

I haven't quite fleshed out the storyline, but I'm trying to brainstorm a bunch of variant pieces and make up movement patterns for each of them. I have a whole spreadsheet for it, as well as a mockup of the title screen. While I was brainstorming I mostly just scribbled random stuff on the piece base in GIMP to see if any cool shapes would make me think of a piece, and so far I've drawn about 130 of them.

I'm thinking the story would be about sentient chess pieces (who exist alongside humans) who do battle, and along the way, the player ends up going toe to toe with some sort of mysterious organization who uses 𝕰𝖛𝖎𝖑 𝕻𝖎𝖊𝖈𝖊𝖘 or whatever, and there'd be some sort of theme of deconstructing the fact that, when you're a sentient chess piece, your role in society is literally injection-molded into your body, but humans have no such restriction and are free to choose their destiny. Maybe some of your standard Yu-Gi-Oh! brand "if you lose the duel, you lose your soul!" type of stuff too. Also, checkers are the main currency of the game because they're also a game piece, but they look like coins. The boss battle pieces are currently Sisyphus, Midas, Icarus, Narcissus, Tantalus and Orpheus. I wanted to give them a "seven deadly sins" theme, with Sisyphus being wrath (in the legend, he was a cruel king who violated the custom of sacred hospitality), Midas being greed (obvious), and I'm not sure what the other sins would have been.

I'd love to hear you guys's thoughts on this, as well as some suggestions for other pieces to make or modifications to existing pieces. You can view the mockup of the title screen here and the list of pieces here.




fennaixelphox: (Default)
Today feels like a perfect day to me. In fact, I'd rate it 10/10
fennaixelphox: (alopex)
So a while back, I was fucking around on Tabletop Simulator, and someone showed me a deck they had found that had 12,000 cards. The deck has the following distributions of cards:
  • 40 ranks per suit: number ranks from 0 to 21, and then in increasing rank order: Banner, Monster, Tower, Dragon, Oracle, Fool, Huntress, Yeoman, Sorceress, Wizard, Lady, Cavalier, Princess, Jack, Queen and King, and then the Ace and Infinity of each suit.
  • 15 suits per color. See below for the suits in each color. Trump suits are listed in bold.
  • 20 colors, for a total of 15 x 20 = 300 suits: black, dark gray, silver gray, white, pink, red, tan, orange, olive, yellow, lime, green, hunter green, cyan, aqua, blue, navy, violet, magenta and lavender.


The deck wasn't really made to be used with all 12,000 cards. In fact, the Steam Workshop page specifically said not to do that. Naturally, the VERY first thing I did was get all 12,000 cards in a deck together. Then, I said to myself, "This is all well and good, but what kind of game would USE a deck this big?"

Blackjack, maybe, although it doesn't really make full use of the deck's suits. Crazy Eights could work, although the eights would be OP because of how many suits there are. Trick-taking games like Spades would go on forever because of how big the deck is.

Then I decided to make poker, but with 12,000 cards.

the rules

The rules are the same as regular Texas Hold'em Poker, with the following exceptions.
  • There is a third Blind: the Victory Blind. Whoever won the previous hand (or, for the first hand of the session, the Dealer) pays a blind bet of the full Big Blind amount.
  • The "Underdog Rule" - Whoever ends up in last place in each hand (or, for the first hand of the session, the Small Blind) is the Underdog. The Underdog will receive twice as many cards in the next hand.
  • Before looking at your hole cards, you may make a Called Shot, naming ten cards of your choice.
  • Each player has four hole cards instead of two.
  • There are 100 community cards, arranged facedown in a 10x10 grid. For the flop, each player takes turns revealing one card until 60 have been revealed. For the turn, the same happens, but with only 20 cards, and for the river, the remaining 20 cards are revealed. A player may only use cards from any one row or column to build their hand.
  • Hands now have 10 cards instead of 5.
  • When two hands tie for the highest-ranking hand, even after kicker cards are factored in, the hand with the most cards of a trump suit beats the other hands. If two hands still tie for most trump cards, compare the highest-ranking trump card in each player's hand, then the second-highest if there's still a tie, and so on. If there's still a tie, split the pot evenly.
the hands

Each player constructs the best possible hand of 10 cards, using their four (eight for the Underdog) hole cards, and any one row or column of 10 community cards in the 10x10 grid. Each hand shown below has an absolute frequency (the number of possible hands that would be classified as that type) and an odds against (the ratio of possible hands that are not that type to the ones that are). Hands are scored by the odds against drawing that hand. Whoever's hand had the highest odds against it wins, and claims all the money in the Pot. The player who had the weakest hand is then declared the Underdog, and the next hand begins.

The card rankings are as follows: Infinity is high, Ace, King, Queen, Jack, Princess, Cavalier, Lady, Wizard, Sorceress, Yeoman, Huntress, Fool, Oracle, Dragon, Tower, Monster, Banner, and then the number cards in numerical order (21 as the highest number card, 0 as the lowest number card).

The hand rankings are as follows. (Side note: While I'd like to think I'm decent at math, these are some pretty big numbers we're dealing with, so I may have made some errors in calculating the odds. If you're calculating them yourself and you notice a discrepancy, PLEASE inform me.)

  1. Called Shot - Ten specific cards which are declared before hole cards are dealt. Odds against: 16.999 decillion to 1.
  2. Royal Flush x10 - The Infinity, Ace, King, Queen, Jack, Princess, Cavalier, Lady, Wizard and Sorceress, all in a single suit. Odds against: 56.663 nonillion to 1.
  3. Double Royal Flush - Two Royal Flushes x5 (see below) in two different suits. Odds against: 47.756 nonillion to 1.
  4. Straight Flush x10 - Ten cards of the same suit, all in sequence. Odds against: 1.954 nonillion to 1.
  5. Royal Flush x9 - The Infinity, Ace, King, Queen, Jack, Princess, Cavalier, Lady and Wizard, all in a single suit. Odds against: 47.255 octillion to 1.
  6. 10 of a Kind Mini-Flush - Ten cards that share both their rank and their color. Odds against: 7.076 octillion to 1.
  7. Straight Flush x9 - Nine cards of the same suit, all in sequence. Odds against: 1.575 octillion to 1.
  8. Rainbow x10 - Ten cards, none of which share a color. Odds against: 153.345 septillion to 1.
  9. Royal Flush x8 - The Infinity, Ace, King, Queen, Jack, Princess, Cavalier and Lady, all in a single suit. Odds against: 35.465 septillion to 1.
  10. 9 of a Kind Mini-Flush - Nine cards that share both their rank and their color. Odds against: 3.541 septillion to 1.
  11. Straight Flush x8 - Eight cards of the same suit, all in sequence. Odds against: 1.144 septillion to 1.
  12. Double 5 of a Kind Mini-Flush - Two 5 of a Kind Mini-Flushes (see below) of different ranks and different colors. Odds against: 801.313 sextillion to 1.
  13. Rainbow x9 - Nine cards, none of which share a color. Odds against: 140.672 sextillion to 1.
  14. Flush x10 - Ten cards of the same suit. Odds against: 66.846 sextillion to 1.
  15. Royal Flush x7 - The Infinity, Ace, King, Queen, Jack, Princess and Cavalier, all in a single suit. Odds against: 23.657 sextillion to 1.
  16. Double Royal Mini-Flush - Two Royal Mini-Flushes x5 (see below) in two different colors. Odds against: 19.549 sextillion to 1.
  17. 8 of a Kind Mini-Flush - Eight cards that share both their rank and their color. Odds against: 2.067 sextillion to 1.
  18. Royal Mini-Flush x10 - The Infinity, Ace, King, Queen, Jack, Princess, Cavalier, Lady, Wizard and Sorceress, all in a single color. Odds against: 1.474 sextillion to 1.
  19. Straight Flush x7 - Seven cards of the same suit, all in sequence. Odds against: 739.276 quintillion to 1.
  20. Flush x9 - Nine cards of the same suit. Odds against: 172.816 quintillion to 1.
  21. Rainbow x8 - Eight cards, none of which share a color. Odds against: 140.766 quintillion to 1.
  22. Double Flush - Two flushes x5, in two different suits. Odds against: 110.298 quintillion to 1.
  23. Straight Mini-Flush x10 - Ten cards of the same color, all in sequence. Odds against: 50.825 quintillion to 1.
  24. Royal Mini-Flush x9 - The Infinity, Ace, King, Queen, Jack, Princess, Cavalier, Lady and Wizard, all in a single color. Odds against: 18.438 quintillion to 1.
  25. Royal Flush x6 - The Infinity, Ace, King, Queen, Jack and Princess, all in a single suit. Odds against: 13.807 quintillion to 1.
  26. 7 of a Kind Mini-Flush - Seven cards that share both their rank and their color. Odds against: 1.379 quintillion to 1.
  27. Double 4 of a Kind Mini-Flush - Two 4 of a Kind Mini-Flushes (see below) of two different ranks and colors. Odds against: 674.280 quadrillion to 1.
  28. Triple 3 of a Kind Mini-Flush - Three 3 of a Kind Mini-Flushes of three different ranks and colors. Odds against: 623.556 quadrillion to 1.
  29. Straight Mini-Flush x9 - Nine cards of the same color, all in sequence. Odds against: 614.600 quadrillion to 1.
  30. Flush x8 - Eight cards of the same suit. Odds against: 461.150 quadrillion to 1.
  31. Straight Flush x6 - Six cards of the same suit, all in sequence. Odds against: 418.386 quadrillion to 1.
  32. Royal Mini-Flush x8 - The Infinity, Ace, King, Queen, Jack, Princess, Cavalier and Lady, all in a single color. Odds against: 207.566 quadrillion to 1.
  33. Rainbow x7 - Seven cards, none of which share a color. Odds against: 152.585 quadrillion to 1.
  34. Royal Flush x5 - The Infinity, Ace, King, Queen and Jack, all in a single suit. Odds against: 6.906 quadrillion to 1.
  35. Straight Mini-Flush x8 - Eight cards of the same color, all in sequence. Odds against: 6.696 quadrillion to 1.
  36. Royal Mini-Flush x7 - The Infinity, Ace, King, Queen, Jack, Princess and Cavalier, all in a single color. Odds against: 2.077 quadrillion to 1.
  37. Flush x7 - Seven cards of the same suit. Odds against: 1.269 quadrillion to 1.
  38. 6 of a Kind Mini-Flush - Six cards that share both their rank and their color. Odds against: 1.034 quadrillion to 1.
  39. Five Pair Mini-Flush - Five Pair Mini-Flushes of five different ranks and colors. Odds against: 1.028 quadrillion to 1.
  40. 10 of a Kind - Ten cards that share the same rank. Odds against: 303.916 trillion to 1.
  41. Straight Flush x5 - Five cards of the same suit, all in sequence. Odds against: 203.125 trillion to 1.
  42. Rainbow x6 - Six cards, none of which share a color. Odds against: 178.105 trillion to 1.
  43. Straight Mini-Flush x7 - Seven cards of the same color, all in sequence. Odds against: 64.902 trillion to 1.
  44. Royal Mini-Flush x6 - The Infinity, Ace, King, Queen, Jack and Princess, all in a single color. Odds against: 18.182 trillion to 1.
  45. 9 of a Kind - Nine cards that share the same rank. Odds against: 7.375 trillion to 1.
  46. 7-3 of a Kind - A 7 of a Kind and a 3 of a Kind, in different ranks. Odds against: 7.258 trillion to 1.
  47. 6-4 of a Kind - A 6 of a Kind and a 4 of a Kind, in different ranks. Odds against: 7.185 trillion to 1.
  48. Double 5 of a Kind - Two 5 of a Kinds of different ranks. Odds against: 7.161 trillion to 1.
  49. Flush x6 - Six cards of the same suit. Odds against: 3.597 trillion to 1.
  50. Four Pair Mini-Flush - Four Pair Mini-Flushes of four different ranks and colors. Odds against: 864.857 billion to 1.
  51. 5 of a Kind Mini-Flush - Five cards that share both their rank and their color. Odds against: 862.418 billion to 1.
  52. Double 3 of a Kind Mini-Flush - Two 3 of a Kind Mini-Flushes of two different ranks and colors. Odds against: 675.011 billion to 1.
  53. Straight Mini-Flush x6 - Six cards of the same color, all in sequence. Odds against: 550.961 billion to 1.
  54. Mini-Flush x10 - Ten cards of the same color. Odds against: 550.030 billion to 1.
  55. Rainbow x5 - Five cards, none of which share a color. Odds against: 222.725 billion to 1.
  56. 6-3-1 of a Kind - A 6 of a Kind, a 3 of a Kind and a lone card, all in different ranks. Odds against: 187.183 billion to 1.
  57. 6-2-2 of a Kind - A 6 of a Kind and two Pairs, all in different ranks. Odds against: 186.557 billion to 1.
  58. 5-4-1 of a Kind - A 5 of a Kind, a 4 of a Kind and a lone card, all in different ranks. Odds against: 185.923 billion to 1.
  59. 5-3-2 of a Kind - A 5 of a Kind and a Full House, all in different ranks. Odds against: 184.679 billion to 1.
  60. 4-4-2 of a Kind - A Double 4 of a Kind and a Pair, all in different ranks. Odds against: 184.057 billion to 1.
  61. 4-3-3 of a Kind - A 4 of a Kind and a Double 3 of a Kind, all in different ranks. Odds against: 183.439 billion to 1.
  62. 7-2-1 of a Kind - A 7 of a Kind, a Pair and a lone card, all in different ranks. Odds against: 180.378 billion to 1.
  63. 8 of a Kind - Eight cards that share the same rank. Odds against: 179.590 billion to 1.
  64. Royal Mini-Flush x5 - The Infinity, Ace, King, Queen and Jack, all in a single color. Odds against: 136.420 billion to 1.
  65. Double Mini-Flush - Two Mini-Flushes x5, in two different colors. Odds against: 27.759 billion to 1.
  66. Mini-Flush x9 - Nine cards of the same color. Odds against: 27.109 billion to 1.
  67. Flush x5 - Five cards of the same suit. Odds against: 10.496 billion to 1.
  68. 5-2-2-1 of a Kind - A 5 of a Kind, two Pairs and a lone card, all in different ranks. Odds against: 4.958 billion to 1.
  69. Fuller House - A 4 of a Kind, a 3 of a Kind, a Pair and a lone card, all in different ranks. Odds against: 4.925 billion to 1.
  70. 4-2-2-2 of a Kind - A 4 of a Kind and three Pairs, all in different ranks. Odds against: 4.908 billion to 1.
  71. Double Full House - Two Pairs and a Double 3 of a Kind, all in different ranks. Odds against: 4.892 billion to 1.
  72. Triple 3 of a Kind - Three 3 of a Kinds, in three different ranks. Odds against: 4.544 billion to 1.
  73. 7 of a Kind - Seven cards that share the same rank. Odds against: 4.388 billion to 1.
  74. 8-2 of a Kind - An 8 of a Kind and a Pair, in different ranks. Odds against: 4.369 billion to 1.
  75. Double 4 of a Kind - Two 4 of a Kinds of different ranks. Odds against: 4.362 billion to 1.
  76. Straight Mini-Flush x5 - Five cards of the same color, all in sequence. Odds against: 4.012 billion to 1.
  77. Mini-Flush x8 - Eight cards of the same color. Odds against: 1.338 billion to 1.
  78. Three Pair Mini-Flush - Three Pair Mini-Flushes of three different ranks and colors. Odds against: 794.186 million to 1.
  79. 4 of a Kind Mini-Flush - Four cards that share both their rank and their color. Odds against: 790.813 million to 1.
  80. Five Pairs - Five Pairs of five different ranks. Odds against: 134.527 million to 1.
  81. 6 of a Kind - Six cards that share the same rank. Odds against: 107.549 million to 1.
  82. Straight x10 - Ten cards, all in sequence. Odds against: 99.268 million to 1.
  83. Mini-Flush x7 - Seven cards of the same color. Odds against: 66.172 million to 1.
  84. Straight x9 - Nine cards, all in sequence. Odds against: 24.008 million to 1.
  85. Straight x8 - Eight cards, all in sequence. Odds against: 5.231 million to 1.
  86. Mini-Flush x6 - Six cards of the same color. Odds against: 3.277 million to 1.
  87. Four Pairs - Four Pairs of four different ranks. Odds against: 3.021 million to 1.
  88. Double 3 of a Kind - Two 3 of a Kinds of different ranks. Odds against: 2.675 million to 1.
  89. 5 of a Kind - Five cards that share the same rank. Odds against: 2.645 million to 1.
  90. Straight x7 - Seven cards, all in sequence. Odds against: 1.014 million to 1.
  91. Two Pair Mini-Flush - Two Pair Mini-Flushes of two different ranks and colors. Odds against: 792,795 to 1.
  92. 3 of a Kind Mini-Flush - Three cards that share both their rank and their color. Odds against: 791,011 to 1.
  93. Straight x6 - Six cards, all in sequence. Odds against: 172,175 to 1.
  94. Mini-Flush x5 - Five cards of the same color. Odds against: 162,560 to 1.
  95. Three Pairs - Three Pairs of three different ranks. Odds against: 69,704 to 1.
  96. Full House - A 3 of a Kind and a Pair of two different ranks. Odds against: 66,468 to 1.
  97. 4 of a Kind - Four cards that share the same rank. Odds against: 65,265 to 1.
  98. Straight x5 - Five cards, all in sequence. Odds against: 25,077 to 1.
  99. Two Pairs - Two Pairs of two different ranks. Odds against: 1,651 to 1.
  100. 3 of a Kind - Three cards that share the same rank. Odds against: 1,615 to 1.
  101. Pair Mini-Flush - Two cards that share both their rank and their color. Odds against: 857.071 to 1.
  102. Pair - Two cards that share the same rank. Odds against: 40.130 to 1.
Incidentally, if you had an actual deck of 12,000 cards, assuming each card has a standard thickness of between 0.17 and 0.24 mm, that would give you a thickness of between 2.04 and 2.88 meters. This deck is likely thicker than you are tall.

fennaixelphox: (Default)
Anyone here know how to set up Dreamwidth to work with PostyBirb?
fennaixelphox: (Default)
I've donated quite a bit of money to the Pokemon Gotcha for Gaza project.
Expect a big influx of art of the Phox Gang coming soon!!
fennaixelphox: (Default)
Ask #12: "Opaque or Translucent?"

"Goo sure can! Sometimes I hide things in there. Sometimes those things aren't mine. Akesi is still kinda mad at me for eating his staff that one slime. Look, it's not MY fault goo decided to put a simply scrumptious-looking apple on the top of it! How was I supposed to know it wouldn't gum off?"

"...hooow aaare yooou speeeakiiing tooo theee aaaskeeer iiif yooou're aaasleeep?"

"...Astral projection?"

"thaaat's uuunsciiieeentiiifiiic."

"Aren't you literally a goost?"

"shiiit, yooou're riiight. caaarryyy ooon."

Fun fact: The things floating inside Gelphox's belly are a reference to the Valentine's Day picture I drew of him. Also, the picture in his dream cloud is another eSIM commission of him, coming soon to a social media site near you.

"Carrot"

Oct. 3rd, 2024 01:52 pm
fennaixelphox: (kasi)
Ask #11: "Carrot"

KASI: Sure, we've got carrots! They're homegrown, and thanks to my power over plants, they grow really fast! Did you want some?

AKESI: Zzz... cornflakesss... sssnzz... pepperoni... mimimimi... kerosssene...

KASI: ...Don't mind Akesi, he's a bit prone to sleep-talking.

I really need to figure out how to draw K&A sleeping. Poor Akesi looks like he broke his neck here lmao

fennaixelphox: (Default)
Ask #10: "Video Games"

Alopex:
Mega Man 8-Bit Deathmatch
Deltarune
Yu-Gi-Oh! Master Duel
5D Chess with Multiverse Time Travel (can play this in real life, too)

Gelphox:
Puyo Puyo
Slime Rancher
LSD Dream Emulator
Baldur's Gate 3 (modded the game so his character can be a gelatinous cube)

Cirrus:
Inscryption
Rain World
Bakugan (2009)
Pac-Man (but to them, it's a horror game, because they're a ghost)

Kasi:
Stardew Valley
Harvest Moon

Akesi:
Castlevania
Shin Megami Tensei

Kasi AND Akesi together:
Any game where the two of them can partner up

Topaz (if you can get her to sit still for long enough to play them):
Bejeweled
Minecraft
Sonic
Tetris (Tetris Effect is the only game she can actually focus on willingly)

Clarion:
Wii Sports Tennis
Insaniquarium!
Touhou
DDR (she does surprisingly well for someone who doesn't have any legs)

"Water"

Oct. 3rd, 2024 01:41 pm
fennaixelphox: (gelphox)
Ask #9: "Water"

"I kinda just absorb the water. Have you ever seen someone drink a bottle of water with their belly before? Now you have."

fennaixelphox: (gelphox)
Ask #8: "Forever Weed"

"I'm having the slime of my life here!"

"Tongues"

Oct. 3rd, 2024 01:37 pm
fennaixelphox: (cirrus)
Ask #7: "Tongues"
Cirrus, against their will.


"hlllp! thiiith iiith phhheeeryyy uuuncooomphhhthhhrbl!"
fennaixelphox: (topaz)
Ask #6: "Under the Full Moon"
"Ssshe getsss very... let'sss sssay... Violent. But not in the way you would exssspect a werewolf to do ssso. Ssshe doesssn't try to maul anyone, or rip their gutsss out, or anything like that. Ohhh no. It'sss MUCH worssse. Ssshe SSSMASSSHESSS thingsss. Ssshe takesss that cryssstal ssstaff of hersss and ssshe sssmassshesss thingsss. Asss the sssun risssesss after every full moon, everyone on her ssstreet, Kasssi and myssself included, wakesss up to broken windowsss. Windowsss are her favorite targetsss."

"HOLYSHITAKESIJUSTSHUTTHEFUCKUPALREADY!!!!!!!!!!!!!GODFORBIDWOMENDOANYTHINGAROUNDHERE!!!!!!!!!!!!!!!!!!!!UGHHHHHHHHHHHHHH>:(((((("
fennaixelphox: (kasi)
Ask #5: "A Day in the Life"
"There's this one other hybrid we know, Topaz. She's a were-Braicanroc, that is, half Braixen, half Lycanroc. I think she's pretty fun to hang around with sometimes, but for some reason, Akesi just can't stand her!"


"Werewolvesss and vampiresss are natural enemiesss, Kasssi. I've sssaid that ssso many timesss. But assside from that, I find her to be quite irritating, even on a persssonal level, due in no sssmall part to her excsssesssssively boisssterousss persssonality."


"As for how we handle taking turns, we use a special skateboard with a pillow strapped to it."


"You sssee, while one of usss sssleepsss, the other sssibling mussst ssstay on the move, ssso thisss allowsss usss to do ssso without dragging each other acrosssss the ground."
fennaixelphox: (akesi)
Ask #4: "Can I Wear You?"
"We weigh about 200 pounds, so..."


"World'sss heaviessst ssscarf?"


"I wouldn't try it if you value having a functioning neck afterward."


"That'sss probably for the bessst."

I like to think every scale says this to them, even the ones that don't have digital displays, and even though 200 pounds isn't all that heavy.
fennaixelphox: (kasi)
Ask #3: "Competition"
"It's a bit difficult for us to actually play against each other, since in most cases only one of us is awake at a time, but in the few hours we get to spend together, we sometimes enjoy playing board games!"


"I've been eating the piecsssesss while Kasssi isssn't looking."


"Hey, no fair!"


Side note, what a shame it is that the two characters with the most interesting dynamic among my cast are also the most bullshit to try and draw.
fennaixelphox: (gelphox)
Ask #2: "What's It Like Being Goopy?"

"It's a little bit strange, and kind of a mess, especially around where my fur meets my slime, but I'll let you in on a little secret."

"I can control how gloopy I am at will! Anywhere from half-slime to all-slime, to not even having any legs, and just slithering around like a big, purple slug!"

Heads-up!

Oct. 3rd, 2024 12:11 pm
fennaixelphox: (Default)
Oh btw I'm gonna be posting my Tumblr asks on here, feel free to ask some of your own although be warned that I have kind of a backlog

"Snuggles"

Oct. 3rd, 2024 12:08 pm
fennaixelphox: (gelphox)
Ask #1
"D'aww, thank you~"

And thank you to Umeja for submitting my very first ask!
fennaixelphox: (Default)

So, I've been thinking about poker lately, and the probability of each hand in a regular deck vs. with one joker in the deck. The probability of each hand, given 0 or 1 jokers in the deck, is as follows. 1

Each hand type is ranked according to the number of unique hands you can make of that type. The lower the number is, the more rare that hand is, and thus, the better it ranks.

Hand TypeWith 0 JokersWith 1 Joker
Five of a Kind(impossible)13
Straight Flush40204
Four of a Kind6243,120
Full House3,7446,552
Flush5,1087,804
Straight10,20020,532
Three of a Kind54,912137,280
Two Pairs123,552123,552
Pair1,098,2401,268,088
High Card1,302,5401,302,540

It is impossible to make a High Card hand with any selection of cards that includes at least one joker, because the joker can always be matched to the highest ranking card in your hand.

You might have noticed that the number of Three of a Kind hands with one joker is actually MORE than the number of Two Pair hands with one joker. Part of this has to do with how any hand of the form XXJYZ (two matching cards X, one joker J, and two unmatching cards Y and Z) can form either a Three of a Kind (if the joker is treated as an X) or a Two Pair (if the joker is treated as a Y; we'll assume that the unmatching cards are always sorted by rank, so the joker will never be treated as a Z because to do so would make a lower hand). To be exact, there are 82,368 possible hands of the form XXJYZ. However, if we're sorting the hands by how rare they are, that should mean that Two Pair outranks Three of a Kind, right? Let's take a look.

Hand TypeWith 0 JokersWith 1 Joker
Two Pair123,552205,920
Three of a Kind54,91254.912

Oops! Once again, the more common hand outranks the less common one, because the 82,368 hands that would have formed a Three of a Kind are now used to form a Two Pair. This won't do at all!

So how do we fix it?

The way suggested in the Data Genetics article that made me think of this is taken from Pai Gow Poker. In that version, a joker can only be used to complete a Straight, Flush or Straight Flush. In any other hand, it is treated as a suitless Ace. (That means that, for instance, a hand of 7777J is a Four of a Kind, not a Five of a Kind, because the Joker would become an Ace instead of another 7. The only true Five of a Kind, then, would be AAAAJ.) The term for a joker that's limited like this is a "bug", and it changes the hand rankings as follows: 2

Hand TypeWith 0 JokersWith 1 "Bug" Joker
Five of a Kind(impossible)13
Straight Flush40204
Four of a Kind6243,120
Full House3,7446,552
Flush5,1087,804
Straight10,20020,532
Three of a Kind54,91263,360
Two Pair123,552138,600
Pair1,098,2401,215,024
High Card1,302,5401,418,964

These hand rankings work perfectly fine, and the "proper" ordering of hands can be preserved without needing to resort to resolving a paradox, but what if you're like me and you want the joker card to be truly wild?

That got me thinking, why does XXJYZ have to be categorized as EITHER kind of hand? Its probability is greater than that of a Three of a Kind, but less than that of Two Pair. It is this thought that made me consider turning XXJYZ into its own hand type, which I have tentatively named the "Troupe."4

Hand TypeWith 0 JokersWith 1 Joker
Five of a Kind(impossible)13
Straight Flush40204
Four of a Kind6243,120
Full House3,7446,552
Flush5,1087,804
Straight10,20020,532
Three of a Kind54,91254,912
Troupe(impossible)82,368
Two Pairs123,552123,552
Pair1,098,2401,268,088
High Card1,302,5401,302,540

Don't get me started on how the odds change with TWO jokers, though.


  1. These statistics are sourced from Data Genetics.

  2. These statistics are sourced from Durango Bill's Poker Probabilities.

  3. This hand is the aforementioned "Five Aces" Five of a Kind.

  4. The name was meant to evoke a performing jester and his two stagehands.

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