Body Count (Literally)
Hi I saw this ask to @bodycountgame and got obsessed.
Question: What is the probability that at least one of the 3 ROs you chose will survive to the end and not be the killer?
[real question: compute the probability that I will get kicked out of grad school for obsessing over interactive fiction instead of interactive nonfiction aka research]
tl;dr: If your choice of 3 ROs included [the first victim], you have a 61% chance that at least one of your remaining 2 ROs will (not be murdered) and (not be a Villa Killa). If your choice of 3 ROs did not include [the first victim], you have about a 76% chance that at least one of your ROs will (not be murdered) and (not be a Villa Killa).
This is based on certain assumptions that you can rule invalid if you want. Assumptions and work under the cut. Don’t feel the need to read this lol, but feel very free to ask questions (and/or correct me).
Assumptions:
There are 13 ROs.
There will be 4 murders, one of which has already been determined to be [redacted].
There is at least 1 Villa Killa (and could be as many as 13-4 = 9)*
No murder victim is also a Villa Killa**
Each RO (excluding [redacted]) is equally likely to be a murder victim.
Each RO (excluding [redacted]) is equally likely to be a Villa Killa.***
*This already includes something like a .002% chance that every RO will either kill or be killed.
**I excluded the possibility? that Killer A killed Killer B because they suspected them of betraying them or something blah blah because that already adds way too many possibilities (even though what a twist.)
***Obviously my beloveds are innocent, but this did not figure into the calculation.
Recall/Trust Me:
The probability of an event is (number of possibilities in which the event occurs)/(the total number of possibilities).
The number of ways to choose k objects from n objects is n choose k = n!/[k!(n-k)!]. (e.g. (5 choose 2) = 5!/[2!3!] = 5x4x3x2x1/[2x1x3x2x1] = 10)
The number of ways to choose any number of objects (including 0) from n objects is 2^n.
Total Number of Possibilities:
We know there are exactly 4 victims, one of whom has been determined. That leaves 3 remaining victims to determine, which we get by choosing 3 people from the 12 remaining people --> (12 choose 3) = 220 possible “victim sets,” consisting of 3 random people plus [redacted].
Once we know the “victim set,” that leaves 13 - 4 = 9 people left from whom we have to choose the “Villa Killa(s)”. There are 2^9 - 1 = 511 possible sets of Villa Killa(s) for each set of victims. [We subtracted the possibility of no Villa Killa(s).]
That gives us 220 x 511 = 112,420 possibilities total for ways to assign victims and murderers.
Your 3 Faves
Choose 3 ROs.
We could count the number of possibilities in which at least one of our beloveds survive and is not a murderer, but it’s perhaps easier to count the number of bad possibilties, that all of our beloveds dies or is a murderer.
If one of your 3 ROs is [redacted] my beloved:
My condolences. :( Let’s call the other 2 ROs A and B.
A and B are also murdered (sorry):
This determines all but 1 person in the victim set, so we get as many victim sets as there are ways to choose 1 person from the remaining 10, which is just 10.
Once we have a victim set, we have to choose a set of Villa Killa(s). We’re choosing at least 1 kiler from the remaining 9 people, which gives us 2^9 - 1 = 511 again.
There are 10 x 511 = 5110 possibilities that all your ROs are just murdered (sorry sorry sorry).
Exactly one of A and B is murdered (and the other is a killer):
Either A is murdered or B is murdered; there are 2 choices here.
Once we know which of A or B is murdered, we have determined 2 people in the victim set and 1 person in the Villa Killa(s) set.
We choose 2 remaining victims from the remaining 10, giving (10 choose 2) = 45 choices for victim sets.
We already assigned one person to be a Villa Killa, so we are choosing at least 0 killers from the remaining 8 people. This gives us 2^8 = 256 choices for Villa Killa(s) sets.
There are 2 x 45 x 256 = 23040 possibilities that one of A and B is murdered and the other is a killer.
A and B are both killers:
We choose 3 remaining victims out of the 10 remaining people, which gives (10 choose 3) = 120 choices for victim sets.
Once that’s decided, we’ve assigned 6 people, including 2 killers, so that leaves 7 people from whom we can choose any remaning killers. That gives us 2^7 = 128 choices for Villa Killa(s) sets.
There are 120 x 128 = 15360 possibilities that two of your beloveds are killers.
This brings us to 5110 + 23040 + 15360 = 43510 possibilities that you will be sad, or a 43510/112420 = 38.703...% chance that you will be sad, or alternatively a 1 - 43510/112420 = 61.296...% chance that at least one of your loves will make it.
If one of your ROs is not [redacted] my beloved:
Congratulations? Let’s call your ROs A, B, C.
All 3 are murdered (sorry sorry sorry):
This determines everybody in the victim set: [redacted], A, B, C.
Once we have a victim set, we have to choose a set of Villa Killa(s). We’re choosing at least 1 kiler from the remaining 9 people, which gives us 2^9 - 1 = 511 again.
There are 511 = 511 possibilities that all your ROs are just murdered (sorry sorry sorry).
Exactly 2 are murdered and 1 is a killer:
Exactly one of A, B, or C is a killer. There are 3 choices.
Once we know who is a killer, this determines all but one member of the victim set. We choose 1 remaining victims from the remaining 9, giving (9 choose 1) = 9 choices for victim sets.
We already assigned one person to be a Villa Killa, so we are choosing at least 0 killers from the remaining 8 people. This gives us 2^8 = 256 choices for Villa Killa(s) sets.
There are 3 x 9 x 256 = 6912 possibilities that 2 are murdered and 1 is a killer.
Exactly 1 is murdered and 2 are killers.
Exactly one of A, B, or C is murdered. There are 3 choices.
This determines 2 members of the victim set. Choose the remaining 2 victims from the remaining 9, giving (9 choose 2) = 36 possible victim sets.
We assigned 2 Villa Killa(s), so we are choosing at least 0 killers from the remaining 7 people. This gives us 2^7 = 128 choices for Villa Killa(s) sets.
There are 3 x 36 x 128 = 13824 possibilities.
You have great taste and all 3 are murderers.
We choose 3 victims from the remaining 9, giving (9 choose 3) = 84 possible victim sets.
We assigned 3 Villa Killa(s), so we are choosing at least 0 killers from the remaining 6 people. This gives us 2^6 = 64 choices for Villa Killa(s) sets.
There are 84 x 64 = 5376 possibilities that all 3 are killers.
This brings us to 511 + 6912 + 13824 + 5376 = 26623 possibilities that you will be sad, or a 26623/112420 = 23.682...% chance that you will be sad, or alternatively a 1 - 26623/112420 = 76.318...% chance that at least one of your loves will make it.
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𝘛𝘐𝘓𝘓 𝘋𝘌𝘈𝘛𝘏 𝘋𝘖 𝘜𝘚 𝘗𝘈𝘙𝘛 [ 𝘭.𝘫𝘯 ]
𝐀𝐒𝐒𝐀𝐒𝐈𝐍𝐀𝐓𝐈𝐎𝐍 𝐢𝐬 𝐭𝐡𝐞 𝐍𝐄𝐖 𝐏𝐋𝐀𝐆𝐔𝐄.
welcome to rouiyan’s debut series, ‘till death do us part,’ a five part royalty au starring prince lee jeno and crown princess y/n. written either in between the lines or explicitly in the lines, there’s a heavy emphasis on power play, innate and learned human nature, as well as the run-of-the-mill, prairie-inspired romance. i mean this sincerely when i say to tread carefully, read the disclaimers below, as well as for each individual part, before continuing.
series disclaimers ! brief descriptions of nudity, mentions of sex, violence in the form of assassination/murder, bloody/gory scenes, character deaths, malintent, mental/emotional parental abuse, childhood trauma
𝐕𝐎𝐋𝐔𝐌𝐄 𝐈 : 𝐨𝐟 𝐭𝐡𝐞 𝐇𝐄𝐀𝐑𝐓
→ was released on 110220 12PM ✧ word count : 7.0k
prince jeno is willing to trade his heart and soul for the throne. but lee jeno is willing to trade his heart and soul for you.
𝐕𝐎𝐋𝐔𝐌𝐄 𝐈𝐈 : 𝐎𝐕𝐄𝐑𝐂𝐀𝐒𝐓 𝐒𝐊𝐈𝐄𝐬 𝐚𝐧𝐝 𝐭𝐡𝐨𝐬𝐞 𝐖𝐇𝐎 𝐃𝐈𝐄
→ was released on 110420 12PM ✧ word counts : 5.0k
“i will keep you,” he says softly, as sweet as black tea, “and i will keep you warm.” (Catherynne M. Valente, Deathless)
𝐕𝐎𝐋𝐔𝐌𝐄 𝐈𝐈𝐈 : 𝐃𝐄𝐀𝐑𝐋𝐘 𝐃𝐄𝐏𝐀𝐑𝐓𝐄𝐃
→ was released on 111120 12PM ✧ word count : 5.0k
prince jeno looks for the man in the moon, he wonders if he’s looking right back at him.
𝐕𝐎𝐋𝐔𝐌𝐄 𝐈𝐕 : 𝐚𝐧𝐝 𝐖𝐇𝐄𝐍 𝐢 𝐅𝐀𝐋𝐋
→ was released on 112420 12PM ✧ word count : 7.4k
and when i fall, will you be there to catch me by the waist?
𝐕𝐎𝐋𝐔𝐌𝐄 𝐕 : 𝐇𝐄𝐀𝐕𝐄𝐍 𝐁𝐄𝐋𝐎𝐍𝐆𝐒 𝐭𝐨 𝐘𝐎𝐔
→ is currently in the works
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