Occasionally, just occasionally, there will appear one or two EpicMafia players that completely astound me. ViktorEldor and VictoriaEldor, you are two such players. Keep up the good work, this is all extraordinarily fascinating stuff.
Very Interesting. Are you familiar with chi-square tests? They're used to see if anything's out of the ordinary. Also, I think you typed your data in wrong for slot 4, as I get 54 total, instead of 52. Using your data, I get:
Slot 1: p = .81 Slot 2: p = .22 Slot 3: p = .36 Slot 4: N/A Slot 5: p = .07 Slot 6: p = .57
Anything above p = .05 is technically considered normal. Although it is very interesting to see Slot 5 have such a low value. Possible Mafia slot? Keep up the good work mate.
One other note I'd like to point out is that calculating the likelihood of blue players landing towards the centre in comparison to non-blue players, still gives you decent results across every set-up. Not just Fancy Pants.
In conclusion, Mafia will have more ability to predict the positions of the PR and Cop than the other way around, unless Cop and PR work together. Although the Mafia unfortunately will have an average of a 50% Chance of killing either the PR or the Cop if they shoot in one of those slots, on Night 1.
The easiest way to determine the likelihood of shooting the Cop or PR would be based on assessing the history of the slot you're aiming at. If it's streaking (this game for example would be the 2nd or 3rd time in a row that a Cop is in that slot), it follows that the Cop is going to be more likely to land in the other options.
To gain total blue players rolled in the slots, we take both sides, add them together and times them by three.
To avoid having to do another simulation, we times it by 4, for non-blue players.
We will find 1x More players arrive in slot 4 given that calculation, however we exceed total game count, therefore we push down on the centre. Eventually we will notice that in 4/7 Cases, the middle is occupied by non-blue, and the rest of the logic follows from that.
It turns out that blue is the best determinant for non-blue positions, it works like this:
Blue is biased to land farther from the centre than the total non-blue players(!) As 3/7, is less than 4/7!
The more likely things are to be even (4/7 > 3/7) the more that the even weights end up bound to the centre, overall!
So we'd see a bigger pile of non-blues in the centre overall, but we have an upper limit, we cannot have more players in slot 4, than we have played games. Because only one person may occupy position 4, and it is more likely to be non-blue.
Therefore, we squish it, basically. Blues are forced into the average positions of 2 & 6 (We see this reflected in the statistics), however even if we have determined the average positions for 6 Players, we still have that extra 1. This extra 1, is more likely to be non-blue!
Therefore, it is more likely that a non-blue player will occupy the slots 1, 4 & 7.
Secondary areas for PR are 3 & 5 (Adjacent to centre).
Choosing the option which gives the highest chances of victory comes before the social aspect of Mafia. You could argue that people who want to choose options which hurt the town are being anti-town, and therefore scum.
Those decisions are based on objective observations, social skills come later, and are completely political in nature.
I'd be happy to receive data from more users, although I can only rely on my own being credible, unless users also provide sample evidence. I've got a whole folder of them.
I conducted a quick chi-square test for mafia/blue/PR/cop distributions on slot 1, and they turned out normal (p=.47) However, you might be on to something. When you collect 100 games let me know. I might start recording mine as well to avoid any user bias.
Today I started the chain again, carrying on from the previous ones. I decided since I had twenty samples, that I'd make a more educated guess about who was who before the game started.
I know before the game starts that I'm likely to roll Mafia given previous observations, the only thing I am not betting on is who the other Mafia will be at present. Primarily this is because if I do roll Mafia, I will already know who it is, my main mode of thought is on "who is likely to be the Cop?"
I pick Fun, and then among my suspicions for the power role, I presume that the power role will not chain in this event, eliminating the possibility of Fizzle and leaving Amanda.
In both cases I am correct, I shoot the Cop on Day 1, immediately point fingers at Fizzle and Amanda, knowing that Fizzle is the one least likely to end up as PR, I primarily point at him.
These events have not shown themselves to be rare, at all. The issue is that in some cases I am equally as likely to hit the PR as I am the Cop if not careful, as they both seem to end up on the same side of the coin.
By the way, my assumptions have saved today, and managed to hit the Cop on the first night in a few instances. I'm hoping that this will become a trend.
