Mansion Party Event - A First Pass Analysis
So how many points can we expect by guessing?
- There are 48 teams left, or 144 contestants (143 not including ourself).
- There are ~250 total participants, including hidden proctors and civilians.
- This means that before taking into account other factors, guessing everyone is ninja will net you 286 - ~212 ~= 74 points baseline.
Extra points based on Village/Team/Name:
- Googling says there are 31 villages total in the Narutoverse, but probably all of them aren't represented. Regardless, the winning strategy here by default (if you don't have any other information) is to just guess everyone is from the most represented village, which IIRC is Hidden Leaf (or at least was before the mid-exam disqualifications). Assuming 10 out of the 48 are Leaf (or equivalently that the most represented village accounts for 10 teams, whatever it may be), this nets you an additional ~30 points.
- Calculating exact EV for guessing teams and names is tricky (and also I'm lazy and calculating it exactly will only increase accuracy by a few points), but assuming you have to guess logically consistently on each ballot (i.e. must guess a team from the village you named, must guess a person on the team you named), then in this scenario...
- You can't get more than 60 points by guessing team affiliation if you're absurdly lucky, and can't get less than 6 if you guess everyone is from the same team. So lets be generous and say you can get 10 points here by chance.
- For names, likewise you can't get better than 60 or worse than 2. Again being generous, assume you can get 6 points by chance.
This is a baseline total of ~120 points following the "random guess" strategy. But wait! Assume everyone else follows this strategy. That means
143 participants guess you to be a ninja as well, meaning you lose 286 points. Also, you probably won't find your partner (and they won't find you) for a total of
-196 baseline.
(This doesn't take into account guessing other's secret roles and losing points if others guess yours -- but this will result in negligible baseline changes if done by simply guessing).
That sucks. How do we do better?
Unfortunately, in addition to this being very easy to enact, everyone is basically incentivized to use this as a starting point, because you get more points in expectation just guessing ninja if you're unsure. But remember that
everyone else can just guess we are ninja too, and by default that means we start at -286 points before we gain any through other means (or -316 even, if you also count in losing 30 from not finding our partner). That's a pretty damned deep well to escape from, and if you can't be assured of winning at least 120 points with a better strategy, you're better off guessing everyone is ninja.
Additional note: Trying to make sure you find your partner gives you +60 points over baseline (go from losing 30 to gaining 30), so this is also somewhat valuable, although it will be difficult to pull off. If you can't do this without outing your own role to at least 12 other ninja, it simply isn't worth it.
Also those ninja can now trade your role for other information at your expense.
LEVEL-1 STRATEGY
I'm going to continue here-on leaving out details about Village/Teams/Names, as those are going to be very difficult to obtain en-masse and also don't contribute much per point of information. That said, I fully expect most people (~60%) will follow a "Level-1" strategy, that is, random guessing (Level-0) plus attempting to:
- Identify every non-contestant (civ + proctor) possible to avoid guessing them as ninja and losing points (can gain up to 212 points this way over baseline).
- Try to get as many people as possible to believe you are actually a civilian or proctor (can gain up to 286 points this way over baseline).
- Identifying other people's secret roles (can gain up to 715 (!) points this way over baseline).
Of course, all of these are rather difficult to do:
- Hard. Depends on the ratio of hidden proctors to civilians. Successfully determining that a person is henged might not be that useful (for instance, by cutting cloth from their disguise or getting them to eat spicy/disgusting food so they spit, and observing if the material dissipates into chakra) -- proctor or contestant?. You can really only count on negative results here, although each positively identified civilian would definitely increase your score. Expect lots of tests like people causing a random commotion or sudden threats and then observing reactions.
- VERY HARD. Again how hard depends on the ratio of hidden proctors to civilians, but unless people are very sure that you are not a ninja (like negative henge test sure), they are incentivized to vote that you are ninja regardless.
- EXTRA SUPER LUDICROUS HARD. Basically won't happen without a more involved plan, unless you have stupid good socials and/or a bullshit bloodline.
Careful use of niche ninjutsu, superior socials, and/or bullshit bloodline limits are the only real things that would let someone outperform others enacting a Level-1 strategy.
Assuming the average ninja can do passably well at 1 -- identifying most civilians at least (45%), maybe kinda okay at 2 (15%), and get a few lucky breaks on 3 (2%), this would result in a
median score of about -40 points or so, with extreme outliers (using bullshit numbers I made up for "bottom of the barrel" and "fucking Itachi-level bullshit") being around
-150 to 225 points. That's not entirely valid though, because succeeding at #2 and #3 changes everyone else's point totals slightly.
Still, close enough for a first-pass, and I'm confident in asserting that basically everyone enacting Level-1 strategies alone who isn't 25th percentile or better is going to lose points overall.
LEVEL-2 STRATEGY
Level-2 Strategy will involve using clever tactics (or just bullshit ninjutsu and bloodlines) to exploit other's attempts at 1-3.
- Possible strategies include:
- Observing and recording other's attempts to discern civilian identities, somehow figuring out their conclusions
- Establishing information networks to exchange information about who proctors and civilians are. Note that this is mostly net positive, but does trade off against #2, especially if you have too many immediate points of contact in your network.
- Other Ideas?
- Possible strategies include:
- Getting other confirmed civilians to vouch for your civilian identity
- Somehow faking a henge test (or the like) and having it be public knowledge (perhaps getting the information to propagate on the coattails of an information-exchange strategy)
- COUNTER-STRATEGY: Forgo points here in favor of forming cliques with other ninja, and exchanging your identity details with everyone else. These don't incur a cost to you personally, so this becomes net positive pretty much immediately, as you gain 3 points for every person who joins the clique, but only forgo the possibility of "winning back" 2 by convincing them you are a civilian. @Anderkent has made a few more posts on this.
- Other Ideas?
- Possible strategies include:
- Playing "Matchmaker", see @Briefvoice's suggestions
- Note that people will be incentivized to buy-in to this if they can be reasonably assured to find their match for a small cost (outing themselves to at most a small handful of reliable matchmakers).
- Note too that this trades off against #2 as well, but the potential gains are probably worth it
- Other Ideas?
I expect Level-2 players to score categorically better than Level-1 players and to come out significantly ahead on points (>100), with the best of the best scoring upwards of 300 or so.
LEVEL-3 STRATEGY
I don't expect there are going to be enough participants attempting Level-2 strategies for it to be worth it pursuing strategies geared to exploit Level-2 players for points (versus just trying to win harder at Level-1 or Level-2). Still, some strategies aimed at mitigating or eliminating Level-2 strategies are worth considering.
- Counter 1.2, Spy-vs-Spy:
- Figure out and leak all such information that is not held solely by yourself, thus making its relative value worthless.
- Is almost certainly going to be done by any proctors if brought into a network
- Can be mitigated against by limiting information flow and failure points in your own network, and by being careful about who you pass information to. Tit-for-tat is a good heuristic.
- Counter 2.3 #1, Parasitism:
- Join a clique and successfully play off the identity of a Village/Team/Person besides yourself, thus netting points while no one else gains any.
- Can be mitigated against by having people corroborate the identity of inductees before reciprocating information exchange
- Counter 2.3 #2, Clique Busting:
- Successfully join a rival clique and then make all their information public, thus making it's relative value worthless.
- Wait, I didn't know this was agar.io simulator...
- Counter 3.1, Poisoning the Well:
- A bunch of people pass themselves as matchmakers and either use the info for personal gain, don't deliver, or just make it infeasible/untrustworthy to promise on finding corresponding roles in general.
- Counter 3.1 Redux, Tragedy of the Commons
- The market is saturated which makes it infeasible/untrustworthy for anyone attempting this to promise to find corresponding roles.
Conclusion
This event is all about the relative value of information. PUBLIC INFORMATION IS USELESS INFORMATION. Personally I think we play most to our strengths by pursuing a mix of Level-1 and Level-2 strategies (weighting much more towards Level-2). We do have pretty good socials which will likely put us net positive if we enacted pure Level-1 strategies, maybe even 100 points or so. But we can do much better and probably even come out on top without too much risk.
- I would advocate for establishing information networks to exchange information about who the civilians and proctors are, so long as we're careful to exchange in-kind and in-measure (quality information for quality information, one piece at a time), and also careful to avoid proctors. Goal should be to construct a robust network that has us as a bottleneck.
- I would advocate against playing for cliques as it is time and concentration intensive to keep track of and to vet people (too high an opportunity cost), and too easily falls prey to clique-busting.
- I would advocate for parasitism + clique busting. Too good to pass up and will screw over others trying these tactics.
- I would advocate for a good Matchmaker strategy, just for the sheer amount of points it could net us. Hopefully not too many people will figure out they can do this. If they do and the market is poisoned or saturated, maybe we can entice other prospective matchmakers to share their info instead (this is the only true Level-3 strategy I'd consider).
- We can also wait towards the end to dump any info we have via pursuing clique-busting or spy-vs-spy strategies, thus maximizing their relative impact.
And of course, be on the lookout for counter-strategies to the above.
That said, we can ignore ALL OF THAT and just do our best to dupe a proctor into giving us a full list of details (or even partial list) before the event proper starts. With that, we can just coast to the tournament.
My preferred plan would be (1) attempting this (see @MadScientist's proposals), with abort/fallback options if we don't think we can pull it off, and then (2) pursuing bulleted points above if we can't get a full list, or to augment any partial knowledge we gain.
I am also very willing to entertain additional clever/creative Level-2 strategies.
