Assume targaryen lynching
Assume Yeti does not stab penguin to help you.
North is hooked tonight. Narrow released from kidnapping. 2 throne 1 islands vs 1 north 1 narrow. Vote is a 1v1 with your -2. Vote ties, goes into night. Narrow kidnapped, North hooked. North killed. Wait until you are released. Vote is 1v0 with 3 players vs your -2 vote. Game is over.
Siding with penguin leads to a guaranteed win.
The only world in a targaryen lynch where you win is if Yeti stabs penguin.
If her stab is to not hook north, north kill could hit her, so this is probably not the stab, as North is almost certainly killing the enemy which only it has. Even if it does not hit her and hits iron islands, day starts with a 1v0 in narrow+north's favor where you have the option of deciding to side with north or with islands. Regardless, Yeti does not make this decision as she will almost certainly die that night if she tries this as her stab.
If her stab is to vote for iron throne with you, you lynch tik. She can then hook penguin ad infinitum. However, Narrow is put into a win + kingmaker whereby Narrow still gets to choose if they should win with Islands or North based on who they kill. If Narrow kill Throne, Narrow is removed and Islands wins. If Narrow kill Islands, Narrow lynches and wins with North. If Narrow kills North for some ungodly reason, Islands is removed and it becomes a 50/50 on priority between North and Throne. This is her best possible stab of Throne but puts the ball in Narrow's court to stab her in return and to win with North should they wish.
There are no other stabs possible and none which can guarantee II win.
Due to the ability for you to potentially choose to screw over Islands anyway even if they wanted to win with you, given the player being behind Islands being the incredibly loyal Yeti, given the game developments leading to penguin and Yeti having worked together thus far, and given penguin being a player who almost certainly has done nothing to anger Yeti, Narrow odds of winning in this scenario are functionally 0.
That said, if there is no chance of winning in a tie vote scenario, then this is the optimal play. However, this is not the case.
Assume lynch tied.
2 throne, 1 islands, 1 narrow, 1 north (kidnapped), 1 targaryen.
Some additional information for you on how these scenarios are even possible. Without the specific buffs Targ received upon death the game would have been called by now in IT/II favor.
Targaryen have a backed up safeguard from Spiffy's death; if you have inspected Ullar post-Spiffy death you can confirm this. Means that our kill tonight will succeed with certainty. He also received a 1 time higher priority kill that was used on lightwolf and a nerfed inspector upon DLE death. An inspection now would probably verify this, although it would fail tonight. If you feel I'm lying, there's no amount of back ups or role changes that would matter barring Targaryen having the chance to kill 2 people in a night which is no longer possible given our forced use of the lightwolf kill and having a nightly 2 kills is fucking silly and you deserve to bitch out walrein if we had it.
But even assuming Targaryen have a nightly kill and an omniguard still (which we don't, and your inspection would confirm this), all of the following scenarios still are true. I'll include these worst (or perhaps best? I suppose it would depend) case scenarios for you into calculations where relevant.
First note that a North kill tonight is impossible and thus irrelevant. From there our kill options are limited to 4 options.
A. Assume a successful narrow kill from targaryen
North released, their kill unsuccessful in any world they do not pass their kill to us, as Ullar self-safeguards.
Even if kidnap fails, game is 2 throne, 1 islands, 1 north, 1 targaryen with ii/it to lynch. If north lynched, it's a 3v1 which ullar can't win, as the most people ullar could even theoretically kill in a night is 1 even if people believe he received a nightly kill + omniguard and he would simply be lynched by the other two the next day if he lived the night.
This is auto loss for Targaryen and thus something Ullar could not do, unless North kill is successful and on an it/ii player. However, North is kidnapped and unable to do their kill and thus could only pass the kill to Narrow or us. He would almost certainly pass it to Narrow if given a choice of preferences between ally and non-ally which would be hooked bar a misplay by it/ii not hooking/kidnapping Narrow and would be outprioritized by Targaryen kill in this world and thus is irrelevant. Targaryen cannot take the risk of assuming a North passed kill and kill Narrow off of that hope.
B. Assume any unsuccessful kill from targaryen/targaryen idle/Targ is lying about the safeguard
North released, 50% chance of kidnap on narrow, 50% chance of kidnap on us. If kidnap is on narrow, it/ii lynch targ first so that ii stay in game, then kidnap north. Narrow kill is unsuccessful that night because narrow kidnapped and north is hooked/kidnapped as well. Narrow is lynched that day in a 3 vs -2 vote with north kidnapped barring ii help, which is unlikely considering the state of the game and that the ii to make this decision is the incredibly loyal yeti.
Only world this plays out well for you is if ii decide out of the blue to help you win and hook/kill it for you, but this risks you then just siding with north due to them still being alive. Yeti does not take this risk and goes for the path of least resistance to win.
This same world plays out in any idle world and is eerily similar to the Targ lynch world.
This world is extremely likely given it being nearly impossible for us+north to avoid hooker + kidnap, and hooker may outprio safeguard (kidnap almost certainly will not though).
Thus you can assume that we will kill one of it/ii tonight.
C1. Assume a successful ii hooker kill from targ tonight
2 throne, 1 narrow, 1 north, 1 targaryen
Narrow 50% chance of kidnap (100% if it knows about Ullar safeguard).
C1i. Assume north support lynch on targaryen.
North are either kidnapped that night and thus cannot die or they are not kidnapped and then have a chance to kill with your kill being passed to them.
They have a 50% chance of outprioritizing the iron throne kill and getting 50% chance of guessing the it killer and icing his kill should they outprioritize.
If the 25% chance of both outprioritization and kill icing occurs, you are released into 1 narrow, 1 north, 1 throne. You win the lynch 100% and win the game with north.
If the 25% chance of outprioritization occurs and the guess is on the wrong it player, the game is a 1v1 between you and iron throne. You have a 50/50 of winning in this position if you outprioritize them, as similarly the iron throne cannot kidnap you.
If the 50% chance of no outprioritization occurs, it's a 2v1 vs you and throne. You cannot be lynched in this position and cannot be kidnapped. Similar position to what North is put through occurs, except you only have a ¼ chance of winning in this position. You would need to outprioritize the Throne and guess the correct Throne killer once (the 2nd kill night after the 2v1 guess is irrelevant as you already outprioritize them, guaranteeing you the win from that 25% chance.)
So your win percentage in this position is 25% + 12.5% + 6.25% = 43.75%
North even have a 25% chance of winning in this world, although they can't do all that much about this lynch.
The only world where lynching targaryen today is worse than this for your winning odds is if you are convinced beyond a 43.75% weighted reasonable doubt that iron islands will side with you over iron throne. Given the circumstances of the game and how Yeti plays, you should realize this is not the case and this scenario does not rely on any other team's arbitrary choices on who wins.
C2. Assume north tie lynch on targaryen.
You pass your kill to North or Targaryen. Given you didn't pass your kill last night even though if we did not receive the sudden buff of a 1 time super prio kill the game was literally over, there's almost no chance you pass it here where you have a good option of not doing so and you probably shouldn't.
C2i. If you pass to North, North is either kidnapped + IT do a Targ kill or IT kill North and kidnap us.
They almost certainly choose the former. Assume kill on Targ succeeds. Throne ties the lynch and kidnaps you. Then they lynch North the next day. Then you have a 25% chance of winning if you outprio and you guess their killer correctly. North has auto loss in this world.
Let's assume Targ kill fails due to having an omniguard. Day is 2 throne, 1 narrow and 1 targ to vote. If you vote Targ, same 25% chance as above. If you vote IT kidnapper, North can martyr the omniguard (redirector outprioritized it on n3, so martyr certainly would as well (I would say you could ask highgarden but I suppose that isn't possible). North martyrs Ullar and you get passed the kill. Even if omniguard is idled, our kill would have to be directed at North due to the martyr giving you an opportunity to idle, kill iron throne, or kill us. Without access to protection, a kill on us succeeds and you have a 50% chance of winning in a priority battle vs throne. If we use omniguard, it gets martyred and you have a 100% win with north. Even if it isn't martyrable, all you have to do is idle your kill and you can easily convince throne to lynch targ off of risk of Targ having a nightly kill as we're essentially forced to use our kill that night or almost guarantee a loss. If North tries to mindgame and not use martyr they lose anyway in the heads up between either us or Throne so they use omniguard
Narrow 50% + 25% = 75% if we have omniguard
Narrow 25% if we do not have an omniguard
North 50% if we have omniguard
North 0% if we do not have omniguard
C2ii. They may choose a North kill and kidnap us. North has your kill.
IT risks the 25% chance of outprio+icing of killer, 25% of outprio but not iced killer, and 50% of being faster.
If outpriod and iced and the killer is the kidnapper, it's 1 throne 1 narrow 1 north 1 targ. Narrow+North have majority and lynch Targ out of fear of what Targ has and you 100% win with North when they kill a kidnapless Throne that night.
If outpriod and iced and the killer is penguin, it's 1 throne 1 narrow 1 north 1 targ. Narrow + North lynch Targ out of fear of what Targ has and there is a 50/50 on whether North passes the kill to you or not. Even if they kidnap correctly on the North kill, it's still auto for you as from the earlier assumption we already showed that Narrow kill has higher priority than Throne.
So outprio and ice is 100% win for you and North.
If outpriod and not iced, Throne kill North and kidnapper dies. 1 throne 1 narrow 1 targ. Throne lynch targ to try to see if faction kill priority is random as it's their only chance of winning, as they lose to targaryen that night from a Targaryen kill. So they lynch Targ and it's a 50/50 on priority that you win.
If faster, 2 throne 1 narrow 1 targ. If you lynch targ then you have a ¼ of winning for the same outprio/ice reasoning i've given like 3 times before. If you lynch throne then Targ wins. If you force a tie then Targ either kills throne or idles. If Targ idles then you get kidnapped and Targ gets lynched; even if targ had omniguard we could not use it to protect both you from kidnap and us from the Throne kill that night and thus we get lynched that day 100%. If Targ kills throne then it's the same 50/50 and you vote to lynch Targ. This is thus a 50/50 for Narrow if you play this way.
25% + 12.5% + 25% = 62.5% win rate for Narrow
25% win rate for North
D. Assume we kill IT
1 north 1 narrow 1 ii 1 throne 1 targ, north is hooked, kidnapper is dead.
Only possible lynch targets here are Targ, Throne, Islands, or no lynch. You + North can stop a lynch on either one of you two.
D1. Assume Targ lynched here.
Literally the same position as the Targ today lynch except with better odds of you winning. IT now only have 1 and no kidnap to stop you or North kills. II siding with you now is more optimal than siding with a kidnap-less Throne as you two form majority together and at least has some merit to being mentioned. You have auto if this happens and II wins the head to head with North because hooker and kill that night.
II kills North and unless you kill II AND II doesn't hook you, then II has auto win here and as such may not pick to let Throne win.
If II decides to dip early and not pick favorites, they hook + kill North and you have a 50/50 of winning here in a prio battle vs Throne.
If II decides to ride or die with Throne and hooks you (or North possibly if you try to predict the hook), you have a 25% chance of outprioritizing the IT kill and avoiding the II hook and guessing correctly on if you give North your kill or if you keep it yourself. If you pass it to North, they may kill Islands instead, and if so, they have a 25% chance of outprioritizing Islands, forcing a 1v1 between penguin and acid. Acid wins this 1v1 because he kills next night. However, acid probably won't realize to kill Islands and you can probably get him to kill Iron Throne without him thinking much about it. If Islands hook you and you try to kill however, you do lose, but you at least have the potential out of a North kill unlike in the lynch Targ today scenario.
So even if II wants you to lose and to actively give IT a win, you can still force yourself or North to win with 25% odds in this world assuming a fairly easy to expect North misplay. You cannot do so in a world where you lynch Targ today. There is also reason enough for Islands to not pick sides which isn't present in the other world either which gives an additional potential 50/50.
I would personally recommend against this choice as you have better win percentages in other scenarios, but even if you would want a Targaryen lynch nearly immediately, you still should tie today to force it to happen tomorrow to give you better odds of winning.
D2. Assume Throne is lynched.
If you lynch throne instead, North is the only person with a kill. North a 50/50 of guessing whether you do the kill or he does in terms of killing Islands. Giving you the kill makes you kingmaker. If you kill targ, you are removed and North loses the 1v1 to Islands. If you kill Islands, you have majority against Targ the next day and win.
I'm still writing
