Often the metagaming problem is about how the DM presents the things to the players. We have lots of questions and good answers in the metagaming tag. Most of them are about concealing information, though, as Make their knowledge uncertain, hide info and add "meaningless" thing, etc.
For PvP scenarios, this also applies: the player can write down a note and give it to the DM. The problem is: when the PvP gets too heavy, every player writing down a note for every action so they can conceal information takes too much time. Also, while concealing the information hides the information itself, there's also meta-information about the fact the player concealed information to start with: "Why is he hiding things from us? He's up to something." - and this leads to metagaming by itself. This question is more on this second problem.
One such scenario that happened to me was, while a group of friends was playing Curse of Strahd, one player decided that he wanted to eventually betray the party and help Strahd instead. An important member of PC's family was in Barovia and kept under Strahd's control (only he knew about it), and he loved more that member than the party.
As I mentioned, the player started to behave suspiciously (the player, not the PC) for the other players. In particular, we (I, the DM, and the traitor player) were trading notes often.
Gradually, the other PCs started becoming too aware of the traitor's PC, even though there was no in-game reason for that (yet). That took around 2 sessions of 4 hours. From this point onwards, everything went astray. They would constantly be suspicious of his (character's) actions and what he said. After they got him lying about I don't even remember what, they would even "try to listen carefully if there was a conversation going on in his bedroom". Note that by this time, the characters already had information enough to actually be suspicious. The problem is that they would never have gotten (okay, they might, but certainly not how they did) this information if the characters were behaving normally from the start.
To be clear, the notes were traded in times the party was split, e.g. when they were about to sleep (separate rooms, rich party).
This might make the question too broad, but I'm interested in solutions as any person involved in the problem, i.e.
- As the DM handling the situation.
- As the player betraying the party.
- As the players being betrayed.
I'm interested in solutions as anyone because I think there were flaws in everyone's actions and I often find myself in the position of any of them, although in this specific scenario I was the DM.
It didn't become a personal problem, and even the traitor player didn't want to argue and make a fuss over it, so we didn't talk about it. It did give me a bad taste, though.
Important Note on the Problem
As you can see, most of the question is in the past tense. That's because it's something that happened a while ago. I'm more interested in how to prevent metagaming based on out-of-game information—specifically during betrayal scenarios—from happening again, since the campaign where it happened is long dead, including the PCs. (I mention the campaign is dead because this means there's no use handling the problem now - it doesn't exist any more. That's why I want to prevent it, not handle it.)
These details are mostly for people thinking "OMG traitor player! Don't do that!"
- We had all agreed with the possibility of betrayals in the campaign, both from NPCs and from other players. This might actually have increased the metagaming problem, as they knew betrayal was a possibility.
- Metagaming was agreed to be "bad", but it seems the players couldn't control themselves on that, because the meta-information was too much.
Honestly, I don't want to tell you how to answer my question, but metagaming questions are having some answers that are not helpful for me. I'll list some that I'm saying in advance: this won't help me.
- "Don't play a PvP campaign" - Check this meta for why this is bad: Can we affirm that RPG.SE embraces a plurality of playstyles? - there are people that have fun playing PvP.
- "Stop caring about metagame" - Same meta.
- "Don't betray your party, the player should have asked for help from the party" - Same meta.
- "Don't create a scenario where your player/PC wants to betray the party" - Really? For me that's one of the most interesting scenarios I can create. Also, it can be done correctly, even if it failed this time.
- "Don't allow them to do X" - As the DM, I don't want to remove player's agency, even if it ultimately means I'm allowing metagame.
The most similar I could find is How to prevent players from metagaming when they split the party?. The question is still pretty different simply because of the PvP nature of mine.
I can see the value of playing online or IRL with everyone having a notebook and having private chatrooms with that. I've done that and it completely solves the issue. Sadly, I can't do that with every group. In particular, my current group is so problematic with Facebook/WhatsApp/Instagram that we had to ban cellphones so they wouldn't lose concentration every 10 secs. We're already low on time and I don't want "hey check this cute cat video" interruptions - and I know I'll be getting them if cellphones/notebooks are on the table.