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My LGS has a policy where you may bring your own packs and only pay a table fee. Last week I won 3 packs, which I decided to save for the next draft. One of the other players opened their prize packs from the same box and with the same art as mine to find they contain a mythic rare.
Now that I know there is a good chance there is a mythic rare card in at least one of my prize packs, does using these packs with this knowledge constitute cheating?
Yes, it would be cheating. Your tournament organizer must either provide the booster packs or randomly distribute them before the drafting phase. If that does not happen and you try to exploit that fact, you are cheating.
Since you are well aware that your packs would give you an unfair advantage, you would be cheating. Whether or not your tournament organizer made it easier for this situation to occur by not pooling the packs is irrelevant.
From the Tournament rules:
7.3 Card Use in Limited Tournaments
Cards must be received directly from tournament officials. This product must be new and previously unopened.
If the Tournament Organizer allows players to provide their own product, that product must be pooled with the rest of the product for the tournament and randomly distributed.
The rules (Judging at Regular REL, Infraction Procedure Guide) don't cover your exact situation, because if the tournament rules were followed, it should never occur.
However, cheating is not allowed at any REL and must be sanctioned with disqualification. Going by the definition in the IPG, cheating occurs when a player does something illegal, tries to gain an advantage, and is aware of the illegality.
As hinted on in the comments, if you're not participating in a sanctioned event, this isn't covered by official rules and will therefore be at your store's disgression.
In a sactioned event, the tournament rules are in effect, handling this problem like this:
7.2. Card Use in Limited Tournaments
Cards must be received directly from tournament officials. This product must be new and previously unopened. (...)
If the Tournament Organizer allows players to provide their own product, that product must be pooled with the rest of the product for the tournament and randomly distributed.
(...)
This means that you're not allowed to bring boosters and hold on to them until you open them. It specifically allows bringing your own boosters as well.
My best interpretation on how to best handle this situation is that a TO will be in charge of until finally given out at the start of the tournament. The respective TO would be responsible to check that the booster hasn't been previously opened and re-sealed. They also have to randomly distribute them, so you wouldn't be guaranteed to gain any advantage from this at all (you would essentially give away your theoretically higher chance of a good pick to someone else, instead of opening the booster yourself, making your chances worse).
I find it much more likely to believe that your store is disregarding the above rule and actually letting players hold on to the packs they brought with them. This isn't acceptable from an official rules perspective.
So, all in all, I can't imagine a sanctioned event in which you could get any advantage from bringing boosters that you only theoretically know having a certain card in them.
I would rule that this isn't cheating from any angle, in my opinion - if the store allows you to bring your own packs and the TO assures that they haven't been previously opened, then randomly distributes them, the player wouldn't and shouldn't be at fault in any way, not only because they're following the store's procedures, but also because the rest of the boosters could (and in practice will) come from booster boxes that might suffer from the same "tell".
Keep in mind that your local Judge might always see things differently, though.
