The tournament policy documents allow judges to deviate from the rules described therein in certain cases. The JAR tells us:
"Our solutions should focus on educating the players and keeping the game going rather than worrying about the impact on the game. You should intervene if you see something illegal happen in a match, but beyond this you can exercise your discretion. For example, whether you step in when you see a player miss a trigger should be determined by the tone you want to strike for your event – it may be appropriate to provide this extra help in a more causal environment, but less so if your play group is more competitive.
If a player accidentally breaks a rule, use the remedies described below and your common sense as guidance to make the best ruling you can. If you feel that the suggested remedy is not suitable to your particular situation you may suggest a more appropriate fix which is applied if both players accept it. Player education is a priority; remind the players to play more carefully, but avoid being heavy-handed in order to keep your events fun and relaxed."
And the IPG says:
"Only the Head Judge is authorized to issue penalties that deviate from these guidelines. The Head Judge may not deviate from this guide’s procedures except in significant and exceptional circumstances or a situation that has no applicable philosophy for guidance. Significant and exceptional circumstances are rare—a table collapses, a draft booster contains cards from a different set, etc. The Rules Enforcement Level, round of the tournament, age or experience level of the player, desire to educate the player, and certification level of the judge are NOT exceptional circumstances. If another judge feels deviation is appropriate, they must consult with the Head Judge.
If the Head Judge chooses to deviate from the Infraction Procedure Guide, the Head Judge is expected to explain [to the players] the standard penalty and the reason for deviation.
These procedures exist to protect officials from accusations of unfairness, bias, or favoritism. If a judge makes a ruling that is consistent with quoted text, then the complaints of a player shift from accusation of unfairness by the judge to accusations of unfair policy. Deviations from these procedures may raise accusations against the judge from the player(s) involved, or from those who hear about it. These procedures do not, and should not, take into account the game being played, the current situation that the game is in, or who will benefit strategically from the procedure associated with a penalty. While it is tempting to try to “fix” game situations, the danger of missing a subtle detail or showing favoritism to a player (even unintentionally) makes it a bad idea."
So when is it actually correct to deviate? Judge Academy has a good module on the subject, but it is unfortunately restricted to the L3 track. Given that the vast majority of tournaments are run by L1s and L2s, and those judges are expected to know how to deviate in their role as head judge, this is rather unhelpful. It also doesn't go into quite as much detail as I'd like to see regarding the nuts-and-bolts of making specific decisions. "Just follow a nebulous 'philosophy of policy' that consists of hundreds of different heuristics and isn't written down anywhere, duh" is not the most illuminating guideline.
Standardized Competitive REL tournament policy exists for three reasons: Accuracy, consistency, and judge protection.
Accuracy: Magic games are complicated. Even the best judges miss things, and figuring out all the ramifications of a certain course of actions is nigh impossible. If judges were simply told to fix things in whatever way made the most sense to them at the time, we'd do our best, but a huge number of well-intentioned fixes would have unintended consequences. The IPG and MTR have been built up via 25 years of experience, experimentation, and feedback, and it's much less likely that one of their fixes goes poorly.
It's also very difficult to remain completely unbiased. While we do try our best, if one of the players is a friend or a known jerk, it's very easy for that information to unconsciously color a judge's view, and result in an unfair ruling. The clear guidelines provided by the IPG and MTR still allow for some judgement and therefore cannot completely prevent this, but they do help mitigate it.
Consistency: In order for Magic to have a serious competitive scene, players need to be able to know what to expect from a tournament. If one judge tells them that a certain action is allowed and then another judge gives them a penalty for doing so, that player is very reasonably going to be upset. Letting judges rely too heavily on their own judgement would lead to wildly different policies at different events, and while this is not necessarily a problem in a vacuum (each policy could be very reasonable on its own), it becomes a problem as soon as a player enters an event run by a different judge and encounters policies they weren't expecting. A standardized set of policies results in a dramatic increase in consistency across events that is more than enough to offset the slight reduction in flexibility.
You know all the times players tell you "But that other judge said it was fine at my last event!"? By deviating, you become The Other Judge. And you can't easily get out of that by telling players that it's a one-time fix and not to expect the same next time, because they'll promptly forget that part.
We also don't want to allow players to gain an unfair advantage by influencing a judgement call. There are many situations with multiple fixes that, in general, would fix the situation equally well. For example, if a player picks up two cards for turn, a fix of "shuffle both away, draw a new one" would be just as good as a fix of "they get a random one of those cards, shuffle the other away". However, when the specific cards involved have been seen by the player, they'll prefer one of these outcomes to the other. (If the two cards are good they'll want a random one of them, if they're bad they'll want a different one from the deck.) If we always left this up to the judge, then the player could argue in favor of whichever fix benefits them the most, and the judge, seeing no real difference between the two, would often give it to them. So while it doesn't matter which fix we use, it does matter that we use it consistently, and that the player does not get any input into the decision of which to use.
Judge protection: Players tend to complain about rulings that didn't go their way. Even if you're a perfect judge who never makes a mistake, players might still perceive you as biased. Having a standardized set of procedures to point at and say "Look, I'm just following policy" protects us from accusations of favoritism or incompetence. "It says right here that I'm supposed to do this" is an incredibly powerful way to defuse an uncomfortable situation with an angry player. When you deviate from those polices, you're on your own; any unintended consequences your deviation may cause are entirely your responsibility.
A caveat: Learnability. Standardized policies would be of no use if nobody could remember what they said, so the documents need to remain simple enough to reasonably be used by humans. As a result, they do not try to be comprehensive; rather, they define general categories of actions players could take and tell us how to handle actions in that category. This works fine for around 95% of situations, but fails for the 5% that fall outside of what the documents were written for. (Note that most judge calls within that 5% are situations where the judge has to correctly interpret an ambiguous line in policy. Situations where an actual deviation is appropriate make up far less than 5% of calls.)
Eliana Rabinowitz's Why Rules and Policy article explores these considerations in more depth.
So when should we deviate? We should deviate only in situations where the learnability constraints put on the policy documents have resulted in a prescribed course of action that doesn't match the underlying philosophy. If we think that what the policy documents are telling us to do is significantly worse than the proposed deviation, and deviating does not compromise the accuracy nor the consistency of the ruling, then a deviation may be appropriate
DEVIATIONS ARE NOT FOR WHEN YOU DON'T LIKE THE POLICY
Why? Because if everyone who thought they'd found an improvement to policy chose to implement their own idea instead, we'd effectively not have standardized policy at all. Tons of judges think they could write policy better if it were up to them, and most of them are wrong. (Not you personally of course. I'm sure your own objections to policy are highly intelligent and completely correct. But all those other judges who are in the same subjective state of mind as you, of thinking that their ideas are definitely correct, they're the ones who are likely wrong. Set a good example for them and don't deviate even given the obvious correctness of your ideas.)
Even if someone is completely right about being able to improve on policy, it's still incorrect for them to deviate, because that breaks our consistency across tournaments. Even if a deviation would lead to a better solution for this game, that won't be true for the confused players wondering why it works differently at a different tournament. Don't be the reason why 1000 players are complaining about bad judges on Reddit/Twitter. If you think policy could be improved, that's great! The people in charge love to hear feedback and often implement third-party suggestions. Going rogue doesn't actually help policy improve, it just makes you "that judge who doesn't follow policy".
Regular REL is a little different. We get told that at Regular, we should "deviate like hell"
The accuracy requirement remains mostly unchanged. If you are considering deviating at Regular REL, you still need to carefully think through what that's going to mean for the game. If you think that you might end up making things worse, just follow the guidance in the JAR. However, we put less emphasis on the philosophy that our fixes should mitigate any advantage that could have been gained from the error. We still don't want a player to end up in a better position due to their error, but if the alternative is to significantly disrupt either player's experience, it's ok if one of them comes out a little ahead.
The guideline that deviations are only for situations where policy is either in error or was not written to cover is still true at Regular REL. The difference is that since the JAR is much shorter than the IPG, there are a lot more situations that it doesn't cover. If you find yourself ignoring a passage of the JAR that was clearly written to handle exactly what you're now dealing with, you've probably missed something and shouldn't be doing that.
One of the most blatant abuses of Regular REL deviation policy was back when rolling a die to determine the winner of a match was still a disqualification. Many judges would choose to completely ignore that section of the JAR and allow the player to remain in the event instead, because it "felt mean" to disqualify them. This fails all of the criteria above for a good deviation. A moment's rational thought on the topic would reveal that Wizards of the Coast obviously doesn't want innocent players being disqualified from their tournaments, as that makes them less likely to return. Therefore, there must have been a very good reason for them having added that line to the JAR; presumably because their lawyers told them that anything less strict would result in a risk of Magic being legally classified as gambling and Magic tournaments getting banned across the country. So while there is a good incentive to deviate (two innocent players would have a better tournament experience), this deviation could have had extremely bad consequences if applied by everyone, and does not fit the philosophy of why the JAR allows us to deviate.
As a general heuristic, if you don't regularly engage in policy discussions with L3 judges, you should not be deviating at Competitive REL at all, and you should think very carefully before deviating at Regular REL.
Here are some examples of situations where someone might consider a deviation. Think about what you would do first, then take a look at the answer.
AT Regular REL, a player casts a spell and the opponent points out that it's banned. The JAR says to shuffle a basic land into the library and remove that card from the hand, without replacing it.
The JAR intentionally included the restriction of "If the error was discovered during a draw effect, have the player complete the draw effect" rather than the shorter and simpler "if any cards were removed from the hand, have the player draw to replace them". This makes it clear that the instruction to not replace the cards in hand if the error wasn't discovered during a draw effect is not an error. A player not knowing that a card is illegal and trying to play it is the most common way for a card in hand to be discovered to be illegal after it's been drawn, so it's clear that the JAR was indeed written with this exact situation in mind. We should therefore not deviate.
At Regular REL, a player misses a trigger that makes their creature unblockable. This is noticed after it was blocked and combat damage has been dealt.
The JAR tells us to not back up for missed triggers, but rather to decide whether it's not too disruptive to put them onto the stack now. This is because backups are complicated and error-prone, and even at Regular REL we largely treat remembering one's triggers as a "skill". While it's true that putting this trigger onto the stack right now would not do anything, that's well within what the writers of the JAR were expecting when writing that section. Backing up in this situation could potentially be awkward if a player had the ability to cast combat tricks or reveal other hidden information, and it sets a precedent that your players will expect from you for any other missed trigger. Deviating here is probably not a good idea.
The JAR says that an illegal card in a deck should be replaced by any basic land. The player wants to replace it with a Snow-Covered Mountain.
This is an error in the JAR. (The JAR only gets updated every few years and is subject to much less scrutiny than the other two documents, so it's unsurprising that it hasn't been fixed yet.) The MTR makes clear in section 3.3 that they can only choose from the 5 "normal" basic lands, and the IPG's handling of Decklist Problems is consistent with this. Allowing the player to add a snow land or Wastes could give them a significant advantage in a limited tournament. You should deviate from the JAR to only let them add one of the 5 traditional basic lands.
At Competitive REL, a player wants to play a card that's been altered to have completely different art from a TV show the player likes. The player points out that the guideline in the MTR of "the art must be recognizable" doesn't make much sense given some of the alternate arts in recent Secret Lairs.
The MTR has been modified many times since those Secret Lairs began being printed, and that line remained. This makes it pretty clear that Wizards still wants that policy in place. This makes sense, since different versions of cards having different arts has been standard practice in Magic ever since the beginning. Secret Lair cards are rare in tournaments, and memorizing what one looks like is not very hard for a player who sees it played consistently. An alter that a player will likely only ever encounter once is subject to very different considerations, and allowing it would potentially cause unnecessary confusion and make that player annoyed at the inconsistency when it gets denied at their next event. We should not deviate from the MTR in this situation.
At Competitive REL, a player has a card in their deck that was banned just last week. The MTR does not list it as banned.
This is an error in the MTR due to it only being updated every 3 months with new set releases. You should deviate from the MTR and treat that card the same as any other banned card.
At Competitive REL, a player controls Phantasmal Image, and the opponent targets it with Path to Exile. As soon as the player puts it into exile, the opponent points out that it should have been sacrificed.
The IPG tells us to ask the opponent to decide whether or not to put the missed trigger onto the stack now. The philosophy behind this is to prevent the infracting player from gaining any advantage, by letting the opponent have the choice of either outcome. However, putting the Phantasmal Image trigger onto the stack now would do nothing, since the Path to Exile has already begun resolving.
This is a relatively rare situation, and not one that the IPG's guidance on triggers had in mind. Since the opponent did not have the ability to point out the missed trigger until it was already too late for the IPG fix to do anything, there's a clear benefit to a deviation. Performing a simple backup to the point where Phantasmal Image is on the battlefield and then putting the trigger onto the stack brings the game state closer to what it "should have been" had the trigger not been missed, and does not give an unfair advantage to either player. This deviation is therefore probably the best course of action, although this one is less clear-cut than some of the other examples, and it would also be acceptable to not deviate.
At Competitive REL, a player activates Lion's Eye Diamond and forgets to announce a color of mana for it. Several spells later, the players realize this. Another judge points out that one of the partial fixes for GRV is "If a player made an illegal choice (including no choice where required) for a static ability generating a continuous effect still on the battlefield, that player makes a legal choice.", and that fix could be applied here.
The reason there's a "choose now" fix for static abilities is that that ability is likely going to stick around for a long time. Leaving it unchosen would mean there's an incorrect game state persisting for several turns or the rest of the game. Letting the player choose now, even though it might give them a bit of an advantage, is better than that result.
Adding mana is not a static ability on the battlefield, and this makes a big difference to the underlying philosophy. We do have a player failing to make a choice, but that failure is not going to remain a problem for the rest of the game; the mana's not going to be there as soon as the game progresses to the next phase. Deviating to apply this line is not in keeping with policy philosophy.
We still have the problem of a player having an unclear color of mana in their pool. In some cases when a player does something ambiguous (such as attack with one of two visually-identical creatures, one of which is getting +1/+1 from some effect), we allow them to clarify the ambiguity later if it ever becomes relevant. However, the fact that mana in a player's mana pool is status information and must be visually tracked and announced upon change shows us that we expect players to be proactively clear about what mana they currently have floating. We therefore shouldn't allow them to get away with that ambiguity here.
The remaining options are to either:
Which one I would pick depends on the player's communication. If they made any statements to the effect of "I get mana", "3 floating", or similar, then it's clear that the ability resolved and I'd go with option 2. If not, option 1 seems more in line with what happened.
Thanks to Charles Featherer, John Brian McCarthy, Steven Zwanger, Kevin Desprez, and Jared Sylva for proofreading and suggestions. Any errors are my own.