Antisynergy in cEDH
Overall, it's safe to say people build decks by grouping 100 cards together because they make each other work better. Synergy. Building a storm deck? Chances are you'll run rituals to chain into. Building stax? Odds are you'll want to double check your stock of Rule of Laws. Midrange? Grab those mana dorks and let's go. Regardless of the archetype, we choose the cards we choose because they help us play more efficiently, more effectively, and more reliably.
But what about when we chose cards that make no sense together? The One Ring is an absurd value engine, capable of winning games on its own if left unchecked. Null Rod is another absurd card, though for completely different reasons; if timed right, this two-mana anti-rock can shut players out of the game completely, leapfrogging you ahead pf the competition simply due to the lack of opposing capacity. Null Rod is a symmetrical card, however, so for every opposing Mana Crypt it shuts off, there is also the risk of slowing you down, too. Or worse: making that The One Ring you just top-decked turn into a dead draw.
So, two powerful cards. The question remains: is my decklist big enough for the two of them? Welcome to the wonderful world of antisynergy, where good cards abound... but sometimes at the cost of each other.
Offensive Picks
First off, everyone's favourite thing to talk about: good cards! These are the cards we play because they're powerful, they work well together in our lists, and they advance our gameplan. I don't mean they advance us comparatively: I mean these cards take a step towards furthering our goals faster than our opponents can stop us. These aren't necessarily the linchpins of our decks; taking them out would make the list worse, but not unplayable. Let's turn back to The One Ring as an example of this.
The One Ring is a pretty busted card. Leave it alone, and odds are its controller will win the game. At the same time, few players are actively building their decks around it. Support pieces exist, but most of the optimal choices are those with zero (or near zero) opportunity cost. Minamo, School at Water's Edge is certainly on the rise, but I haven't seen a Voltaic Key at a cEDH table... ever? The point is, The One Ring is the perfect "good card." It's a threat, it's powerful, you don't need to build around it, and it makes games better (for its controller, that is).
It may seem intuitive, but it's actually really important to remember that playing good cards often makes decks better. Sure, a pile of 100 independently good cards is almost certainly worse than a pile of 95-or-so synergistic cards and 5 value pieces (don't quote me on these exact numbers), but having top-deckable threats presents an out when things go wrong and all your synergy pieces can't line up together. Rituals are great when you're chaining into an Ad Nauseam, but I know it feels awful to draw a Desperate Ritual of all things after having my Underworld Breach line exiled with a Mindbreak Trap. That's where cards like The One Ring comes in. Not just a win, but also an escape.
Defensive Picks
As for defensive picks, we've already gotten the ball rolling on good ol' Null Rod, so why not start off the discussion with the bane of every cEDH deckbuilder's existence: sacrificing slots for what essentially amounts to the main-board sideboard.
Cards like Null Rod here exist in a bit of a strange no-man's-land in terms of playability: these symmetric stax pieces can be incredibly back-breaking, but their power lies in shutting down opponents, not in directly accelerating their controllers. It's like reverse ramp: suddenly you're making the most mana at the table, but that's because you were harmed the least in the process.
These silver bullets also suffer from the problem of probability: how likely are you to both play against an opponent who suffers asymmetrically from their effect, while also playing a game where you draw into them? The result is a valuation dilemma with three counterbalancing factors (prevalence of their intended target in the meta, repercussions on your own gameplan, and reliability of deployment per game), each of which must be weighed against the opportunity cost which is using the slot for a card which, while potentially weaker, serves to synergize with the rest of your list. Going back to Null Rod, let's take a look at how it stax up to the competition (pun very much intended).
First, the best use-case. These are the lists which play green (maybe red and black as well, if you really want to add all the possible sources of nonartifact mana) and seek to reign supreme in mana production via an army of dorks after Null Rod is deployed. Sol Ring, be gone! It's Elvish Mystic's time to shine. In terms of the first factor, prevalence of target, it's safe to say that a lot of decks want to be running artifacts. Even mono-green has a hard time explaining why it would ever want to say no to Mox Diamond or the like. Your opponents will be playing artifacts, and Null Rod will be hurting them. Next, repercussions. Green brings with it an army of Elves for mana, so turning off rocks won't hurt as much from a comparative perspective, but it's still a loss. Compared to the nongreen players, however, this looks like a loss worth taking. Finally, deployment reliability. If you're looking for Null Rod in a green deck, you better be on another color as well, because otherwise odds are you won't be drawing it that often. Not a significant negative, considering the low cost of including Null Rod, but definitely a weakness. Powerful? Yes. Reliable? Not necessarily.
Next, the worst use-case. These lists definitely don't play green, and odds are they are some variation of blue/blue-black/blue-white. Every opportunity for ramp in these lists comes from a rock, and even though you can tutor Null Rod far more reliably, facing down one will wreck you in all likelihood as well. Powerful? Still a yes. A blowback? Almost certainly.
Balancing the Two
We've talked about offensive cards, like The One Ring, and defensive cards, like Null Rod; now comes the problem of putting the two together.
These two cards are the pinnacle of the antisynergy problem: one completely shuts off the other, no questions about it. So, how does the risk of running both stack up to the bonuses they each seek to offer? Let's look at this through the defensive opportunity cost calculation from before.
First, prevalence. This part doesn't apply as much to the antisynergy dilemma, as the question is more self-contained to your own list. Null Rod essentially presents applicability across all game environments, so the question to ask here is instead directed inwards: rather than how many artifacts will your opponents run, now you need to ask how many artifacts will you run. Now, add The One Ring to that list.
Alright, with the quantity/prevalence question out of the way, on to repercussions. This is the big one. We've already set our definition for cards like The One Ring to be inclusive of potential win-cons, but not strictly defined as our primary win routes. These are powerful cards, not the crux of our gameplan. Remove these, and we feel worse, but not defeated. When it comes to The One Ring, losing this sucks, and when we add it to the list of mana rocks we also lose out on, the opportunity cost shifts greatly towards the negative. We need to be on mana dorks, or something else like it, to justify Null Rod. No longer can we balk at losing some mana; now we're losing card advantage, too.
Finally, it's time to talk statistics: more specifically, the likelihood of us seeing both cards in a the same game. Thankfully, unless we use a mass draw effect, odds are we won't see both even if they are in the same list. Once we draw one, we almost certainly won't be tutoring for the other. We aren't using Fabricate to grab a Null Rod with The One Ring in play, that's for sure. However, what we do suffer from is the issue of sub-optimal deployment. Neither of these cards can substitute for the other, meaning drawing one when we would prefer the other weakens our potential later down the line. Having one in play effectively turns the other into a dead draw.
Wrapping Up
Ultimately, the balance between offensive and defensive picks comes down to the severity of their antisynergy. Some will work with others, just not at peak efficiently, while others (like our pair from before) will absolutely crush any hopes of using their counteracting agent. In a singleton format like cEDH - primed with variety - there is undoubtedly room for experimenting with cards that make each other worse, but which cards you use for this is heavily dependent on how much you want to incorporate either into your strategy. I know I like drawing cards more than shutting off mana, that's for sure, so I encourage you all to double check to cross compatibles. Sometimes you might be surprised.