Another fun consequence to think about, if we considered the "I can have 150 rats" a valid argument because we are taking the text of Relentless Rats literally and assuming it overrides all other rules:
"I can have a Commander deck of 150 non-Relentless cards and negative fifty Relentless Rats, because '-50' is a number and Rats says 'ANY' number."

Also by that logic the amount of rats you can include in the deck includes 30/17, pi, e, and the square root of 189

Just get me a good ruler, a magnifying glass, and some sharp scissors...

So then a Battle of Wits deck works as long as I have 250 Relentless Rats? Got it.

It's actually kind of ambiguous. Fortunately, this'll never happen, so there's no need to really worry about it, and the "well, your commander would be illegal" is usually plenty to stop them in their tracks.

I wouldn’t want to do this even if I could. I’m firmly in the build as small a deck as the rules allow camp, valuing consistency above all else. I was only asking out of curiosity. I currently have a Rat Colony deck that’ll likely never make it past party favor curiosity. It sparked a google search to make sure I had read the latest verdict on its legality, as the topic was once quite contentious. My curiosity just sort of ran on a tangent.

Negative Numbers, pi, etc are all covered by the rules. However, 150 is still sorta open to that interpretation of ANY.

107.1. The only numbers the Magic game uses are integers.

107.1a You can’t choose a fractional number, deal fractional damage, gain fractional life, and so on. If a spell or ability could generate a fractional number, the spell or ability will tell you whether to round up or down.

107.1b Most of the time, the Magic game uses only positive numbers and zero. You can’t choose a negative number, deal negative damage, gain negative life, and so on. However, it’s possible for a game value, such as a creature’s power, to be less than zero. If a calculation or comparison needs to use a negative value, it does so. If a calculation that would determine the result of an effect yields a negative number, zero is used instead, unless that effect doubles or sets to a specific value a player’s life total or a creature’s power and/or toughness.
Example: If a 3/4 creature gets -5/-0, it’s a -2/4 creature. It doesn’t assign damage in combat. Its total power and toughness is 2. Giving it +3/+0 would raise its power to 1. Example: Viridian Joiner is a 1/2 creature with the ability “{T}: Add an amount of {G} equal to Viridian Joiner’s power.” An effect gives it -2/-0, then its ability is activated. The ability adds no mana to your mana pool.
Example: Chameleon Colossus is a 4/4 creature with the ability “{2}{G}{G}: Chameleon Colossus gets +X/+X until end of turn, where X is its power.” An effect gives it -6/-0, then its ability is activated. It remains a -2/4 creature. It doesn’t become -4/2.
107.1c If a rule or ability instructs a player to choose “any number,” that player may choose any positive number or zero, unless something (such as damage or counters) is being divided or distributed among “any number” of players and/or objects. In that case, a nonzero number of players and/or objects must be chosen if possible.

Would there be any function difference if the card was changed from saying "any number" to "more than 4" ?


to

Yes. According to that wording a commander deck could have either 0, 1, or 5+ Relentless Rats, but not 2, 3, or 4.

thats what I thought...

I wonder if that would stymie people thinking that 150 was allowed. "ANY number" sounds far more permissive to me than "more than 4." Might be worth giving up the Commander options for 2 3 or 4 relentless rats

Well I mean if text was going to change on anything the 100 card rule could also say "No card can override this limit", not that it seems necessary by any means.

Unless we start hearing stories about someone turning up to a FLGS somewhere with their 500-card relentless rats / rat colony / shadowborn apostle EDH deck.

... because if that is a thing I would love to start hearing those stories.

I heard tales way way back of an EDH deck that used Spawnsire of Ulamog to get 200+ Eldrazi, return them to the library (there are various ways to that but I think this one went with killing them all and triggering the "shuffle your graveyard" clause on Kozilek, Butcher of Truth), and then win with Battle of Wits back when sideboards were a thing. It was never actually legal as far as I know because sideboards were never allowed to be that big (and "outside the game" doesn't work in Commander, so you needed the sideboard rule to make Spawnsire work). Sounded like fun, but I suspect it was all theory and no one ever built it.

Thank you for this story.

None of those rules explicitly prevent including a negative number of Relentless Rats in your decklist. They prevent you from choosing and/or using a negative number for effects in game.

Even if there were a rule explicitly stating that a negative number of cards cannot be used in deck construction, my point was that Rat's rules text could be interpreted to override such text, which is silly, but it seems to be exactly the same argument proposed for how a 150 card deck with at least 50 Rats could be considered a valid interpretation of the rules. Also, why stop there? Why shouldn't it override Color Identity rules as well? Put 40 Rats into an Arcum Dagsson and tutor out a Thrumming Stone (and 2 mana 'of any color' - Coalition Relic, Chromatic Lantern, etc.) as soon as you are able.

As long as I'm enjoying thread derails...

If you were playing in a "cards as written" group where wish-style effects can get you any card you own, you could build a Battle of Wits deck around Research // Development. You'd need a shoebox full of them, and every time you Research, get 4 more to shuffle into the deck. Nothin like sitting down for some EDH and having a game of Dominion break out.