My DM is questioning my use of a deck of playing cards as the signature weapon for my gambler Assassin.
He said "do you really think a playing card can do damage, and let you tack on Sneak Attack damage?" and I countered "you're enforcing actual physics and logic on a fantasy game where spells, variant races, dragons, gods and demons are common place?"
Am I right or is the DM right? Can a thrown playing card deal 1d4 + str mod if used with the Tavern Brawler's Improvised Weapon ability?
You may not like the rulings a DM gives at a table, but the DM is given the freedom to adjudicate their table as they see fit.
This doesn't mean it is a dictatorship. Snap decisions are sometimes necessary during a game that can later be discussed at greater length to find a solution that works for all parties.
More information on this can be found in the DMG, page 5 under Master of Rules.
The rules don't account for every possible situation that might arise during a typical D&D session...Sometimes mediating the rules means setting limits...
From a RAW perspective, it may seem like any potential object can be an improvised weapon, but that is not necessarily the case. It remains up to the DM to decide if it is unreasonable and would work as such in their world. (See PHB, p. 6)
If you are able to convince the DM to allow it, that's wonderful. If it isn't, you need to decide if that is preventing you from having fun (which, I think, is the goal here.)
Maybe you can work together to treat it something like a "Magic Stone" Cantrip (elemental evil) type of action. Replace stone with card. This would effectively replace the Tavern Brawler feat with Magic Initiate (and you'd get another cantrip and 1st level spell). You could also work out a different way with your DM to get this cantrip if you like it.
You touch one to three pebbles and imbue them with magic.
You or someone else can make a ranged spell attack with one of the pebbles by throwing it or hurling it with a sling. If thrown, it has a range of 60 feet. If someone else attacks with the pebble, that attacker adds your spellcasting ability modifier, not the attacker's, to the attack roll.
On a hit, the target takes bludgeoning damage equal to 1d6 + your spellcasting ability modifier. Hit or miss, the spell then ends on the stone. If you cast this spell again, the spell ends early on any pebbles still affected by it.
Or, since you're asking for something that doesn't seem realistic to the DM, what about trading off the ability to use the cards as a weapon, but not be able to use other improvised items as weapons in this manner?
RAW gives very little guidance on what constitutes an improvised weapon, but I would say the default is yes, unless your GM says no.
Given your edit that the DM is saying it's not possible, then no, the answer is it's not possible. Your DM adjudicates the game, and his or her ruling is what you play by. If you think this should be an integral part of your game, work with him to find a way that your character can chose to use playing cards in this way - either as a minor magical object, or made of a special material, or due to specialized training.
Either way you would not get sneak attack damage. The text of sneak attack says it must use a "finesse or a ranged weapon." An improvised thrown card is not a ranged weapon, and it's not finesse. If you're looking to do this ask if your character would be allowed to find a way to acquire an item that is card-like or can be used as playing cards but statistically resemble a dagger (metal cards, with a sharpened corner, for instance).
PHB Page 148:
An object that bears no resemblance to a weapon deals 1d4 damage (the DM assigns a damage type appropriate to the object). If a character uses a ranged weapon to make a melee attack, or throws a melee weapon that does not have the thrown property, it also deals 1d4 damage. An improvised thrown weapon has a normal range of 20 feet and a long range o f 60 feet.
How to Play chapter has a three enumerated steps to play D&D.
The Rules exist to guide the DM on how they should adjudicate, but the DM's word is law. That said, according to the rules as they are written, your cards should cause as much issue as they are creating.
An object that bears no resemblance to a weapon deals ld4 damage (the DM assigns a damage type appropriate to the object). If a character uses a ranged weapon lo make a melee attack, or throws a melee weapon that does not have the thrown property, it also deals ld4 damage. An improvised thrown weapon has a normal range of 20 feet and a long range of 60 feet.
Rules as Written/Intended, that would be 1d4 + (Str or Dex mod) would be the damage; the DM would decide which stat applies. The damage die even in the Weapons table leaves off the modifier, so I believe the RAW/RAI is that you'd add the relevant modifier.
I'd assume because it is ranged, that it would be Dex, not strength, though, I think an argument could be made that the playing card is a stand in for a dagger which has finesse and can either way.
You are proficient with improvised weapons and unarmed strikes.
All this adds is that your attack strikes are made adding your proficiency bonus... Which is a huge boon at higher levels, but doesn't affect damage calculations.
In fact the numbers match daggers and darts so well, if I were DM, I'd limit the number of cards you have to 20 (saying the game of cards you play only uses 20 cards, without buying more) and wouldn't require Tavern Brawler... Because all you're really doing is skinning darts to be cards.
The only issue I could see a DM having a problem with is weight and concealability. Because you change the form factor from the dart (almost as long as a modern Javelin) to a card would take up less carrying capacity and you could stock up on many more "quivers"/"decks" of them. Moreover, cards being small they would be easier to hide, often thought harmless when searched and could cause a more cautious DM some pause. That said, we see the Monk's passage call shurikens re-skinned darts, and daggers are fairly concealable, too.
So, that brings us the truest and most-oft repeated advice on the site: Talk to your DM. Which the reworded question makes it clear you're doing. The key here is to do it in advance of the game and sell the idea as reskinning the look of an item to another. Perhaps try selling the idea of letting you spend downtime crafting throwing stars or shuriken into custom cards, that when examined closely (investigation check with a set DC) can be discovered to be a weapon.
Ask what problem they are trying to solve for by disallowing cards as weapons, and ask them to work with you on a compromise that will give you the flavor you want and the mechanics they want.
I would probably allow that for flavor, and as you suggest, use the "Tavern Brawler" feat to make it function. I would rule, however, that playing cards (and other such light objects) would not be suitable for applying a Strength bonus; that they would be more like ranged weapons that use Dexterity for their modifiers.
Player intent counts for a lot on things like this. If the goal is simply fun, and a roleplaying flavor, I'm willing to bend the rules (and physics) a fair bit to accommodate. If, OTOH, the intent turns out to be a sneaky power play to find a way to have an armed character in places where everyone else is unarmed, I'm a lot less likely to be such a softie.
