Explaining the rules of Balatro would take too long, but here is an overview of the relevant strategies I used aiming for the highest score:
TL;DR: Perkeo amassing Cryptids eventually copying Red Seal Steel Kings. Brainstorms and Blueprint copying Baron and Mime. Win.
First, increase speed of the game, unlock all jokers, and then play through the unskippable tutorial.
Start a new Ghost Deck game, so that Spectral Cards appear in shops. Critical for my high-score strategy.
#### Ante 1 ####
I pick up Brainstorm, a very useful copying joker. I use Hex to help with earlier rounds.
• Brainstorm (Joker): "Copies the ability of leftmost Joker"
• Hex (Spectral Card): "Adds 'Polychrome' to a random Joker, and destroys the rest."
• Polychrome (Modifier): "X1.5 Mult"
Then I use Soul to get my Perkeo joker.
• Soul (Spectral Card): "Creates a Legendary Joker"
• Perkeo (Joker): "Creates a Negative copy of 1 random consumable card in your possession at the end of the shop"
• Negative (Modifier): Negative cards don't take up a slot, so you can have an infinite amount of them
I then pick up a Cryptid card, to start copying, which is the main strategy.
• Cryptid (Spectral Card): "Creates 2 exact copies of a selected card in your hand."
#### Ante 2 ####
For scoring purposes I pick up Earth.
• Earth (Planet Card): Makes Full Houses give a higher score.
For early scoring I pick up the Flash Card (Jj) joker.
• Flash Card (Jj): "This Joker gains +2 Mult per reroll in the shop "
I use Deja Vu to create a Red Seal on my King, part of the scoring strategy.
• Deja Vu (Spectral Card): "Adds a Red Seal to 1 selected card."
• Red Seal (Modifier): "Retrigger this card 1 time"
#### Ante 3 ####
I use Ectoplasm to make room for more jokers.
• Ectoplasm (Spectral Card): "Add Negative to a random Joker, but -1 hand size."
I use a Chariot to make a Steel Ace. I actually want the Steel to land on the Red Seal King, but that's later.
• Chariot (Tarot Card): "Enhances 1 selected card into a Steel Card"
• Steel Card (Modifier): "X1.5 Mult while this card stays in hand"
I need money to reroll, luckily I have valuable jokers, so I use Temperance.
• Temperance (Tarot Card): "Gives the total sell value of all current Jokers"
Conveniently, a Showman appears right before the next Brainstorm, the copying joker I already have. I can pick up the Showman and reroll and sell it again.
• Showman (Joker): Usually jokers can't appear in the shop if you already have them, but holding Showman allows them to reappear.
With Mail-In Rebate landing on Kings, I can duplicate my Red Seals, making it more likely to draw later on a Chariot, and also discard them for a lot of reroll money.
• Mail-In Rebate (Joker): "Earn $5 for each discarded [rank], rank changes every round"
Three of a Kinds are faster for scoring than Full Houses, so I switch to those with a Venus card.
• Venus (Planet Card): Makes Three of a Kinds give a higher score.
With the reroll money, I can reroll to the Blueprint, which is yet another copying joker.
• Blueprint (Joker): "Copies ability of Joker to the right"
#### Ante 4 ####
I replace my Flash Card (Jj) with The Trio and pick up another Venus. This together is now enough to beat the Ante 6 and 7 bosses, which get in the way of my scoring strategy.
• The Trio (Joker): "X3 Mult if played hand contains a Three of a Kind"
I can finally use Chariot to Steel one of my Red Seal Kings, which completes the deck setup for the final hand. Now all I need is find the necessary jokers and amass enough Cryptids.
#### Ante 5 ####
I can skip a blind, because I'm getting close to having enough Cryptids. In fact, I even use a Cryptid to copy my Red Seal Steel King, which allows it to show up faster in the final Ante.
#### Ante 6 ####
I simply reroll for the Baron.
• Baron (Joker): "Each King held in hand gives X1.5 Mult"
#### Ante 7 ####
I immediately skip to the boss blind, because I don't need any more Cryptids. I only need the Mime of Ante 8.
#### Ante 8 ####
I reroll until the Mime, completing the scoring setup.
• Mime (Joker): "Retrigger all card held in hand abilities"
#### Final Hand ####
This is what happens:
Every Red Seal Steel King held in Hand has the following:
• 4 X1.5 Mult abilities: Steel + Baron + Brainstorm + Brainstorm
• 4 retriggers: Base Trigger + Red Seal + Mime + Blueprint
This gives 4x4 = 16 X1.5 Mult calculations, which is X1.5^16 = X656.8 for each card.
I use 54 Cryptids, which gives 1 + 54*2 = 109 cards. This means a mult of X656.8^109 = X1.2e307.
With the non-steel Red Seal King we get another X1.5^12 = X129.7, which puts us beyond X1.7e308 = 2^1024, which is the largest number represented by the double-precision floating-point format used by Lua in the LÖVE framework, which Balatro is programmed in.
Due to implementation details, it results in a "nan" value before the "e" and a "inf" after it, so we get a score of "naneinf".