Clowns as Algebra: Arithmetic in Balatro

Note: The following article contains mild spoilers for Balatro.

Maths can't mind its own business. Most other academic fields comment on a single area of interest: living organisms, the events of the past, human communication, etc. These subjects can stick to each other: you can combine biology and chemistry into biochemistry or history and art into the history of art, but each topic has a clear centre of gravity. Their perspective is local because the concepts that comprise them are localised. Physics describes "baryonic matter", but anthropology and philosophy mostly wouldn't. Anthropology cares about "social customs", but physics and geology? Not so much. Maths, on the other hand, is this carpet of vines that stretches over every one of the sciences and humanities because ideas like numbers and logical operations are applicable to entities in any other topic, from meteorology to music to family lineages. The number 5 could refer to 5 cloud types, 5 notes, or a house which produced 5 monarchs. A sociologist could normalise data about a population, or an architect could use Pythagoras's theorem to calculate the length of a slope. Patterns like numbers, manifolds, and formulae don't assume anything about the underlying systems or objects they describe, and so, maths becomes universal.

There is another edge to this sword. The same abstraction which makes maths a multitasker also makes it saltine dry for most people. Academic subjects usually include elements that clearly relate to people's everyday lives. Food science has cooking and meals, and psychology has our memories, thoughts, and beliefs. Maths has... The percent sign? Educators have long strived to increase the personal relevance of maths by demonstrating how its models apply to the real world. They might use probability theory to prove a Minecraft speedrunner was cheating, or calculus to marry the perfect Mario Kart drivers to vehicles.^[1]

Maths in Video Games

Already, we're seeing that video games have a role in maths education. Yet, anyone who's played an edutainment game knows that such software often educates better than it entertains. Even that phrase "maths education" sounds a bit stodgy, uncool, summoning up memories of exhaustively copying boring equations from a whiteboard onto grid paper. So, while video games outside the classroom have their heads swimming with sums, they rarely lift the curtain on their number crunching or task the audience with acting as a human calculator. Then there's this freak: Balatro.

The motor of the computer is mathematics: figures and flags are how the machine determines and remembers, which means quantifiable data are also the basis of video games, and any attempt to manipulate a computer game's state is an attempt to manipulate its mathematics. Picking up a new claw in Trials of Mana adds to our attack value in the equation that the game uses to calculate damage. In Age of Empires, we might rush the Egyptians with a wall of troops, intimidating them into retreat. Our army would act as a keypad through which we could enter new internal variables for the AI, moving them from advancing to fleeing. However, Trials of Mana and Age of Empires don't stencil their AI algorithm or damage calculations onto the screen or ask the player to think of charging elephants or spiky gloves as mathematical constructs. But we're not here to talk about Trials of Mana or Age of Empires, we're here to talk about Balatro, and on the left side of Balatro's interface, in ultramarine and fiery red, are the figures that govern your success.

How Balatro Works

I'm about to give quite an involved description of Balatro's rules, so if you are already a certified Ringling Brother, please scroll down to "The Bare Bones" header. Balatro is the "poker roguelike". It is played across multiple rounds, and each of these rounds has a target score. At the start of a round, we receive a set number of "Hands" and "Discards" and draw a fan of cards from a standard deck. As long as we still have Discards to disburse, we can select up to five cards in our hand and spend a Discard to throw them in the trash. We draw five new cards in their place. We may otherwise select up to five cards from our hand and play them to score points, losing a "Hand" in the process. If we run out of Hands before we satisfy the target score, we lose. Otherwise, we pass the round and may enter the shop before the next round or skip past the bazaar for a bonus reward.

When we play a hand, our score is calculated using the following equation:

Chips x Mult = Score

You don't need to know what Chips and Mult are yet. In fact, that's what we'll learn by running through the following steps. We're going to discover how the game calculates the "Chips" and "Mult" values for the above sum. In order, the steps are:

1. Determining the base Chips and Mult for your hand. The hands of Balatro are the hands of poker: five cards of the same suit count as a Flush, two cards of the same value count as a Pair, etc. Each trick has a base number of Chips and Mult associated with it, and the sets that score higher in poker are also the sets that score more Chips and Mult. You can upgrade the Chips and Mult you receive for each hand with "Planet Cards".
2. Scoring the cards. The value of each card in your hand is added to the base Chips number. Face cards count for 10 Chips each and aces for 11. Some special cards are also "Enchanced", providing other stipends. Foil cards add 50 to the base Chips, and striped cards add +4 to the Mult, for example.
3. Adding Joker effects. Between rounds, players can purchase "Joker" cards, which sit in a cubicle at the top of the screen. They twist and knot the play with clownish mischief. A Joker may confer one more Discard per round or pay out 4 dollars each time you snatch victory from the jaws of defeat. A Joker might also add to the Chips or Mult, often with a catch or condition. Some gurning fools multiply your Mult by 2 if your hand contains Three of a Kind or pay out 30 Chips for each remaining Discard you have, but a player can only have a limited number of Jokers. You organise your Jokers from left to right in their cosy little rectangle, and their bonuses are generally added in order from left to right.

A Sample Hand

To decode this program, let's take a look at Balatro in action. I start a round holding these eight cards:

J♠ 10♠ 7♠ 9♥ 7♥ 8♣ 4♣ 2♦

From them, I choose and play the following five:

J♠ 10♠ 9♥ 8♣ 7♥

That's a Straight, and the base Chips and Mult for a Straight are 30 x 4. We sum the values of all the cards in my hand (remembering that face cards are worth 10), and we get 44. We add that number onto the base Chip value (30), so the new score equation is 74 x 4. In this imaginary hand, we'll say we have only one Joker: Wrathful Joker. This gives us +3 Mult for every spade in our played hand. We played two spades, so we add 6 to our base Mult. The new score equation is now 74 x 10. 74 x 10 is 740, so we score 740 for that hand. If you have danced with Balatro's devils, you might be calling foul on my description. There are often extra steps to scoring, and the procedures I outlined are remixed by certain bosses or Jokers, but there are only so many conditionals and outliers a newbie can account for before their head blows up. This napkin sketch of the game will suffice for a beginner's understanding.

The Bare Bones

Earlier, I said that maths got its share of tomatoes thrown at it for being transcendently immaterial. I said it like five minutes ago if you were even listening! However, there is also a gap in interest between maths enthusiasts and maths haters caused by differing conceptions of what the topic entails. To the professor with the bushy moustache and Fulltouch chalk, maths is a sandbox where the same few components can be endlessly rearranged in creative and elegant structures, but to the average person, maths is the rote clockwork of calculating your taxes. To flaunt the infinite possibilities of numerics, ambassadors of maths often break from the basic operators: the plus, minus, divide sign, etc. to soar into the boundless skies of geometry, imaginary numbers, and the like. Balatro, however, is a simple boy and believes in getting by with nothing more than the addition and multiplication on his back, but it is a heavy sack of addition and multiplication.

I grabbed the Jokers that performed in one of my recent rounds of Balatro and wrote out the logic of each below. This is going to be one of those examples which you don't need to understand in full. I'm just trying to engender a sense of the game's abstract complexity. Here are the effects of our five Jokers:

• Stuntman: +250 Chips and -2 hand size.
• Even Steven: +4 Mult for every played card that has an even number value.
• Greedy Joker: +3 Mult for every diamond card played.
• Fibonacci: +8 Mult for each Ace, 2, 3, 5, or 8 played.
• Seeing Double: x2 Mult if scoring hand has a card with a club suit and at least one card of any other suit.

With those modifiers on deck, I played the following hand:*

5♣ 5♥ 6♠ 6♣ 6♦

*Hand may not have actually been played and is only intended for educational purposes.

That's a Full House, which at level 1 would score:

40 Chips x 4 Mult

Based on our hand and Jokers, the following maths would determine the number of Chips in the equation:

40 + 5 + 5 + 6 + 6 + 6 + 250 = 318

And the Mult would be totalled using:

(4 + (3 x 4) + 3 + (2 x 8)) x 2 = 70

Simplified:

(4 + 12 + 3 + 19) x 2 = 70

Giving us:

318 Chips x 70 Mult

For:

22,260 points

Signifiers

Again, these aren't just pistons inside the game's engine block; these are equations exposed to the player and that the player must construct using the cards available. But does any of this look fun, or does it look like a hell known only to the Maths Blaster generation? Gorging on all this data is going to fry your brain, but for a mathematical problem, Balatro finds a mathematical solution. The first thing we learn in algebra is that a symbol can fill in for a value. We later learn that we don't have to write out every number that went into making an equation each time we reference it; one of those symbols will do.

Density is a concept that pops up in numerous physics equations. You calculate it by taking an object's mass (m) and dividing it by its volume (v), but you don't need to write "m/v" every time density appears in the maths; you can just write the density sign (usually ρ or d).^[2][3] Plenty of theorems incorporate the difference between two numbers, but instead of writing n1 - n2 every time we want to express that gap, we can just write Δ for difference. Balatro knows this; it doesn't have to garrulously restate the rules for every card in its equation or even repeat the numeric products created by those rules. Instead, it drops the base numbers (Chips x Mult) and then represents everything else with a PNG of a playing card or clown. Even Steven is algebraic notation for "4 x no. of even cards in hand". Stuntman is a symbol for "+250 Chips, -2 cards in hand". No data overload, no ugly number spam, just a gang of jesters leering from inside your monitor, the way god intended.

All graphical games have pictorals stand in for mechanics, but Balatro is grounded in arithmetic, and we assemble both hands and troupes of Jokers from left to right. That gives Balatro the particular aesthetic of writing equations. It's not that every time you play a hand or add a Joker to the balcony, that you're calculating what you'll score down to the digit. A dedicated player may run the numbers when the gauntlet is thrown down, but most of the time, you're looking up base Chip and Mult values in the table of hands, or you're making qualitative judgments about tricks and cards. Example. Begin brain simulation. If I have a Joker that adds 12 to the Mult every time I play a Straight, I know it's generally good to play Straights even though I almost never know the figure that will light up when I drop my Straight onto the felt. Or, assume I can score relatively high Mults. If, from this position of power, I can replace a Joker that adds 4 to my Mult with one that doubles my Mult, that's going to make for high-scoring hands even if I can't name a particular number that might be produced by my Mult-doubling card.

The Essence of Maths

These vibe calculations might sound too imprecise for a game I'm describing as having a mathematical spirit. However, a useful skill for any mathematician, and one you naturally attain with practice, is intuiting the broad effects of an equation on sight. Off the top of my head, I couldn't tell you what the result of πr² or 2πr will be for any one r, but I can tell you that if r is above 2, πr² will give a larger result than 2πr just because of the absurd amplifying power of the ². You can test this out for yourself with a calculator app.

Here's another: This equation will draw a parabola on a graph:

-8𝑥²

Here's a graphing calculator in which you can play with it yourself. At first glance, I don't know where most of the points of that parabola will fall, but I do know that the curve will form a rough U shape because there is a minus before the set of numbers being squared.^[4] If it started with a positive figure, the curve would form a rough arch. The same intuition lives in Balatro. I'm clueless to the exact numeric repercussions of placing the Greedy Joker to the left of the Ramen Bowl Joker, but I know I'll score more points than if I did the opposite. But in this circus of numbers, the joke is on you, as your intuition for even basic arithmetic might not be all you thought it was cracked up to be.

Unintuition

Let's say my hands generally produce Mults around 35. I check back into the shop and have the option to buy either a Joker that will increase my Mult by 12, or one that will multiply the Mult by 2. Logically, I know that the x2 buff is superior to the +12 because 35 + 12 is 47, but 35 x 2 is 70. But there's still that irrational part of my mind telling me that 12 is a much bigger number than 2, and so, I should take the Joker that buffs my Mult. Other times, it's the positioning of a multiplier in a set that confuses.

Look at this equation:

3 x 2 + 3

And now this one:

3 + 3 x 2

Now look at this picture.^[5]

That last bit wasn't part of the experiment. I just like that image. As for the equations, I think most people wouldn't clock that they are all that different at first. Both sums start with the same number, and have + 3 and x 2 as their two operations. However, that first equation gives 9 as its result, while the second gives 12. The second result is one-third larger than the first. This delta becomes salient in Balatro because if you have a Joker that adds to the Mult and one that multiplies the Mult, you're going to want to place the one that multiplies the Mult towards the right end of your queue of Jokers. In other words, you get higher results by situating a multiplication nearer the end of an equation. On the flip side, the order in which you place your additive or multiplying Jokers does not matter. Whether I perform:

3 + 6 + 11

Or:

11 + 6 + 3

The result is 20. It would be the same situation if I were to reorder the numbers in 1.5 x 2 x 3. There's no way to make those operands multiply to equal anything but 9. This property that lets us reorder numbers around an operation and still get the same answer is the commutative property. Both addition and multiplication are commutative, and therefore, so are their Jokers.^[6]

As if these eccentricities in the maths weren't troublesome enough, you can also underestimate the potency of multiplying multipliers. Let's say I'd normally score 400 points, then a card comes along that multiplies my Mult by 2. Later, I have the choice to either take another Joker that doubles my Mult or collect something else entirely. My gut tells me that that second x2 Joker is just as valuable as the first, but it's not; it's twice as valuable as the first. If I have 400 points and can double them, that's 400 + 400, but if I have 400 points and can double that and double that again, that's 400 + 400 + 400 + 400. This sounds obvious written out, but Balatro often squeezes itself into the gap between what we know and what we intuit. For those of you who are already more arithmetically minded, you'll notice that Jokers that multiply our Mult effectively raise the Chips value to an exponent. Such Jokers clean up in rounds because they are fertilisers for exponential growth.

Order of Operations

Now we've internalised that multiplication is this powerful supersizing ray, a hierarchy of Jokers seems to emerge, descending from their greasepaint thrones. The Jokers that garnish our base Chips matter least, the ones that increase our Mult matter more than that, and the ones that multiply the Mult are the be-all and end-all. But that's still to misunderstand what multiplication does. If I have a choice between a Joker that adds 80 Chips and one that adds 4 Mult, which one should I get? We can't give a definitive answer, only one that applies in the context of the Chips and Mult that I'm generally attaining already. Let's imagine a scenario where I'm regularly scoring 50 x 4 for 200 points. If I added 4 Mult, I'd score 50 x 8 for 400 points. However, if I added 80 Chips, I'd be cashing out at 130 x 4 for 520 points, 120 more. The proof is in the pudding: A Joker that offers a mere 80 Chips can trump one that raises your Mult in the right context. But what if I were in an alternate universe where I was making around 100 x 4 Chips per hand? If I take the Chips-increasing Joker, I step up from 400 points to 180 x 4 or 720 points. However, if I added 4 to my Mult instead, I'd be getting a greater return on my hands: 100 x 8 or 800 points. Cards that increase our Mult are potent once we already have a healthy basis of Chips to multiply.

Cards that multiply our Mult are subject to the same conditionality. If I'm made to pick between a Joker that doubles my Mult and one that provides a flat increase of 20, the correct Joker depends on my current Mult. If I usually end a hand with a respectable Mult of 41 then I should take the doubling card. 41 x 2 gives me a larger figure than 35 + 25. However, if I was expecting to post a Mult of 10 when I played a hand, the +20 Joker would be superior. 10 + 20 is bigger than 10 x 2. With these principles in mind, a picture forms of the crack squad of Jokers we should be convening. We want a Joker that increases the number of Chips we score. With that taken care of, we need cards to multiply the number of Chips, and only after we have one or more of them should we unlock the duplicative immensity of cards that multiply our Mult. Maybe if we can master all those levels of summation, Balatro 2 will let us play with division. Thanks for reading.

Notes

1. The latter video makes a few minor errors when discussing the gameplay of Mario Kart 8. See the comments for details.
2. Density by The Editors of Encyclopaedia Britannica (October 8, 2025), Britannica.
3. Schön, J.H. (2011). Handbook of Petroleum Exploration and Production vol. 8. ScienceDirect (Chapter 4: Density).
4. Redden, J. (Date Unknown, Accessed November 10, 2025). Beginning Algebra (v. 1.0). The 2012 Book Archive (Sec. 9.5: Graphing Parabolas).
5. The time Yo-Yo Ma met a wombat on the bathroom floor by Classic FM Staff (May 29, 2020), Classic FM.
6. The NROC Project (Date Unknown, Accessed November 10, 2025). Developmental Math. LibreTexts (Sec. 9.3.1: Associative, Commutative and Distributive Properties).

All other sources linked at relevant points in article.