How Polymarket uses “mechanism” to cast “probability”

Author: Movemaker; Source: X, @MovemakerCN

Classifying Polymarket as a speculative platform is a serious misunderstanding.Its core function is to compress and securitize human collective judgments of future events into a tradable financial asset in real time.So to truly understand its pricing system, we have to go beyond the superficial intuition of “$0.9 represents a 90% probability.”

This article will start from a simple question that you must ask when trading, revealing the rigorous pricing logic behind Polymarket and why this logic is unbreakable.

1. The two cornerstones of Polymarket: the hard constraints of “mathematics” and “money”

To understand Polymarket, you don’t need to delve into a complex model at the outset, just understand the two “hard rules” that make it work.

Cornerstone 1: Hard constraints in mathematics (probability must = 100%)

First of all, every market on Polymarket is mathematically a “complete and mutually exclusive” event.

complete: means all possible outcomes are listed.
mutually exclusive: means that two results cannot occur at the same time.

In the simplest binary market (for example: “Will event A happen?”), there are only two outcomes: {yes} or {no}.

According to the basic probability axiom, the probabilities of all possible outcomes must add up to 1 (i.e., 100%).Thus, we have the first mathematical constraint that cannot be violated:P(yes) + P(no) = 1$

This equation serves as the mathematical anchor for all subsequent analysis.

Cornerstone 2: Hard constraints of money (price must ≈ 1 USD)

Mathematical axioms are just theories. The advantage of Polymarket is that it uses financial engineering to enforce this constraint in reality.

This mechanism is the “$1 Redemption Guarantee.”

1. Create a “full share”

You can’t just buy “yes” or just “no.”To participate in a market you must:

Deposit Collateral: You deposit 1 USDC to the smart contract.
Obtain a “set”: The contract will immediately mint and issue a complete set of outcome tokens to you, namely:1 USDC → 1 A-Token (yes) + 1 B-Token (no)

2. “Winner takes all” settlement

When the contract expires and is settled, since the events are mutually exclusive (only one of “yes” and “no” can win), the value of this set of shares is strictly locked:

When the oracle determines “A”:- Your A-Token (is) is now worth 1 USD and can be redeemed back to 1 USDC.- The value of your B-Token (NO) returns to zero.
(If the result is B, then vice versa).

3. “No arbitrage” price anchoring

The most critical impact of this mechanism is: at the moment the event is finally settled, the total value of a complete set of {A-Token, B-Token} share combinations is undoubtedly equal to 1 US dollar.

Since we know that this share is guaranteed to be worth $1 in the future, its market price today must be infinitely close to $1.If the price deviates, arbitrageurs will immediately appear and force the price back:

Scenario 1: The sum of the prices is less than 1 (for example: $0.95).If A-Token sells for $0.60 and B-Token sells for $0.35, the total price is $0.95.The arbitrageur would immediately buy an entire share in the market for $0.95 and hold it until maturity.Upon maturity, this set of shares is 100% redeemable for $1.The arbitrageur purchases a $1 “safe bond” at 95 cents, locking in a risk-free return of (1−0.95)/0.95≈5.26% (assuming the platform and USDC are risk-free).This buying pressure could push the price back up to $1.
Scenario 2: The sum of the prices is greater than 1 (for example: $1.05).If A-Token sells for 0.70 and B-Token sells for 0.35, the total price is $1.05.The arbitrageur would immediately deposit 1 USDC himself, mint a new set of {A, B} shares, and immediately sell them on the market for $1.05 USD.Using a cost of $1, they instantly cashed out $1.05, making a profit of $0.05 out of thin air.This selling pressure would bring the price back down to $1.

This two-way arbitrage pressure forces the market price to form a strong equilibrium, which we call the anchor relationship at the financial level: V(A) + V(B) ≈ $1

Now we have two “hard constraints” from different domains:

Mathematical constraints: P(A)+P(B)=1
Financial constraints: V(A)+V(B)≈$1

Polymarket’s pricing system is built on these two cornerstones.jie x, we will explore how these two constraints come together and ultimately derive the core logic of “price is probability”.

2. Why does it sell for $0.9 with a 90% probability?

In the previous chapter, we established two “hard constraints”:

mathematical constraints: The probabilities of “yes” and “no” for an event must add up to 1.P(A) + P(B) = 1$
financial constraints: The yes and no token prices of an event must add up to approximately $1.V(A) + V(B) ≈ $1

2.1 Price is probability: an intuitive derivation

When you put these two constraints side by side, the core logic of Polymarket is obvious: the structure of the two formulas corresponds exactly.

This strongly implies that the price of a token, V(A), is the market’s best estimate of the probability of that event, P(A).

Why does this equation have to hold?We can understand it from the perspective of “fair value”.

What is “fair value”?Suppose an event (A) has a 90% probability of occurring and a 10% probability of not occurring.The future cash flow of the A-Token (YES) you hold is:

There’s a 90% chance it’s worth $1.
There is a 10% chance that it is worth $0.

So, what is the reasonable “fair value” (or “expected value” EV) of this “lottery” today?

EV(A) = (90% x $1) + (10% x $0) = $0.9

*Fair value is $0.90.In a rational market, prices will always tend to their fair value.
If price < fair value: Suppose the market price V(A) is only 0.8.Professional traders will see this as a “discount probability” and they will buy in large quantities until the price is pushed up to 0.9.
If price > fair value: Suppose the market price V(A) sells 0.95.Traders will think this is the “probability of selling at a premium” and they will sell in large quantities until the price is pushed down to 0.9.

Therefore, continued arbitrage pressure in the market will force the price V(A) to always be anchored near its expected value P(A).V(A)≈P(A)

2.2 An important correction: Price = Probability – “Risk Fee”

Now we have to introduce a professional fix.You will often find that an event is polled as having a 95% chance of happening, but the price on Polymarket may only be stable at $0.90.

Does this mean the market is “wrong”?No.This is exactly what the market is doing “right” because it is pricing risk.

In financial engineering, we must distinguish two concepts:

true probability (P): That is, the objective probability of occurrence of “God’s perspective” (for example, 95% of the poll).
Risk-neutral probability (Q): That is, the price actually traded in financial markets (such as Polymarket).

In the real world, investors are risk averse.By holding a token, they not only have to bear the risk of the event itself, but also bear a series of platform structural risks:

Will the Oracle make mistakes?
Can smart contracts be hacked?
Will USDC break its anchor?
Will the platform face regulatory crackdowns?

In order to bear these additional unhedged risks, investors will demand a “discount” as compensation, which is called a “risk premium” in finance.

Therefore, a more precise pricing formula is:V(A) = Q(A) – λ

where Q(A) is the risk-neutral probability of an event, and λ (Lambda) is a compound risk discount (or “risk fee”) that represents the market’s compensation requirements for all the above structural risks.

=When you see a $0.9 price on Polymarket, the professional message it conveys is: “The risk-neutral probability that this event will occur that market participants are willing to bet real money on, and that this price has been revised downwards (net of) all perceived platform and event risks.”

This is the fundamental difference between Polymarket and polls: Polls reflect “opinion,” while Polymarket prices “risk.”

3. How are prices formed?

Up front, we established two cornerstones:

Mathematically, the probabilities must add up to 1.
money, the prices must add up to approximately $1.

Now, let’s get into actual combat.That $0.9 price you see on the screen, where did it come from?And what’s stopping it from deviating?

3.1 Price formation

The most common mistake for novices is to imagine Polymarket as an AMM like Uniswap, thinking that the price is calculated according to a fixed mathematical formula (such as x times y = k).

This is wrong.

At its core, Polymarket is a “Central Limit Order Book” (CLOB) that works exactly like Binance, Nasdaq, or any stock exchange.

The $0.9 you see is the real-time transaction price formed when the “highest bidder” and the “lowest asker” meet in the market.
The price is “discovered” by all participants, not “calculated” by the platform.

Polymarket’s system combines “fast” and “safe”:

Lightning fast (off-chain matching): You submit an order, modify the price, cancel the order… all of this is done for free and instantly on a centralized server.
Absolutely safe (on-chain settlement): Only when your order is completed, the final settlement information will be sent to the blockchain to ensure the safety of your assets.

What does this mean for market makers?

Meaning “no slippage”.They placed a buy order of $0.8, and the transaction price was $0.8.This allows them to steadily earn a $0.01 spread by placing a $0.8 buy order and a $0.81 sell order, just like in the real stock market.

3.2 Why are prices always “good” and “stable”?

You may ask: If everyone is free to place orders, wouldn’t the price go haywire if no one places orders?

This is the most exquisite incentive design of Polymarket, which has two layers:

Incentive 1: Return “profit fees” to “market makers”

Polymarket charges no trading fees, but it does charge a “performance fee” (e.g. k%) of your net profits after the market settles.

Key point: the money does not go to Polymarket!
The platform returns most of this fee directly to the market makers who “provide liquidity” (i.e. place orders) in this market.This incentivizes professional players to flock to you, providing you with stable and deep offers.

Incentive 2: “Quadratic scoring” (forcing you to come up with the best price)

The platform’s method of returning rewards is not “equally distributed” but uses a terrifying weapon of “quadratic scoring”.

In human terms: the better the price you offer (the smaller the bid-ask spread), the rewards you get will increase exponentially.

Example: In a market where the qualifying spread is 4 cents.- Player A offers a spread of 2 cents, and he receives a score of 0.25.- Player B offered a 1 cent spread (only twice as good as A), but he received a score of 0.5625 (2.25 times as good as A!).(This is the simplified formula: ∝(…)²)

This non-linear incentive forces all market makers to “desperately push prices toward the most reasonable midpoint.”

What does this mean for newbies?

This means that as an ordinary user, you can always enjoy the extremely narrow bid-ask spread and extremely low transaction costs brought about by the competition among professional players.