How Polymarket uses "mechanisms" to forge "probability"

Classifying Polymarket as a speculative platform is a serious misinterpretation. Its core function is to compress and securitize collective human judgments about future events into a tradable financial asset in real time. Therefore, to truly understand its pricing system, we must go beyond the superficial intuition that "$0.90 represents a 90% probability."

This article will start with a simple question you will definitely ask when trading, and reveal 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 complex models from the start; you only need to understand two "hard rules" that make it work.

Cornerstone 1: The hard constraint of mathematics (probability must equal 100%)

First, every market on Polymarket is mathematically a "complete and mutually exclusive" event.

• Complete : means that all possible outcomes have been listed.
• Mutual exclusion means that two results cannot occur simultaneously.

In a very simple binary market (e.g., "Did event A occur?"), there are only two possible outcomes: {yes} or {no} .

According to basic probability axioms, the sum of the probabilities of all possible outcomes must equal 1 (i.e., 100%). Therefore, we arrive at the first inviolable mathematical constraint: P(是) + P(否) = 1

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

Cornerstone Two: The hard constraint of money (the price must be approximately $1).

Mathematical axioms are merely theoretical; the advantage of Polymarkets lies in its use of financial engineering to enforce this constraint in reality .

This mechanism is called " US$1 redemption guarantee ".

1. Creating a “full share” means you cannot simply buy “yes” or only buy “no.” To participate in a market, you must:

1. Deposit Collateral : You deposit 1 USDC into the smart contract.
2. Obtain the "Set" : The contract will immediately mint and issue you a complete set of result tokens, namely: 1 USDC → 1 A-Token (Yes) + 1 B-Token (No)

2. "Winner-Take-All" Settlement: At contract expiration and settlement, because the events are mutually exclusive (only one can win, either "yes" or "no"), the value of this share is strictly locked in:

• When the oracle determines the result as "A":
• Your A-Token is currently worth $1 and can be redeemed for 1 USDC.
• Your B-Token (No) has zero value.
• (If the result is B, then the reverse is also true).

3. “No-arbitrage” price anchoring: The most critical impact of this mechanism is that at the moment of final settlement of the event, the total value of a complete set of {A-Token, B-Token} shares is definitely equal to $1 .

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

• Scenario 1: The sum of prices is less than 1 (e.g., $0.95). If A-Token sells for $0.60 and B-Token sells for $0.35, the total price is $0.95 . An arbitrageur will immediately buy a complete set of shares on the market for $0.95 and hold it until maturity. Upon maturity, this set of shares is 100% redeemable for $1. The arbitrageur has purchased a $1 "safe bond" at a price of 0.95 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 will cause the price to rise back to $1.
• Scenario 2: The sum of prices is greater than 1 (e.g., $1.05). If A-Token sells for 0.70 and B-Token sells for 0.35, the total price is $1.05 . Arbitrageurs will immediately deposit 1 USDC to mint a new set of {A, B} shares, and then immediately sell them on the market at $1.05. They instantly cash out $1.05 with a cost of $1, making a profit of $0.05 out of thin air. This selling pressure will cause the price to fall back to $1.

This two-way arbitrage pressure forces market prices to reach a strong equilibrium, which we call the financial anchoring relationship : V(A) + V(B)≈$1

We now have two "hard constraints" from different domains:

1. Mathematical constraint : P(A) + P(B) = 1
2. Financial constraint : V(A) + V(B) ≈ $1

Polymarket's pricing system is built upon these two cornerstones. Next, we will explore how these two constraints are combined and ultimately derive the core logic of "price as probability."

2. Why is there a 90% probability that it will sell for $0.9?

In the previous chapter, we established two "hard constraints":

1. Mathematical constraint : The probabilities of an event being "yes" and "no" must add up to 1 .
2. P(A) + P(B) = 1
3. Financial constraint : The sum of the token prices for the "yes" and "no" of an event must be approximately equal to $1 .
4. 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 becomes obvious: the structures of the two formulas are completely corresponding .

This strongly suggests that the price V(A) of a token is the best estimate of the probability P(A) of that event occurring in the market .

Why must this equation hold true? We can understand it from the perspective of "fair value".

What is "fair value"? Assume an event (A) has a 90% probability of occurring and a 10% probability of not occurring. The future cash flows of your A-Token (yes) are:

• 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 ticket" today?

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

• The fair value is $0.90. In a rational market, prices will always tend toward their fair value.
• If price < fair value : Assume the market price V(A) is only 0.8. Professional traders will see this as a "probability of selling at a discount," and they will buy heavily until the price is pushed up to 0.9.
• If price > fair value : Assume the market price V(A) is 0.95. Traders will perceive this as a "probability of selling at a premium," and they will sell heavily until the price is driven down to 0.9.

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

2.2 An important correction: Price = Probability - "Risk Fee"

Now, we must introduce a professional correction. You will often find that an event has a 95% probability of happening in a poll, but the price on Polymarket may only remain stable at $0.90.

Does this mean the market is "wrong"? No. This is precisely a sign that the market is "right," because it is pricing in risk .

In financial engineering, we must distinguish between two concepts:

1. True probability (P) : the objective probability of the occurrence of the "God's-eye view" (e.g., 95% in a poll).
2. Risk-neutral probability (Q) : the actual price traded in a financial market (such as a polymarket).

In the real world, investors are risk-averse . Holding a token means bearing not only the risk of the event itself, but also a range of structural risks associated with the platform :

• Can oracles malfunction?
• Can smart contracts be hacked?
• Will USDC become unpegged?
• Will the platform face regulatory crackdown?

To cover these additional, unhedged risks, investors demand a “discount” as compensation, which is known in finance as a “risk premium.”

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

Here, Q(A) is the risk-neutral probability of the event, while λ (Lambda) is a composite risk discount (or "risk premium") that represents the market's requirement to compensate for all of the aforementioned structural risks.

When you see a price of $0.90 on Polymarket, the professional message it conveys is: "Market participants are willing to bet real money on a risk-neutral probability of the event occurring, and this price has been adjusted down (subtracted) from all perceived platform and event risks."

This is the fundamental difference between Polymarket and polls: polls reflect "opinions," while Polymarket prices "risk."

3. How are prices formed?

Above, we have established two cornerstones:

1. In mathematics , the sum of probabilities must equal 1.
2. In monetary terms , the sum of the prices must be approximately equal to $1.

Now, let's get into a practical example. Where did that $0.9 price you see on the screen come from? And what's preventing it from deviating from that price?

3.1 Price Formation

The most common mistake beginners make is imagining Polymarket as an AMM like Uniswap, assuming that prices are calculated using a fixed mathematical formula (such as X*Y = K).

This is incorrect.

At the heart of Polymarket is a Central Limit Order Book (CLOB), which 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 askder" meet in the market.
• Prices are "discovered" by all participants, not "calculated" by the platform.

Polymarket's system combines speed and security:

1. 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.
2. Absolutely secure (on-chain settlement) : The final settlement information will only be sent to the blockchain after your order is completed, ensuring the safety of your assets.

What does this mean for market makers?

This means "no slippage." They place a buy order at $0.80, and the transaction price is $0.80. This allows them to consistently earn a difference of $0.01 by placing a buy order at $0.80 and a sell order at $0.81, just like in the real stock market.

3.2 Why are prices always both "good" and "stable"?

You might ask: If it all depends on everyone placing orders freely, what if no one places orders, wouldn't the price become chaotic?

This is Polymarket's most ingenious incentive design , which has two layers:

Incentive 1: Return the "profit fee" to the "market maker".

Polymarket does not charge transaction fees, but it will charge a "performance fee" (e.g., k%) from your net profit after market settlement.

• Key point : This money does not belong to Polymarket !
• The platform directly returns the vast majority of this fee to market makers who "provide liquidity" (i.e., place orders) in the market. This incentivizes professional players to flock to the platform and provide you with stable and deep quotes.

Incentive Two: "Square Scoring" (forcing you to offer the best price)

The platform does not distribute rewards equally, but instead uses a terrifying "quadratic scoring" method.

In layman's terms: the better the price you offer (the smaller the price difference between buying and selling), the more exponentially your rewards will increase.

• For example , in a market where the acceptable price difference is 4 cents.
• Player A offered a 2-cent difference and earned a score of 0.25.
• Player B offered a 1-cent difference (only twice as good as A), but he scored 0.5625 points (2.25 times that of A!).
• (This is the simplified formula: Score ∝ (...)^2)

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

What does this mean for beginners?

This means that as a regular user, you can always enjoy the extremely narrow bid-ask spreads and very low transaction costs that come with the competition from professional players.

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