A Comprehensive Explanation of Polymarket: Why YES + NO Must Equal 1?

Author: Dfarm

When it comes to Polymarket, many people know that the core concept is: YES + NO = 1, but do you really understand this simple formula? Today, I will explain the shared order book of Polymarket!

If you check the official documentation of Polymarket, you will find that the explanation for price calculation is as follows:

You might not fully understand it after reading, but that's okay; let me give you an example.

A Dollar Torn Apart

Some friends might think that YES 0.7 + NO 0.6 = 1.3 is acceptable, right? The free market can set prices freely, right?

This is incorrect. Although it is a free market, YES and NO are not two separate stocks; they are two halves of the same one dollar.

Imagine that what Polymarket sells is not a lottery ticket, but a future voucher worth one dollar.

The value of each voucher is always one dollar.

The market tears this one dollar into two halves, one half labeled YES and the other half labeled NO.

On the settlement day, if the event occurs, then the YES voucher = 1 dollar, and the NO voucher = 0. If the event does not occur, the YES voucher = 0, and the NO voucher = 1 dollar.

From this, we can see that at settlement:

Occurs: 1 + 0 = 1
Does not occur: 0 + 1 = 1

Under the premise of an effective market with the same market and the same settlement conditions for a pair of complementary outcomes, when you combine YES + NO, you are essentially buying something that will definitely be worth 1 dollar at expiration.

Multi-Option Markets

Many friends might say that some trades are not just YES and NO, but have many options.

For example, predicting the price of Bitcoin will have many price points, and the number of tweets from Musk will also have many options.

In fact, if you have used Polymarket's API, you will find that each option will have YES and NO, and when taken separately, they are independent trades.

Taking the Musk tweet market as an example, we can see that there are many options.

In fact, from the API, each title is:

Will Elon Musk post 0-19 tweets from December 23 to December 30, 2025?
Will Elon Musk post 20-39 tweets from December 23 to December 30, 2025?
Will Elon Musk post 40-59 tweets from December 23 to December 30, 2025?
……

So they also conform to YES + NO = 1.

Some friends who are enthusiastic about sports markets may find that games like the NBA do not have YES and NO, but instead have the names of the two teams.

We note that currently it is Moneyline, which predicts which team will ultimately win, because every NBA game will definitely have a winner and a loser, and sometimes if it ends in a tie, there will be overtime, so the home team and the away team correspond to YES and NO.

To add, in soccer markets, a draw may occur, so in soccer, you can buy YES and NO for the home team, YES and NO for the away team, and YES and NO for a draw.

Other markets are generally similar, and I won't list them all; the core idea is that all markets conform to YES + NO = 1.

Shared Order Book

Many people think that Polymarket's order book is the same as that of cryptocurrency trading markets, but this is an incomplete understanding; the differences are significant, as it is a combination of YES + NO.

Let's return to the example in the official documentation, which states: "If you place a limit order for YES at a price of 0.60 dollars, when someone places an order for NO at a price of 0.40 dollars, that order will be executed. This becomes the initial market price."

How should this sentence be understood? Many people's intuition is that they feel they are trading without interacting with others; why would such matched trades occur?

This is the magic of the shared order book; let's do a practical example.

I found a market that is not very active and placed a YES buy order at a price of 18 with a quantity of 10:

At this point, let's quickly switch to the NO market to take a look:

What do you see? We actually have a sell order for quantity 10 at price 82 in the NO market!

At this moment, do you feel like the market can be shorted? Just like contract trading, borrowing coins to sell? When you try to sell, it prompts:

It tells you that your balance is insufficient to sell because you do not have NO vouchers, so naturally, you cannot sell. But why is there a sell order at price 82?

Please take a closer look at the screenshots of the YES and NO markets; what do you notice?

Did you find that the ask and bid in the two markets are like mirrors!

My buy order at price 18 and quantity 10 corresponds to a sell order at price 100 – 18 = 82 and quantity 10 on the other side!

You can see that other price points can also correspond one by one; the price follows the formula: YES + NO = 1. Of course, 18 corresponds to 0.18, and 82 corresponds to 0.82; here, it is displayed as two decimal places to help everyone understand that this is a probability.

Now, when you look back at the example in the official documentation: "If you place a limit order for YES at a price of 0.60 dollars, when someone places an order for NO at a price of 0.40 dollars, that order will be executed. This becomes the initial market price."

You should be able to understand it now. Taking my order as an example, if I place a YES buy order at 18, if someone sells to me, it actually means they bought the NO sell order at 82. After the transaction, I have the YES at 18, and they have the NO at 82; our two vouchers combine to satisfy: YES + NO = 1.

You might be curious why not just create two independent order books? Why mirror them?

The answer is liquidity! A combined order book allows liquidity to be concentrated, improving the efficiency of price discovery!

Arbitrage Illusion

Now that you understand YES + NO = 1 and what a shared order book is, let's look at many arbitrage strategies recommended by KOLs. In the same market, YES + NO = 1; do you think this arbitrage exists? You can think about it for a minute before moving on.

The understanding of YES + NO = 1 is: YES has someone selling at 0.4, NO has someone selling at 0.4, I buy both for 0.8, and finally redeem for 1 dollar, netting 0.2 dollars!

This strategy cannot exist in the context of a shared order book.

Because when you place an order to sell YES at 0.4, the system receives that you want to buy NO at 1 – 0.4 = 0.6. (This point has already been explained in the shared order book section; if you don't understand, you can review the shared order book example.)

At this point, another person says they want to sell NO at a price of 0.4.

What happens?

Your true intention is to buy NO at 0.6.

Their true intention is to sell NO at 0.4.

The buy price is higher than the sell price! Your bid of 0.6 is higher than their sell price of 0.4.

The result is that the system will instantly match your trades, and no third party can see it.

If you still don't quite understand, you can imagine that the shared order book is like a self-balancing scale.

The rule it follows is YES + NO = 1.

If you try to break this balance, the system will make you two complete the transaction directly, and others will not see any unbalanced orders appearing.

What remains are only orders where YES + NO > 1.

So stop thinking about YES + NO = 1 in the same market; this scenario will never appear on your screen!

Some people might say, "I am doing a Bitcoin 15m YES + NO = 1 strategy," but this does not count as arbitrage; it is essentially a volatility strategy. You need to place an order on one side and eat the other side at the moment of execution, which can indeed be profitable. However, this carries unilateral risk; if the price moves in the direction of your order and does not return, it will result in a loss.

Correct Arbitrage Strategies

After discussing the incorrect strategies, let's talk about some correct arbitrage strategies.

In fact, if we really talk about arbitrage, there could be many strategies. Today, I will just casually mention a few, which do not represent the quality of the strategies.

Multi-Option Arbitrage

Here, I will take mutually exclusive and fully covering multi-options as an example.

Let's take the earlier example of the number of Musk tweets, where the options start from 20 and go up to 580+, with one option every 20 tweets, totaling about 30 options.

These 30+ options cover the entire range of tweet counts from 0 to over 580, and the final tweet count will definitely fall within this range.

So if you buy all 30+ options for YES, ultimately, one of them will turn into 1 dollar at settlement, while the others will go to zero.

If you buy all 30+ options and the total cost is less than 1 dollar, congratulations, you will earn a profit of 1 dollar minus your cost!

Are there such opportunities? Yes, but they are guarded by a large number of bots, and you definitely won't find such opportunities manually.

Of course, you might say that it's impossible for it to happen below 20; this is just your personal opinion. You can also choose a range for arbitrage based on your own calculations, but this is not strictly arbitrage and carries risks, which is not within the scope of this discussion.

Cross-Event Arbitrage

This screenshot is from a user on platform X: @PixOnChain

This screenshot was taken on a day in September when the two leaders had not yet met, comparing the two events.

You can see that the two options for these events are basically semantically the same, both indicating a meeting in September.

Here, 3 + 94 = 97 indicates that there is still a profit of 100 – 97 = 3 that can be arbitraged, but you might find this profit relatively low, and the key liquidity may also be insufficient, so the actual earnings might not be much.

Cross-event arbitrage bots are fewer than the multi-option arbitrage mentioned above; this requires strict judgment and has a slightly higher technical threshold.

Cross-Platform Arbitrage

The most common is arbitrage between Polymarket and Kalshi. Of course, Kalshi can only be used by U.S. users. Here, we are just discussing this strategy; we can also use other prediction platforms, such as Opinion, to replace Kalshi.

If you can buy:

On platform A, buy YES at price = a

On platform B, buy NO at price = b

And both describe the same event, with settlement based on the same fact.

Then the yield at expiration = 1 dollar, cost = a + b.

If a + b + all friction costs = 1, then it is close to risk-free arbitrage.

The most challenging part here is the phrase "same event." You need to carefully compare the settlement rules on both sides; if there are differences in time zones or sources of evidence, arbitrage could turn into a nightmare.

However, I have previously done arbitrage between Polymarket and Opinion, and many of the rules are identical, so there are no issues there.

But you also need to be aware of the time cost; you have funds trading on both sides, and you cannot withdraw them before settlement. Unless the prices move in your profitable direction, you may have to wait until after the settlement date to withdraw your funds.

Due to the high time cost, many people do not engage in this arbitrage.

Conclusion

Alright, looking back, this is about three thousand words. I wonder if you have truly understood YES + NO = 1 this time. If you really get it, I hope you share this article with more people.

Don't be deceived by those so-called KOLs promoting the strategy of YES + NO = 1 for the same event; they may have just generated a piece of content using AI. After all, I recently asked ChatGPT 5.2 and Gemini, and they both didn't understand the shared order book.

Only by having them consult the official documentation can they discover this issue.

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