A comprehensive explanation of Polymarket: Why must YES + NO equal 1?

Author: Dfarm

When talking about Polymarket , many people know that its core is: YES + NO = 1. But do you really understand this simple formula? Today, I'll explain Polymarket's shared order book in detail!

If you consult Polymarket's official documentation, you'll find that the price calculation is explained as follows:

You might not have fully understood it after reading this, that's okay, I'll give you an example below.

The torn dollar

Some people think that 0.7 for YES + 0.6 for NO = 1.3 would also work, right? The free market allows for free pricing, doesn't it?

This is incorrect. Although it is a free market, YES and NO are not two stocks; they are the same dollar bill cut in half.

Imagine that Polymarket isn't selling lottery tickets, but rather a voucher for the future.

Each voucher is always worth $1.

The market tore that $1 in half, one half saying YES and the other half saying NO.

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

Therefore, at the time of settlement:

• Occurred: 1 + 0 = 1
• This will not happen: 0 + 1 = 1

Under the premise of a market-efficient, same-market, same-settlement-condition pair of complementary results, if you get YES + NO, you've essentially bought something that will definitely be worth $1 upon maturity.

Multiple Choice Market

Many people might say that some transactions aren't just a matter of YES and NO, but involve many options.

For example, there are many price levels to predict the price of Bitcoin, and there are also many options for the number of tweets Musk makes.

If you've ever used Polymarket's API, you'll know that each option has a YES and NO option, and each option can be considered an independent transaction.

Taking Musk's tweet marketplace as an example, we can see that there are many options.

Actually, looking at each title on the API, it's like this:

• 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?
• ...

Therefore, they also meet the condition YES + NO = 1.

Some friends who are keen on the sports market will notice that games like the NBA don't have "YES" and "NO" signs; instead, they show the names of the two teams.

We noticed that it's currently Moneyline, which predicts which team will ultimately win. Since every NBA game has a winner and a loser, and sometimes even a tie can lead to overtime, the home team and the away team are represented by YES and NO, respectively.

One more thing: draws are possible in the football market, so in football, you can bet on the home team (YES or NO), the away team (YES or NO), and a draw (YES or NO).

Other markets are probably similar, so I won't list them all. The core point is that all markets meet the condition that YES + NO = 1.

Shared order book

Many people assume that Polymarket's order book is the same as that of cryptocurrency trading markets, but this is not entirely accurate. There are significant differences, as it is a combination of YES and NO.

Let's go back to the example in the official documentation. The original text reads: "If you place a 'yes' limit order at $0.60, the order will be filled when someone places a 'no' order at $0.40. This becomes the initial market price."

How should this statement be understood? Many people intuitively feel that they are making transactions without interacting with others, so why does this kind of matchmaking occur?

This is the magic of the shared order book; let's try it out.

I found a market with less active trading and placed a buy order for YES at a price of 18 and a quantity of 10.

Now let's switch to the NO market and take a look:

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

At this point, do you feel like you can short sell in the market? Like in contract trading, borrowing and selling? When you try to sell, you'll get the following message:

It tells you that you don't have enough balance to sell because you don't have a "NO" voucher, so you can't sell it. Then why is there a sell order for me at price 82?

Please go back and take a closer look at the screenshots of the YES and NO markets. What did you notice?

Have you noticed that the ask and bid functions in the two markets are almost mirror images of each other?

My buy order is priced at 18 and the quantity is 10. On the other side, there is a sell order priced at 100 - 18 = 82 and the quantity is also 10!

You can see that the other price points can also be matched one by one. The price is the formula: YES + NO = 1. Of course, 18 corresponds to 0.18, and 82 corresponds to 0.82. It is displayed as a two-digit number here to make it easier for everyone to understand that this is a probability.

Now, if you look back at the example in the official documentation: "If you place a 'yes' limit order at $0.60, the order will be filled when someone places a 'no' order at $0.40. This becomes the initial market price."

Now you can understand, right? Let's take my order as an example. I place a buy order for YES at 18. If someone sells it to me, they are actually buying my order for NO at 82. After the transaction, I have YES at 18 and they have NO at 82. When we combine our two vouchers, we get YES + NO = 1.

Here you might be wondering, why not just create two separate trading platforms? Why use mirroring?

The answer is liquidity! Consolidating order books allows liquidity to be pooled together, improving the efficiency of price discovery!

Arbitrage Illusion

Now you understand that YES + NO = 1, and you also understand what a shared order book is.

Now let's look at the arbitrage strategies recommended by many KOLs, which involve YES + NO < 1 in the same market. Do you think this arbitrage strategy exists? You can think about it for a minute before continuing.

The meaning of YES + NO < 1 is: if someone sells YES for 0.4 and NO for 0.4, I buy both for 0.8 and eventually exchange them for 1 US dollar, making a net profit of 0.2 US dollars!

This strategy is simply impossible in the case of a shared order book.

Because when you place a sell order for YES at 0.4, the system receives the order as a buy order for NO at 1 - 0.4 = 0.6. (This has already been explained in the shared order book example above; if you don't understand, you can review it again.)

At this point, another person said, "I want to sell NO, price 0.4."

What happened?

Your real intention is to buy NO at 0.6.

His real intention was to sell 0.4 of NO.

Your bid is higher than your ask price! Your bid of 0.6 is higher than his ask price of 0.4.

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

If you still don't quite understand, you can imagine a shared order book as a balance scale that automatically keeps itself in equilibrium.

The rule he follows is YES + NO = 1.

If you try to disrupt this balance, the system will automatically complete the transaction, and others will not see the unbalanced order.

All that remained were orders with "YES + NO > 1".

So stop thinking about the same market with YES + NO < 1; that scenario will never appear on your screen!

Some might say, "I'm using a 15m Bitcoin YES + NO < 1 strategy. This isn't arbitrage; it's essentially a volatility strategy. You place an order on one side and try to profit from the other side the moment it's filled." However, this carries the risk of a one-sided move. The price might go in the direction of your order and never come back, resulting in a loss.

Correct arbitrage strategy

Having discussed the incorrect approaches, let's now talk about the correct arbitrage approaches.

In fact, there are many arbitrage strategies, but today I'm just mentioning a few, which doesn't represent the quality of the strategies.

Multi-option arbitrage

Here we take a set of mutually exclusive multiple-choice options that cover the entire range as an example.

Let's take the example of the number of Musk's tweets. The options start from <20 and go up to 580+, with one option for every 20 tweets, for a total of 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, at the final settlement one of them will become $1, and the others will become zero.

So if you buy all 30+ options and the total cost is less than $1, congratulations, you can make a profit of $1 minus your cost.

Do such opportunities exist? Yes, but they are all guarded by a large number of robots, and you definitely can't find such opportunities manually.

Of course, you might say that it's impossible for it to fall below 20, but that's just your personal opinion. You can also choose a range for arbitrage based on your own calculations, but that's not arbitrage in the strict sense; it's a risky strategy and not within the scope of this discussion.

Cross-event arbitrage

This screenshot is from X platform user: @PixOnChain

This screenshot was taken sometime in September, before the two leaders had even met. It's a comparison of two events.

It can be seen that the two options for these two events are basically the same in meaning, both being a meeting in September.

Here, 3 + 94 = 97 means there is still a profit of 100 - 97 = 3 that can be extracted. However, you may find that this profit is relatively low, and the liquidity may not be sufficient. In reality, you may not earn much.

There are fewer cross-event arbitrage robots than the multi-option arbitrage robots mentioned above. This requires strict judgment and has a slightly higher technical threshold.

Cross-platform arbitrage

The most common arbitrage is between Polymarket and Kalshi. Of course, Kalshi is only available to US users. This is just a suggestion for this strategy. We can also use other prediction platforms, such as Opinion, to replace Kalshi.

If you can buy:

Buying YES on platform A costs a

Purchase NO on platform B at price b

Furthermore, both describe the same event, and the settlements are based on the same facts.

Therefore, the yield at maturity is $1, and the cost is a + b.

Arbitrage is close to risk-free if a + b + all friction costs < 1.

The most difficult part here is achieving the phrase "the 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've done arbitrage between Polymarket and Opinion before, and many of the rules are exactly the same, so there's no problem.

However, it's important to note that there is a time cost. Since you have funds being traded on both sides, you cannot withdraw them before settlement, unless the price moves in your favor. Otherwise, you may have to wait until after the settlement date to withdraw your funds.

Because of the high time cost, many people do not engage in this arbitrage.

at last

Okay, it's almost 3,000 words now. I wonder if you've truly understood YES + NO = 1 this time. If you have, I hope you'll share this article with more people.

Don't be fooled by those so-called KOLs' strategy of posting "YES + NO < 1" for the same event. They may just be using AI to generate content. After all, I recently asked ChatGPT5.2 and Gemini, and neither of them understood the shared order book.

They can only discover this problem by consulting the official documentation.