Understanding Mutually Exclusive Events: Unlocking the Complete Logic of YES+NO=1 in Polymarket

When we talk about prediction markets like Polymarket, the core concept is the seemingly simple formula YES + NO = 1. But what is hidden behind this formula? Why must the prices of YES and NO sum to 1? The answer lies in understanding the fundamental principle of mutually exclusive events in prediction markets. Today, we will thoroughly dissect Polymarket’s shared order book mechanism and explain why understanding mutually exclusive events is crucial for mastering arbitrage strategies.

The Essence of Mutually Exclusive Events: Dividing the Value of a Voucher

Imagine Polymarket is not selling lottery tickets but selling future redemption vouchers. Each voucher’s value is always $1 — that’s the baseline. The market’s job is to split this $1 into two parts: one labeled “YES” and the other “NO”.

This is precisely the definition of mutually exclusive events: two outcomes cannot occur simultaneously, and one of them must happen. On Polymarket:

• If the event occurs, YES voucher = $1, NO voucher = $0
• If the event does not occur, YES voucher = $0, NO voucher = $1

The math at settlement always holds:

• If the event occurs: 1 + 0 = 1
• If the event does not occur: 0 + 1 = 1

Under the same market and settlement conditions, as long as you hold both the YES and NO vouchers for this mutually exclusive pair, you are effectively holding an asset that will be worth $1 at expiration. This is the clever design of Polymarket — all predictions are built on the solid logic of mutually exclusive events.

The Structure of Mutually Exclusive Events in Multiple-Choice Markets

Many people are confused when first seeing Polymarket: why aren’t all trades just YES and NO? For example, predicting Bitcoin’s price range or Elon Musk’s tweet count involves multiple options.

In fact, this also conforms to the logic of mutually exclusive events. If you check Polymarket’s API, you’ll find that each option generates a pair of YES and NO. For example, in Elon Musk’s tweet prediction market, these options are:

• 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?

Each option forms a pair of mutually exclusive events. These options are mutually exclusive and cover all possible tweet counts, ensuring that at expiration, exactly one option’s YES will be worth $1.

Sports markets follow the same principle. The NBA Moneyline market predicts which team will win — essentially mutually exclusive events between the home and away teams (excluding overtime). Soccer markets require three mutually exclusive events: home win, away win, or draw, because a draw is possible.

All Polymarket markets adhere to this rule: mutually exclusive events ensure that YES + NO = 1 holds mathematically.

How the Shared Order Book Maintains the Balance of Mutually Exclusive Events

This is the most critical part of understanding Polymarket. Unlike ordinary cryptocurrency order books, Polymarket’s order book is shared and mirrored between YES and NO markets.

Suppose you place a buy order at $0.18 on the YES market (for 10 shares). The system will automatically generate a corresponding sell order at $0.82 (which is 1 - 0.18) on the NO market, with the same quantity. This is no coincidence — it’s the core mechanism of the shared order book.

You can see this mirrored relationship in screenshots of both markets:

• The buy order price in the YES market + the corresponding sell order price in the NO market = 1.00
• The quantities are exactly the same

Why design it this way? Liquidity concentration. Merging order books allows liquidity to be pooled together, improving price discovery efficiency. This design ensures that the supply and demand for mutually exclusive events always stay balanced.

When you place a buy order on YES, the system interprets your intent as: I am willing to pay X for this outcome, and I accept the counterparty giving me the NO voucher. This single order effectively expresses both sides of the mutually exclusive event.

Why There Is No “Risk-Free Arbitrage” with YES + NO < 1

It’s time to bust a long-standing myth. Many influencers claim that such a strategy exists: someone sells YES at 0.4, someone sells NO at 0.4, and by buying both at 0.8, they can settle at $1 and earn a net profit of $0.2.

This strategy is impossible under the shared order book.

Why? When someone sells YES at 0.4, the system receives an instruction that they want to buy 0.6 of NO (since 1 - 0.4 = 0.6). Conversely, if you want to sell NO at 0.4, you are effectively trying to buy 0.6 of YES.

What happens? Your buy price (0.6) exceeds their sell price (0.4), and the system will instantaneously match your trades, leaving no “unbalanced” open orders. Other users will never see a YES + NO < 1 situation.

From another perspective: the shared order book is an automatically balanced scale, following the rules of mutually exclusive events. Any attempt to break this balance will be immediately matched and settled by the system. Ultimately, the orders remaining on the book will always satisfy YES + NO ≥ 1.

Some claim they can quickly enter and exit within 15 minutes to execute such strategies, but that’s actually a volatility strategy, not arbitrage — it involves risk, and prices may move against you. It’s not risk-free arbitrage.

Genuine Arbitrage Strategies

Since arbitrage with YES + NO < 1 is impossible within the same market, where are real arbitrage opportunities? Mainly three types:

Multi-option arbitrage: exploiting the mutually exclusive and exhaustive design

Take Elon Musk’s tweet market as an example. It has about 30 mutually exclusive options covering all tweet counts from 0 to over 580. No matter the final count, exactly one option will be true.

If you buy YES for all 30 options, does the total cost fall below $1? Theoretically, yes — when market participants are dispersed. But in practice, such opportunities are monitored by many bots, making manual execution difficult.

The key point: this arbitrage leverages the property of mutually exclusive events — these options are mutually exclusive and cover all possibilities, guaranteeing a payoff of $1 at expiration.

Cross-event arbitrage: arbitraging between mutually exclusive events with similar semantics

Sometimes Polymarket shows two markets with nearly identical descriptions. For example, some users have found that two markets about leadership meetings on the same day display different prices: one might be 3+94=97, another different.

Here, the 3 refers to the arbitrage profit space (100-97=3). But such arbitrage opportunities are rare, with limited liquidity and fierce bot competition.

The key difficulty is ensuring that both markets describe the same mutually exclusive event. Small differences in time zones, evidence sources, or settlement rules can turn arbitrage into a nightmare.

Cross-platform arbitrage: pairing mutually exclusive events across different prediction markets

The most common example is arbitraging between Polymarket and Kalshi. The principle is simple:

• Buy YES for a certain mutually exclusive event on platform A at price a
• Buy NO for the same event on platform B at price b
• If a + b + friction costs < 1, profit is possible

But the biggest challenge is confirming that both descriptions refer to the same mutually exclusive event. Rules between Polymarket and Opinion are often aligned, but Kalshi may have subtle differences in time zones, evidence sources, etc.

Additionally, time costs are an invisible killer. Your funds are locked until settlement, and unless prices move favorably, you must wait until the settlement date to fully realize the profit. This is why many give up on such arbitrage.

Final Thoughts

The entire Polymarket system is built on the solid foundation of mutually exclusive events. YES + NO = 1 is not just a mathematical formula; it reflects the deepest logic of prediction markets — any prediction involves two mutually exclusive outcomes, and one will inevitably be true.

Once you understand how mutually exclusive events drive the shared order book, why risk-free arbitrage within the same market is impossible, and how to create genuine arbitrage opportunities across multiple options and events, you grasp the core secret of Polymarket.

Those influencers claiming to have found YES + NO < 1 arbitrage are often just using AI-generated content, with no real understanding of the clever design of the shared order book. When you share this article with others, I hope it helps them avoid these misconceptions. Because in prediction markets, understanding the logic of mutually exclusive events is far more valuable than blindly following any strategy.