The "Trap" of Predictive Markets: Why the Portfolio You Buy Always Loses

Author: Terry Lee

Original Title: Why prediction markets are mispricing parlays – the correlation blind spot

Translation and Editing: BitpushNews

Introduction

On platforms like Polymarket, most people (including myself in the past) tend to price “parlays” (multiple event bets) by simply multiplying the probabilities of each individual event.

For example:

• Probability of Event A occurring P(A) = 80%
• Probability of Event B occurring P(B) = 70%
• Probability of Event C occurring P© = 60%

Then, the total parlay probability = 80% × 70% × 60% = 33.6%

(Note: Parlays are terms used in betting and investing, often called “parlays” or “accumulators” in English. Definition: You combine two or more independent bets. Rule: You only win if all selected events are predicted correctly. If any one is wrong, the entire bet loses.)

It sounds simple, right?

The issue isn’t the math itself, but the hidden assumptions behind it.

This multiplication presumes that each event is independent of the others. That is, the outcome of A has no influence on B. But in reality, this is often not the case.

For example:

1. A decision by the Federal Reserve at one meeting can significantly influence its next decision.
2. A presidential candidate winning states in the Rust Belt can signal their chances in Pennsylvania, affecting the overall election outcome.

Most events worth combining in a “parlay” are correlated. Ignoring these correlations can lead you to pay too much or miss profitable opportunities.

This article will present a simple framework to teach you how to price parlays scientifically, similar to how the traditional finance industry has priced multi-leg options for decades.

Why Are There Pricing Errors?

In my view, most prediction markets focus on “execution” rather than “correlation analysis.” Additionally, these niche markets are still relatively immature. While parlays are common in sports betting, in handling specific social or economic events, the markets are still in early stages, and the pricing mechanisms are not yet refined.

Case Study: Federal Reserve Interest Rate Decisions

(Figure 1: The Fed tends to repeat actions; 83% of the time, maintaining rates is followed by another maintenance)

Using data from the St. Louis Fed (FRED) (from 1994 to early 2026), I built a transition matrix specifically capturing the decision changes between two consecutive meetings.

The results are very clear:

• Maintain -> Maintain: probability 83.1%
• Cut -> Cut: probability 69.2%
• Raise -> Raise: probability 62.5%

Clearly, the Fed’s behavior exhibits “coherence.” As a forward-looking, data-dependent institution, they tend to repeat the same action until a “regime shift” occurs.

How Strong Is This “Coherence”?

To test this, I built a model to identify historical “decision streaks” (i.e., consecutive periods of maintaining, cutting, or raising rates).

Results:

• Rate maintenance streaks: 32 occurrences, averaging 5.4 meetings each
• Rate cuts: 12 streaks, averaging 3.3 meetings each

Next, I simulated 1,000 “parallel universes” of Fed decisions. In these simulations, each meeting was independent (like flipping a coin). Based on historical aggregate data, I set the probabilities as: maintain 66%, cut 15%, raise 19%, with no correlation between decisions.

(Figure 2: Actual Fed decision coherence is 2-3 times higher than random probability)

Under the assumption of independence, the average length of a rate-maintaining streak is only 2.9 meetings, while for cuts and raises, it’s about 1.2 meetings.

Comparing actual history with the random simulation:

• Maintain: actual 5.4 vs. random 2.9 (1.9× longer)
• Cut: actual 3.3 vs. random 1.2 (2.8× longer)
• Raise: actual 2.6 vs. random 1.2 (2.1× longer)

Note that the coherence of rate cuts is nearly three times what the random model predicts. The reason: when the Fed starts cutting, it’s usually to respond to ongoing economic deterioration. These issues can’t be fixed in a single meeting. They cut, then assess data; if conditions remain poor, they’re very likely to cut again.

Simple multiplication to price “parlays” completely ignores these correlations. The real-world coherence is 2-3 times stronger than the independent random model.

What Happens After Two Consecutive Meetings?

Looking only at the last meeting isn’t enough. Pricing “three-event” combinations requires analyzing the conditional probabilities based on the previous two decisions.

The analysis can be divided into two parts:

Continuation of the Same Path

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(Figure 3: After two identical actions, the third almost always matches)

From Figure 3, it’s clear that when the Fed repeats the same action twice, the probability that the third action continues that pattern is overwhelming:

• Two maintains -> third maintain: 87%
• Two raises -> third raise: 84%
• Two cuts -> third cut: 68% (a bit weaker)

It’s also notable that cells with 0% probability exist: the Fed has never, after two consecutive raises, suddenly cut; nor after two cuts, suddenly raise. They always go through a “pause” (maintain) phase. Recognizing this can help you eliminate a host of “naive models” that assign value to invalid combinations.

After a Regime Shift

(Figure 4: Post-regime change, the differences in directional shifts are huge)

This is the most interesting part for traders. Not all directional changes are equal:

• Maintain -> Cut -> Cut: 75%. Once the Fed breaks the maintenance phase and starts cutting, the “gate” opens, and subsequent cuts are highly probable.
• Cut -> Maintain -> Maintain: 100%. Historically, after a pause in cuts, the Fed has never immediately resumed cutting. A pause means a full stop.
• Maintain -> Raise -> Maintain: 79%. The first rate hike after a maintenance period is often tentative; they pause to observe effects.
• Raise -> Maintain -> Raise/Maintain: 60% and 40%, respectively. Unlike cuts, pauses during rate hikes have real uncertainty.

This asymmetry is the core insight. The “Maintain -> Cut -> Cut” combination is worth far more than the simple product suggests. Conversely, “Cut -> Maintain -> Cut” has almost zero historical value. The same sequence of events can have vastly different true values depending on order. Independent multiplication models cannot capture this.

What Does Overall Pricing Imply?

This is the overall picture. Instead of blindly using average probabilities, we should use the observed conditional probabilities from history.

For example, “three consecutive rate holds (Hold-Hold-Hold)”:

• Initial model: using the total probability (67% hold), calculated as 67% × 67% × 67% = 30.1%
• Corrected model: using conditional probabilities, calculated as 67% (first) × 83% (second | first) × 87% (third | first two) = 48.4%

(Figure 5: Combinations of same-direction actions are systematically undervalued, while those involving direction changes are overvalued)

Real-Time Market Detection

Taking Polymarket data as an example:

(Figure 6: Comparison of Polymarket odds distribution with actual probabilities)

Combination 1: Maintain – Maintain – Maintain (severely undervalued)

• Initial model pricing: 93% (March) × 75% (April) × 38% (June) ≈ 26%
• Conditional probability pricing: 87% × 87% × 87% ≈ 65.8%
• Conclusion: The market severely underestimates this at by about 39 percentage points.

Combination 2: Maintain – Maintain – Cut (severely overvalued)

• Initial model: 93% × 75% × 49% = 34.2%
• Conditional model: 87% × 87% × 8.5% = 6.4%
• Conclusion: The market prices this at about 34%, but the actual probability is only 6.4%. Overvaluation by more than 5 times.

Can You Profit From This?

I ran a simple backtest. Since 1994, for each pair or triplet of Fed meetings, if the corrected (conditional) price was higher than the market price (meaning undervalued), I bet $100.

(Figure 7: Example of cumulative profit/loss from two-event parlays)

(Figure 8: Example of cumulative profit/loss from three-event parlays)

Since 1994, betting $100 on each undervalued combination has yielded $169,000 from two-event parlays and over $1 million from three-event parlays. The sharp jumps in profit correspond to the Fed’s easing cycles in 2001, 2008, 2020, and 2024-2025, during which repeated similar actions occurred, but the initial models consistently underestimated this coherence.

The “step-like” pattern indicates profits are made during periods of sustained Fed action. However, the limitation is that in the 1990s and early 2000s, prediction markets may not have been mature enough to execute these trades.

Beyond the Fed: Where Else Can This Be Applied?

The Fed case is classic because of abundant data and strong correlations. But the same framework applies to any related events:

1. Presidential primaries: If a candidate wins one state, their chances in similar states change.
2. Cryptocurrency and macro/growth stocks: Bitcoin’s movements are linked to macro risk appetite. Betting “Bitcoin above X and Nasdaq above Y” has a value exceeding the product of independent probabilities because they share common drivers.

In any case, the method is the same: analyze historical data, measure true correlations, replace blind averages with better data, and compare with market prices.

Conclusion

Prediction markets are still in their infancy. Most retail participants price parlays with the primitive “simple multiplication, leave it to chance” approach.

This framework requires contextual knowledge, but fundamentally, the key question is: does the outcome of the first event tell you something about the next? If yes, naive parlay prices are wrong, and historical data can tell you exactly how wrong.

The Fed case study shows this advantage is real and measurable. But the principle is universal. Wherever correlated events are priced as independent, opportunities may exist that are yet to be discovered.

The only question is: can you see it and act on it?