Buffon’s Needle and the Probabilistic Nature of Breakouts – When the Parquet Ground Turns into a Chart
Colleagues, in the present day we embark on an uncommon journey—from an 18th-century Parisian salon straight into the MetaTrader terminal of 2026. And on the heart of this journey lies a needle. An unusual stitching needle, tossed onto a parquet flooring.
Rely de Buffon and His Immortal Needle
In 1733, the French naturalist Georges-Louis Leclerc, Rely de Buffon, formulated an issue that, three centuries later, would power us to rethink monetary charts via a completely new lens.
Think about an infinite parquet flooring. The planks are completely uniform, equivalent in width. You’re taking a needle of size L and toss it randomly. What’s the chance that the needle crosses the seam between the planks?
Buffon’s reply: P = 2L / (π × D)the place D is the width of a plank.
At first look—pure geometry, an train for the curious thoughts. But this very method would, centuries later, develop into a bridge between chance principle and worth conduct inside help and resistance channels.
From Needle to Perpendicular
Now allow us to complicate the experiment.
Think about we drop the needle not randomly, however strictly perpendicular to the seams. The needle now not rotates—it falls straight, like a plumb line. On this case, the chance of crossing relies upon solely on the ratio of the needle’s size to the plank’s width:
P = L / D
If the needle is shorter than the plank’s width, the chance will increase linearly with its size. If the needle is longer than the plank, it can at all times cross the road—however we’re particularly within the area the place L < D, as a result of in an actual buying and selling vary, candles hardly ever span the complete channel width in a single motion.
Now think about we toss not one needle, however a sequence. What’s the chance that a minimum of considered one of N needles crosses the road?
P(N) = 1 – (1 – L/D)^N
This perform grows with every new toss. After 10 needles, the chance exceeds that after 3. After 30, it approaches unity. The market is anticipation. The longer worth holds inside a spread, the upper the chance that the subsequent candle will breach the boundary.
Crimson and Inexperienced: Diverging Possibilities
Now allow us to divide candles into two camps and look at their conduct on the higher boundary of the vary—the resistance degree.
A inexperienced candle is a needle falling point-first. A crimson candle falls blunt-end first.
We calculate P(N) individually for inexperienced candles and individually for crimson candles. Then we evaluate these possibilities.
The Vary as Parquet, Candles as Needles
Now we arrive on the central analogy.
Help and resistance strains are the seams between parquet planks. The value channel is the width of a plank. Every candle is a tossed needle. The time elapsed because the final contact of the extent is the variety of tosses.
If we assemble a curve that accumulates breakout possibilities, accounting for: – The present distance to the extent – The length of consolidation
we get hold of an indicator that doesn’t observe worth—it evaluates the very chance of motion. It won’t say “purchase” or “promote.” It would say: “Consideration, the chance of a line crossing has reached 73%.”
Now think about that someplace within the huge expanse of MQL5, an Skilled Advisor already exists, quietly and unobtrusively buying and selling gold. Hmm… may or not it’s GOLD QUEEN? Nobody is aware of what lies inside. Boards barely point out it. But its fairness curve crawls upward with astonishing consistency.
Some say neural networks. Some say volatility clustering. Others merely shrug.
What if, inside, it’s merely Buffon’s needle—tossed at simply the appropriate angle?
How can one confirm this? Solely by opening the code. Solely by working the checks. Solely by witnessing with one’s personal eyes how the EA responds to an extended inexperienced candle at resistance—and evaluating that response to what chance principle prescribes.
Coincidence? Sample? Randomness?
The query stays open. Exactly till somebody opens the commerce log and matches the entries in opposition to the peaks of the probabilistic curve.
In Lieu of a Conclusion
We now have grown accustomed to pondering of buying and selling as a struggle of indicators, a battle of bulls and bears, a conflict between basic and technical evaluation. However typically it’s helpful to step away from the charts and picture that each one our work is merely an 18th-century parquet flooring upon which an invisible hand tosses infinite needles.
The dealer’s activity is to not predict the place the subsequent needle will fall. The dealer’s activity is to discern whether or not it can cross the road.
And if Buffon taught us to calculate this chance for chaotic tosses, the market teaches us to calculate it for directed tosses. And this, you need to admit, is a completely completely different order of arithmetic.
P.S. If this studying has stirred in you the urge to sketch a script testing the Buffon speculation on actual candles—you might be decidedly not alone. Share your leads to the feedback. Probably the most surprising discoveries will definitely discover their method into our discussions.