The object in my hand is a sheared-off cotter pin, a small, bent piece of metal that was never intended to hold the weight of a world, yet here it is, snapped clean in two. In the carnival inspection business, this tiny failure is what we call a “polite warning.” It’s the metal telling you that the geometry of the machine has reached a point of no return. You can grease the bearings and you can paint the cages, but once the shear force exceeds the material’s tolerance, the result is binary: it holds, or it breaks. There is no middle ground where the pin is “sort of” holding. It’s either intact, or it’s a memory.

I sneezed seven times in a row this morning, a violent, rhythmic series of shocks that left my sinuses buzzing and my eyes watering in the sharp morning light of the fairgrounds. It’s a strange thing, the sneezing fit; it’s a physical system that takes over your body, demanding a completion that you cannot argue with. You don’t “draw” with a sneeze. You either finish it, or you are suspended in a state of agonizing, itchy potential. My friend Marcus doesn’t understand systems like that. Marcus is the kind of man who believes that with enough caution, enough careful maneuvering, and enough “defensive” thinking, he can navigate any conflict toward a clean, respectable tie.

The Illusion of Defensive Strategy

Last Tuesday, I watched him do it. We were sitting at a small table behind the Tilt-A-Whirl, a grease-stained notebook between us. Marcus was playing a game of dots and lines, a pencil-and-paper exercise he’d picked up from some corner of the internet. He was meticulously connecting six dots in a circle, alternating colors with an invisible opponent he’d mapped out in his head. His goal, as he explained it, was to reach the end of the match without either side forming a triangle. He wanted a perfect balance, a stalemate where the board was full but no one was “out.”

He leaned back, clicking his pen, looking satisfied. He had three moves left. To his eyes, the board looked like a masterpiece of avoidance. He had successfully steered both colors away from each other, weaving a web of lines that seemed to defy the very possibility of closure. He thought he was playing a game of endurance. He thought he was proving that if you are just smart enough, you can keep the game going forever.

Then, he made the penultimate move. A triangle of blue appeared, almost as if by magic, connecting three of his points. He stared at it. “That shouldn’t be there,” he muttered. He tried to re-trace the lines, looking for a way he could have placed his stroke differently. He was looking for the door marked “Tie,” but he didn’t realize that in this particular system, that door had been bricked over before he even picked up the pencil.

He was playing a game where losing was the only exit strategy, and no one-not the app he’d read about, not the casual rules he’d skimmed-had bothered to tell him that a draw was mathematically impossible. There are seven distinct ways a weld can fail under lateral shear, though most inspectors only check for three, and the ASTM International Standard E165/E165M provides the required protocols to ensure that these failures are caught before the ride starts spinning.

The Law of Ramsey Theory

In my world, the rules are the only thing keeping the teenagers from flying off the Zipper and into the cotton candy stands. But in the world of casual gaming and digital distractions, the rules are often the first thing to be obscured. Why? Because the truth is a buzzkill. If Marcus knew from the first stroke that a tie was impossible, he wouldn’t have spent forty minutes agonized over his “defensive” strategy. He would have played differently. Or worse for the platform, he might have stopped playing altogether.

There is a specific kind of profit in keeping people ignorant of a system’s limitations. When you are inside a game like the sim pencil game, you are working within the constraints of Ramsey Theory, specifically the result known as R(3,3) = 6. This is a load-bearing fact of mathematics: if you have six points and you connect every pair with either a red or blue line, you are guaranteed to have at least one monochromatic triangle.

You cannot escape it. It is a mathematical certainty, as rigid as the laws of gravity that govern my carnival rides. Yet, most casual sites that host this game bury this fact in the “About” section or omit it entirely. They want you to believe in the stalemate. They want you to think that if you just try a little harder, if you’re just a little more careful, you can “solve” the game without the messy indignity of losing.

The High Cost of Effortful Ignorance

It reminds me of a specific ride I inspected three years ago in a dusty town outside of Reno. It was an old-fashioned “Test Your Strength” machine, the kind with the heavy mallet and the bell. The owner had subtly adjusted the tension on the spring so that the bell would only ring if the hit was perfectly centered-not just hard, but centered to within a fraction of a millimeter. He didn’t tell the customers that, of course. He let them believe it was purely a matter of muscle.

He watched them swing until their shoulders burned, letting them think they were “almost there,” when in reality, the outcome was dictated by a mechanic they didn’t even know existed. The most expensive ignorance is the kind that feels like effort while it’s happening. Marcus felt like he was doing something profound. He felt like he was a master of strategy. But he was actually just a man walking into a wall he couldn’t see.

In the 1960s, a mathematician named Gustavus Simmons introduced this game to the world. He knew exactly what he was doing. He wasn’t just creating a pastime; he was illustrating a fundamental truth about how structures work. When you reach a certain level of complexity-six points, in this case-certain patterns become inevitable. You cannot have complexity without consequences. You cannot have a full board without a triangle.

But try telling that to the modern interface designer. Transparency is bad for “engagement.” If a game tells you upfront that there is no way to tie, it introduces a sense of finality. It forces you to accept that someone has to lose. And losing feels bad. So, instead, they offer the illusion of the infinite middle ground. They let you chase the stalemate because the chase keeps you clicking.

Cheating Physics: The Brake Pad Trap

I’ve made my share of mistakes in this department. I once spent two days trying to “balance” a set of brake pads on a Ferris wheel that I knew, deep down, were beyond saving. I told myself I could adjust the tension just enough to get through the weekend. I was looking for a tie-a situation where the brakes weren’t quite replaced but weren’t quite broken. I was trying to cheat the physics of the machine.

On the second night, a sneeze-much like the ones I had today-distracted me just long enough to hear the metal groan in a way it never should. I realized then that I wasn’t being “efficient” or “clever.” I was just lying to myself about the rules. We rarely ask who benefits from our lack of knowledge. In the case of the game Marcus was playing, the benefit goes to the person who wants his attention.

“I think the pen is skipping. I must have miscalculated.”

– Marcus, staring at the inevitable blue triangle

By not highlighting the impossibility of a draw, the game presents itself as a more “open” challenge than it actually is. It disguises its own rigidity. It’s a trick of the light, making a closed loop look like an open road. Marcus eventually closed the notebook. He looked tired. He didn’t look like a man who had enjoyed a game; he looked like a man who had been lied to by his own logic.

Acceptance and Victory

I didn’t have the heart to tell him about R(3,3)=6 right then. I just handed him the sheared cotter pin I’d been carrying in my pocket. He turned it over in his hands, feeling the sharp, jagged break where the metal had finally given up. “What’s this?” he asked. “A reminder,” I said. “Sometimes, the structure doesn’t care how careful you are. Sometimes, the only way out is to accept that someone has to lose.”

He looked at the pin, then back at his notebook. I could see the gears turning. He was beginning to realize that the effort he’d put into avoiding the triangle was the very thing that had made the triangle inevitable. Every line he drew to “save” a corner just pushed the remaining possibilities into a tighter and tighter space. His defensive play was the architect of his own defeat.

This is the hidden tax of the “no ties” reality. When we don’t know the rules, we use our best qualities-our persistence, our caution, our desire for fairness-against ourselves. We build the very traps we are trying to avoid, all because we believe the system is more flexible than it is. There is a certain peace that comes with knowing a tie is impossible. It shifts the focus from “avoidance” to “victory.”

If you know the game must end in a result, you stop playing to survive and start playing to win. You stop wasting energy on the treadmill of “almost” and start engaging with the reality of “is.” I walked away from the Tilt-A-Whirl, my seventh sneeze still echoing in my chest, feeling a strange sense of clarity. The rides were starting up for the day, the mechanical groans and whistles filling the air.

Each one was a system of fixed rules, of shear points and load limits. There are no ties in a carnival ride. Either the gear catches, or it doesn’t. Either the pin holds, or it shears. Once you accept that, you can finally stop worrying about the middle ground and start focusing on the things that actually hold the world together.

Marcus stayed at the table for a long time, staring at his notebook. I hope he eventually turned the page. I hope he stopped looking for the stalemate and started looking for the truth, even if the truth meant he had to lose a few games along the way. In the end, the most expensive thing you can own is a map that doesn’t show the dead ends. It’s better to know where the wall is before you start running.