68 trillion ways to ride Nerang

Every time I roll out of the Velodrome trailhead I end up doing some version of the same few loops. So I got curious: how many different rides are actually possible from the main gate? Not a rough guess. An actual count.

The answer is about 68 trillion. That’s 68,000,000,000,000 different loops on the official trails and fire roads alone, without riding any section twice.

If you rode a new one every day, you’d be finished in about 190 billion years. That’s roughly 13 times the age of the universe, so you might want to start this weekend.

What counts as a ride

Counting needs some rules, so here are mine:

• It starts and finishes at the main gate (the Velodrome trailhead on Hope Street).
• It never rides the same section of trail or road twice. A section is the stretch between two junctions. You can cross a junction as often as you like.
• It follows one-way trails in their marked direction (Taipan, Barneys, the Comm Games loops, Top Drop, Hateful 8, 9/11, Hike A Bike, BB’s and Explorer).
• It ends the first time it gets back to the gate.
• It uses the sanctioned trails, fire roads and link roads on the map. The unsanctioned trails get their own section further down.
• The same loop ridden clockwise and anticlockwise counts as two rides. They feel like two rides, too.

That leaves a network of 119 sections and 70 junctions covering 57.9 km, with 7 ways out of the gate. Junctions closer together than 15 m were treated as one, so a little kink in a junction doesn’t create fake extra rides.

How I counted them

Up to 8 km, the computer simply lists every ride, one by one. There are 2,462,496 of them, and it takes a couple of minutes.

Past that, listing them is hopeless. The count grows four- to five-fold with every extra kilometre, so the longer rides are estimated with a technique called sequential Monte Carlo. A crowd of 50,000 virtual riders leaves the gate together. At every junction each one picks a random way it can still get home from, and keeps a tally of how many choices it had. Multiplying those choices together says how many rides look like that one. Riders on ground where rides multiply get copied, and the rest drop out, so the effort goes where the rides are.

I ran the whole thing 16 times with different random turns, then did the same on the network with the black trails taken out, so the rare rides that avoid them get a proper count of their own. Easy rides are few enough to list every one at any length. The spread between runs gives the ± figures below, which are one standard error. As a check, the estimates for 1 to 8 km land within 7% of the exact counts.

Rides by length

Here’s every ride, rounded to the nearest kilometre. A 1 km ride is anything from 0.5 to 1.5 km.

At the short end you can count them on your fingers: 27 rides of about 1 km. Each extra kilometre multiplies the choice, and by 29 km there are about 5.63 trillion rides of that length alone. After that it falls away, because you start running out of trail you haven’t ridden yet. The longest ride any virtual rider found was 45.9 km, which is 79% of the whole network in one loop.

On an ordinary scale, nearly all of them are long. Half of all rides are 31 km or longer, and the average is 31 km. Rides of 10 km or less add up to about 47.3 million, which sounds like plenty until you see it’s about 1 in 1.4 million of the total.

Are they really all different?

Yes, in the strict sense: every one is a different sequence of trail sections, and nothing is counted twice. But some of those differences are small, so I also counted them more loosely.

Direction barely matters. Almost every long ride uses at least one one-way trail, so its reverse isn’t a ride at all. It only makes a difference for short loops: the 466,333 rides up to 7 km become 303,136 if you ignore direction.

Order matters a lot. Picture a figure eight: out to a junction, one loop, back through the junction, the other loop, then home. Doing the loops the other way round is a different ride on exactly the same trails. Long rides pass through ten or more junctions twice, so the possible orders multiply. A typical set of trails for a 25 to 35 km ride can be ridden in about 580 different orders, and some in over 400,000.

So even counting only genuinely different combinations of trails, there are about 1.1 trillion (give or take 5%). For short rides that’s exact: the 466,333 rides up to 7 km use 170,812 different sets of trails.

Still not convinced? Neither was I, so I’ve written up the checks separately: How do I know there are 68 trillion rides?

Easy, medium or hard?

I rated each ride the way trails are rated: by the hardest trail on it. Fire roads and link roads don’t count towards the rating.

• Easy: green trails, fire roads and link roads only.
• Medium: at least one blue trail, but no blacks.
• Hard: at least one black.

There are no double blacks on the sanctioned network, so nothing is rated harder than Hard.

The result is lopsided. Exactly 984 rides are Easy (all of them under 10 km), and about 5.6 billion are Medium. That leaves about 68 trillion Hard rides. Only about 1 ride in 12,000 avoids every black.

Short rides have the most variety. The longer the loop, the harder it gets to dodge every black, but it can be done: the longest ride without one that the virtual riders found is about 39 km.

How big a day?

The trail rating is about skill. For legs, I used a simple effort score: kilometres plus one for every 100 m of climbing, a common rule of thumb. A flat 20 km and a 10 km ride with 1,000 m of climbing both score 20.

Because most rides are long, nearly all of them are a big day (50%) or an epic (50%). About 190 million rides take under an hour at Park Nav’s average speeds. That’s plenty for a lunchtime spin for the rest of your life, but it’s still only about 1 in 350,000 of the total.

Other ways to slice it

The trails you can’t avoid

Some trails turn up in almost every ride. Baileys is on 99.6% of them. That’s mostly because the typical ride is around 31 km, so it takes in about 55% of the network.

What about the unsanctioned trails?

Park Nav has an Include unsanctioned trails option, so I ran the count that way too (illegal trails always stay out). The network grows to 193 sections and 93 km. The count goes from big to silly: about 110 sextillion rides (that’s 1.1 × 10²³, give or take 13%). That’s around 2 billion times as many as the sanctioned network.

Those trails aren’t part of the managed network, so treat this as a curiosity, not a suggestion. Mostly it shows how much every extra junction multiplies the possibilities.

The fine print

• Above 8 km these are estimates. The totals are probably right to within about 7%, and the individual lengths within the ± shown.
• It’s based on the trail map’s data. Closures, conditions, works and the odd missing junction aren’t modelled, and trails change.
• Two rides that differ only by a short connector count as different rides. That’s how the maths works, even if you’d call them the same ride (see “Are they really all different?”).
• Climbing comes from Geoscience Australia’s 5 m LiDAR elevation model (© Commonwealth of Australia (Geoscience Australia) 2025, CC BY 4.0). Riding times use Park Nav’s speeds and are only a guide.
• None of this is a recommendation to ride any particular route. Ride within your limits and follow the signs on the ground.

Try one

Can’t pick from 68 trillion? Open the map, tap Park Nav and use Random loop. Set a distance and it picks one for you, following the same one-way rules. Each roll heads somewhere different from the last, so you’ve only got about 68 trillion to go.