Road Crossing Game
A faster lane is not a more dangerous one. How much of the time a lane is blocked does not depend on its speed at all.
A faster lane is not a more dangerous one
A lane carries vehicles of length L with gaps of G between them at speed v. At any fixed point the road is clear for G ÷ v seconds and blocked for L ÷ v. So what decides whether you can get across is G ÷ v, not v — and a lane moving nearly three times faster can have a longer clear window than a slow one, if its vehicles are spaced further apart. On the Deceptive level the fastest lane, at 170 pixels a second, gives you 1.88 seconds, while the slowest at 55 gives you only 1.45. Reading the speeds gets you killed.
Stranger still: the share of time a lane is blocked does not depend on its speed at all. It is L ÷ (L + G), which has no v in it. Speeding a lane up does not block it for more of the time — it chops exactly the same total blockage into shorter, more frequent pieces. And shorter is what stops you, because a window briefer than the time it takes to step across is no window at all.
That is why occupancy is not difficulty here: a lane blocked 46 per cent of the time with long gaps is easy, and one blocked 40 per cent of the time with tight gaps can be impossible. Every lane in every level is checked at build time to leave at least 1.6 × 0.34s of clear window, so no level is ever impossible by construction — if you cannot get through, it is the timing rather than the game.
Every lane, and what it actually gives you
A step takes 0.34s. Windows under about 1.6 steps are where a lane starts to bite.
| Level | Lane | Speed | Gap | Clear window | In steps | Blocked |
|---|---|---|---|---|---|---|
| Quiet road | 1 → | 55 px/s | 200 px | 3.64s | 10.7 | 22% |
| 2 ← | 70 px/s | 210 px | 3.00s | 8.8 | 22% | |
| 3 → | 45 px/s | 260 px | 5.78s | 17.0 | 29% | |
| 4 → | 85 px/s | 240 px | 2.82s | 8.3 | 19% | |
| Deceptive | 1 → | 150 px/s | 260 px | 1.73s | 5.1 | 18% |
| 2 ← | 55 px/s | 80 px | 1.45s | 4.3 | 42% | |
| 3 → | 170 px/s | 320 px | 1.88s | 5.5 | 25% | |
| 4 ← | 60 px/s | 95 px | 1.58s | 4.7 | 38% | |
| 5 → | 140 px/s | 250 px | 1.79s | 5.3 | 19% | |
| River crossing | 1 → | 60 px/s | 90 px | 1.50s | 4.4 | 57% |
| 2 ← | 75 px/s | 100 px | 1.33s | 3.9 | 55% | |
| 3 → | 90 px/s | 110 px | 1.22s | 3.6 | 52% | |
| 4 ← | 65 px/s | 95 px | 1.46s | 4.3 | 56% | |
| Rush hour | 1 → | 120 px/s | 130 px | 1.08s | 3.2 | 31% |
| 2 ← | 135 px/s | 140 px | 1.04s | 3.1 | 29% | |
| 3 → | 105 px/s | 190 px | 1.81s | 5.3 | 35% | |
| 4 ← | 150 px/s | 160 px | 1.07s | 3.1 | 27% | |
| 5 → | 130 px/s | 145 px | 1.12s | 3.3 | 29% | |
| 6 ← | 95 px/s | 175 px | 1.84s | 5.4 | 37% |
How to use
- Pick a level and press Start, then cross with the arrow keys, WASD or the buttons.
- Watch the gaps rather than the speeds — they are not the same thing.
- On the river level you ride the logs; falling in the water is the failure.
- Try Deceptive, where the fastest lane is the safest one.
Frequently asked questions
Is a faster lane more dangerous?
Not on its own. A lane carries vehicles of length L with gaps of G at speed v, so a fixed point is clear for G divided by v seconds. What decides whether you can cross is that clear window, not the speed — a lane moving nearly three times faster can give you a longer gap if its vehicles are spaced further apart. On the Deceptive level here the fastest lane is deliberately the safest.
Does speeding up a lane make it busier?
No, and this is the genuinely surprising part. The share of the time a point is blocked is L divided by (L plus G), which contains no speed term at all. Doubling the speed does not block the road for more of the time — it chops exactly the same total blockage into shorter, more frequent pieces. Occupancy is set by spacing alone.
Then why does a fast lane feel harder?
Because shorter windows are what stop you. A window briefer than the time it takes to step across is no window at all, however often it comes round. So a lane blocked forty-six per cent of the time with long gaps can be easy, while one blocked forty per cent of the time with tight gaps is close to impossible. What you feel is window length, not busyness.
Can a level be impossible?
No, by construction. Every lane in every level is checked to leave a clear window of at least 1.6 times the step time, and the check runs in the test suite rather than being a design intention. If you cannot get through, it is the timing rather than the game — which is worth knowing, because the alternative is spending ten minutes on a lane that was never crossable.
How is the score worked out?
From the lanes rather than assigned. Each lane contributes in inverse proportion to how many step times fit in its clear window, summed across the level, so both things that make a level hard count: how tight the windows are and how many of them you have to get through. Doubling every speed and every gap together leaves the windows unchanged and the score identical.
What is different about the river level?
The model is the same, read the other way round. You ride the logs instead of dodging them, so a long vehicle is help and a long gap is the hazard — falling in the water is the failure rather than being hit. It is a useful check on whether you are thinking in terms of gaps or in terms of obstacles.
Why do the lanes go in both directions?
Because a road with traffic in one direction only reads as a conveyor belt, and it also removes a real part of the skill: two lanes running opposite ways have gaps that drift in and out of alignment, so a route that worked a moment ago does not now. Every level here is checked to have traffic both ways.
Is there an optimal strategy?
Cross the tightest lane first when you can. Waiting on a bank costs nothing, while waiting halfway across means standing in a lane whose window is running out — so spending your patience before you commit is nearly always better than spending it in the middle. The lane table on this page lists which lane that is in each level.
Why does the game use pixels rather than real units?
Because the arithmetic only cares about ratios. Clear window is gap over speed, and as long as both are in the same units the seconds come out right whatever those units are. Using pixels keeps the numbers on the page identical to the numbers the game actually runs on, which is worth more than a made-up conversion to metres per hour.
What is the step time?
A third of a second, roughly, which is how long the player takes to move from one lane to the next. Every window figure on this page is expressed against it, because a window is only meaningful relative to how long you take to use it — a two-second gap is generous for a step and useless for a lane you have to cross twice.
Does the traffic pattern repeat?
Yes, and deliberately. Vehicles are generated from the spacing rather than stored in a list, so the pattern on screen always matches the numbers the difficulty is computed from. A stored list would be free to drift out of agreement with the model, which is exactly the sort of gap that makes a game feel unfair without anyone being able to say why.
Does this store anything?
Only if you post a score. The game runs entirely in your browser and nothing is saved between runs unless you choose to put a score on the global board, which sends the name you type and the number.
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