3 min read

Eight corners, and 2.5% of pieces had nowhere to land

The planet's one geometric flaw, eight corners where three squares meet instead of four, turned into pieces freezing in mid-air over gaps that didn't exist. The fix cost the hardest difficulty a third of its survival time. We measured that cost before deciding it was worth paying.

EngineeringDesign

The report, after the first real playtest, was specific: pieces "struggle on corners, won't land on the base and hang or die mid-fall." Not a vague sense that something felt off, an exact, reproducible complaint.

Measuring it, not guessing

Three hundred games of random input later, the shape of the bug was clear. 362 of 14,319 piece locks, 2.5%, came to rest only because the grid refused the next step down, not because anything was actually in the way; in 159 of those, there was nothing under any cell of the piece at all. A more deliberate autopilot hit the same wall: 169 of 14,757 locks, 21 of them completely unsupported.

2.5%of piece locks in 300 games of random input rested over a gap that nothing was blocking, just the grid's own geometry

Statically, the cause was exactly 84 of the 5,028 distinct legal placements at the default planet size, every single one of them with its pivot just above the rim next to a cube corner. The rule that governs how a piece's four cells must touch each other treats a cube corner as a no-go spot, correctly, geometrically, but left that spot empty. A piece coming down onto it had to bend to keep falling, couldn't, and locked over a hole that nothing could ever fill.

The fix, and the ones we didn't ship

The twelve cells that touch the planet's four south corners now start as solid ground, drawn grey, slightly raised, same idea as the solid core at the pole. A refused step then always means what it should: something solid is actually in the way.

Three alternatives were built and measured before this one, and rejected with numbers, not taste. Letting a piece slide sideways off a corner fixed most stalls but not the hardest bot's; when both sides are already piled up, there's nowhere to slide to. A plain cylindrical floor removes the corners entirely, but an earlier sweep had already shown that shape plays too shallow. And a hexagonal floor doesn't actually remove the problem at all: any closed surface built from squares has a fixed amount of "corner debt", eight corners where three squares meet, always. You can move it or hide it. You can't make it zero.

What it cost

The fix isn't free. For a human-speed autopilot at the fastest, most pressured gravity tested, median pieces survived dropped from 250 (the test's own cap, it just didn't lose) to 165; average holes per game rose from 0.2 to 1.8; rings cleared per 100 pieces fell from 18.6 to 14.9. A two-cell-wide, two-cell-tall solid bump on an otherwise flat floor makes real overhangs, and a player, or a bot, who can't cover every angle in time pays for that.

250 to 165median pieces survived by the fastest-reacting test bot, at the hardest gravity, before vs. after the corner fix

A placement-only bot with unlimited time barely notices (19.6 vs. 19.7 rings cleared per 100 pieces). A time-pressured one does. Whether a person feels it the same way the test bot does is the one number nobody can measure by simulation, that part waits for people to actually play it.