Bubble Shooter

The shot most people miss

• Aim at the support, not at the colour. Any bubble left with no path back to the ceiling falls, whatever colour it is — so clearing one bubble that is holding up a chunk of twenty takes all twenty with it.
• Dropped bubbles are worth double popped ones, precisely to make that shot worth hunting for.
• Use the walls. The aim line shows the real bounce, because it is drawn by the same code that fires the shot — it cannot show you a path the bubble will not take.
• You are only ever given a colour that is still on the board, so there is no such thing as a wasted turn from a dead colour.
• Clear the board to move up a level. Levels add rows first, then colours.

Dropping bubbles is the famous mechanic. It's worth an eighth of your score.

Clear the one bubble anchoring a chunk of twenty and all twenty fall, even though none of them matched — it's the rule the genre is remembered for. We wrote in this game's own source that it was "the rule that makes or breaks this genre", then measured it and had to walk that back.

Simulating 80 complete games at each palette size — every turn taking the best-scoring shot available, until the board is clear or nothing more can be popped — drops account for 13.2% of all points with six colours in play. The other 86.8% comes from ordinary matches, and only 10.5% of scoring shots drop anything at all. The median drop is a single bubble.

A first pass put this at 5%, because it fired one shot into a freshly generated board and never played on. That was wrong in a useful way: a dense starting board has almost no overhangs, so nothing can fall. Overhangs are something you build over the course of a game, which is why the figure more than doubles once the simulation plays to the end.

So what are drops for? They own the top of the distribution rather than the bulk of it. A dropped bubble scores 20 against a popped bubble's 10, and the number that can fall at once is unbounded in a way a pop is not — the smallest legal pop is 3 bubbles for 30 points, while the best single shot across all 240 simulated games was worth 1060, over 35 times as much. Drops aren't how you score; they're how you score a lot at once. Playing for a total rather than a highlight, take the reliable threes.

More colours makes drops matter more

The share of points coming from drops rises with the palette, which runs opposite to the obvious guess given that more colours makes the game harder in every other respect:

The two effects turn out to be the same effect. With three colours something matches almost every turn, so the board erodes steadily and evenly and nothing is ever left hanging by a thread. With six you pop rarely, the board thins into spindly structures held up at one or two points, and when one of those finally goes it takes a lot with it. Difficulty and fragility come from the same scarcity.

The grid isn't the grid the numbers suggest

Hexagonal packing means rows are nested, not stacked. Each row sits sin(60°) of a bubble diameter below the last — 27.71px rather than 32 — so consecutive rows overlap by 13.4% of their height, and 14 rows occupy 392px where a square grid would need 448.

The half-bubble offset also costs a cell on every odd row: even rows hold 12 bubbles, odd rows 11, so the board is 161 cells rather than the 14 × 12 = 168 the constants suggest.

Only 114 of the 161 cells — 70.8% — have all six neighbours. The rest are edges, which is why clusters behave differently against the walls, and why exactly two cells in the whole grid have only two neighbours at all.