About

Block stacking is a constrained optimization problem. Each placed block creates an overhang h relative to the block beneath it. The remaining contact width shrinks by h on every drop. After n imperfect placements, the surviving width equals w₀ − n∑i=1 |h_i|, where w₀ is the initial block width. When that sum exceeds w₀, no contact surface remains and the tower collapses. This simulator enforces that constraint in real time. Gravity follows Euler integration at g = 980 px/s², and horizontal swing speed increases logarithmically with stack height, compressing your reaction window from roughly 1.2s down to 0.3s per cycle.

The scoring model rewards sub-pixel accuracy. A "perfect" placement (overhang < 2px) grants a width-restore bonus and a score multiplier. Consecutive perfects chain the multiplier. This is not forgiving: a single sloppy drop at block 30 can reduce your platform to a sliver that makes block 31 nearly impossible. The tool approximates rigid-body stacking under ideal friction (no sliding after contact). Real-world stacking would involve center-of-mass torque analysis, which this simulation omits for playability.

Reference Data

Stack Height	Swing Speed	Reaction Window	Difficulty Rating	Perfect Bonus	Multiplier Cap
1 - 5	120 px/s	1.2 s	Beginner	+4 px width restore	×2
6 - 10	160 px/s	0.9 s	Easy	+4 px	×4
11 - 15	200 px/s	0.72 s	Medium	+3 px	×6
16 - 20	240 px/s	0.6 s	Hard	+3 px	×8
21 - 25	280 px/s	0.51 s	Very Hard	+2 px	×10
26 - 30	310 px/s	0.46 s	Expert	+2 px	×12
31 - 35	340 px/s	0.42 s	Master	+1 px	×14
36 - 40	360 px/s	0.4 s	Grandmaster	+1 px	×16
41 - 50	380 px/s	0.38 s	Legendary	+1 px	×20
50+	400 px/s	0.36 s	Impossible	+1 px	×25

Frequently Asked Questions

When the overhang is less than 2 pixels, the game treats it as a "perfect" drop. The block snaps to exact alignment, a small width bonus is added to the next block (see reference table), and your score multiplier increments by 1. Consecutive perfects chain the multiplier. A single imperfect drop resets the multiplier to 1.

The simulator slices off the overhanging portion. If you drop a 120px block and it overhangs by 15px, the settled block becomes 105px wide. The next falling block inherits this 105px width. This models a rigid stack where unsupported material falls away.

The angular frequency increases linearly with block count using ω = ω₀ · (1 + 0.08 · n). However, because the amplitude stays constant, the perceived difficulty feels logarithmic - early blocks feel dramatically faster, while later increases are less perceptible but still punishing at narrow widths.

This simulator uses simplified stacking without center-of-mass torque analysis. Blocks are stable as long as contact width is greater than zero. Real-world stacking would require the center of mass of all blocks above to fall within the contact region, which would make the game significantly harder and is omitted for playability.

Yes. If the overhang exceeds the current block width (|h| ≥ w_n), the resulting width is zero or negative, triggering game over. The sliced-off piece animates falling to one side as visual feedback.

The high score is stored in localStorage under the key "block-balance-high-score". It persists across browser sessions. Clearing your browser data or localStorage will reset it. There is no manual reset button by design to preserve achievement integrity.