What is the shortest possible game of Scramblefall?

What is the fastest way to lose at Scramblefall?

Doing nothing sounds like the obvious answer. But Scramblefall gets faster as your score rises, so there is another possible strategy: solve a few words very quickly, make every later word fall faster, then stop playing and let the board fill.

Suppose you can solve one word every 0.5 seconds. Is the early time investment worth it?

The short answer

No. The shortest ideal game is to do absolutely nothing.

The ten words take 48.4576 seconds to land, followed by the final one-second chance to save the game. That gives a total of:

49.4576 seconds

In a real browser it will be fractionally longer because movement is updated one animation frame at a time. The displayed timer rounds down to whole seconds, so it should say 0m49s.

Solving one word first produces an ideal time of 49.4778 seconds. That is only about 20 milliseconds slower than doing nothing.

How fast do the rows fall?

The board has ten playable rows and a three-row extension above them. The first word has the furthest to travel. As the board fills, each new word lands one row higher and has a shorter journey.

At a score of zero, the ideal landing times are:

Those add up to 48.4576 seconds. Scramblefall then gives you one last second to clear a row before declaring game over.

What scoring does to the speed

Each solved word makes the current speed 1% faster, so the speed multiplier is:

1.01 ^ score

So a score of 1 means 1.01x speed, a score of 10 means about 1.1046x, and a score of 100 means about 2.7048x. The increase compounds.

If you solve n falling words in 0.5 seconds each and then give up, the ideal total time is:

0.5n + 48.4576 / 1.01^n + 1

The first part is the time spent solving. The middle part is the board-filling time at the new speed. The last part is the final grace period.

Here are some possible strategies:

At the assumed half-second pace, every extra word still makes the result slower.

Why it is so close

At score zero, the whole falling phase lasts 48.4576 seconds. Raising the multiplier from 1.00x to 1.01x cuts that to about 47.9778 seconds, a saving of roughly 0.4798 seconds.

But the word took 0.5 seconds to solve. You spend 0.5 seconds to save 0.4798 seconds, losing by just over 0.02 seconds.

If you could solve the first word in less than about 0.48 seconds, solving before giving up would begin to win. At the assumed half-second pace, it does not.

How fast would you need to be?

The answer changes within an extremely narrow range.

The first solved word saves 0.479778 seconds of later falling time. The second saves another 0.475028 seconds, the third saves another 0.470325 seconds, and so on. Each successive saving is slightly smaller because the preceding increases have already shortened the board-filling time.

If every solve takes the same amount of time, these are the ranges in which each strategy is fastest:

At an exact boundary, the two neighbouring strategies tie. For example, at exactly 475.028 milliseconds per word, solving either one or two words gives the same result.

The general test for whether one more word is worthwhile is:

time per solve < 0.484576 / 1.01^next_score

For example, if you can solve consistently in 470 milliseconds, the fastest strategy is to solve three words and then stop. The first three speed increases save more than they cost, but the fourth does not.

This calculation gives the speed-up strategy every advantage. It assumes you solve falling words, which reset without removing any rows already filling the board. Solving a landed word would clear a row and move you further away from game over, so it cannot produce a shorter game.

The fastest way to lose

Press Start, enter nothing, and wait about 49.46 seconds.

The margin is much smaller than I expected, but doing nothing is still the fastest possible strategy if every solved word costs half a second.