Drop7 is a solo puzzle on a 7 by 7 grid. Each turn gives you a numbered disc to
drop in an available column. Gravity pulls it down. It explodes when its number
matches the length of its row or column, and falling pieces can start a chain
reaction. Explosions give you points, and the goal is to maximize your total score
before the board overflows.
Every five turns, a new row of gray hidden discs pushes the board upward, and
you get a large survival bonus. How hidden discs get cracked and revealed is
explained below, or you can play the game first.
score0
rise
4
Watch a game, or hover the board and click a column to drop the next disc.
The board and the pieces
Each cell is either empty, numbered, a solid hidden disc, or a cracked disc.
numbered disc (1-7)
explodes when its row-run or column-run is exactly equal to its number
solid gray disc
hides a number, counts as occupied, needs two adjacent explosions to open
cracked gray disc
has taken one explosion, and one more adjacent explosion reveals the number underneath
empty cell
discs fall through it, a run stops at it
On every turn, the player sees the board, the next numbered disc, and the number of remaining
drops until a new row of hidden discs appears. This is the information that goes into any "legal"
autonomous playing strategy.
The visible board, the next disc, and the rise clock are public. What is under a gray disc is unknowable until it is opened, and nobody knows which discs are coming after the next one.
Pick a column each turn
Choose one of the seven columns, and gravity does the rest.
1. Before the move
2. The disc drops to the lowest empty cell
3. Settled — ready for the next disc
Result: score +0
The simplest possible move: the disc lands and nothing matches.
A column can only accept a new disc if its top cell is empty.
A disc explodes when its number matches its run
Count the unbroken occupied cells through the disc in its row and its column,
including the disc itself. It explodes if either run length exactly equals its number.
The 3 sits beside a 5 and a 6, making a run of three occupied cells. The 3 clears because its own number matches that run; the 5 and 6 stay.
Each animation steps through a single turn, where a column is chosen to drop
a particular incoming disc, and the result plays out. Below each animation, the steps
of a multi-stage explosion are also laid out as a filmstrip.
1. Before the move
2. The disc drops to the lowest empty cell
3. Wave 1: 1 disc match and clear (+7)
4. Cleared
5. Settled — ready for the next disc
Result: score +7 · 1 wave (wave 1: 1 × 7)
Only the disc whose own number matches the run length explodes.
The same rule reads downwards. A column-run counts the occupied cells stacked
directly above and below the disc:
1. Before the move
2. The disc drops to the lowest empty cell
3. Wave 1: 1 disc match and clear (+7)
4. Cleared
5. Settled — ready for the next disc
Result: score +7 · 1 wave (wave 1: 1 × 7)
A vertical clear. A disc only needs one of its two runs to match.
The match has to be exact. A run that is too long does nothing:
This 2 sits in a run of three. 3 is not 2, so it stays. A disc is never cleared for being in a run longer than its number.
1. Before the move
2. The disc drops to the lowest empty cell
3. Settled — ready for the next disc
Result: score +0
Too long is as good as too short. The surrounding values do not need to match one another; each disc compares its own number with its row-run and column-run.
Gray discs count toward the length of a run, even
though they have no visible number to compare. A 3 beside a 5, a 6, and a gray
disc is in a run of four, not three.
The 3, 5, 6, and gray disc form a run of four. The gray disc lengthens the run, so the 3 does not clear.
1. Before the move
2. The disc drops to the lowest empty cell
3. Settled — ready for the next disc
Result: score +0
A gray disc has no visible number, but it still counts as an occupied cell when every numbered disc measures its run.
Cracking and revealing gray discs
A solid gray disc hides a number from 1 to 7. It opens in two
steps. Whenever a disc directly next to it explodes (above, below, left, or right,
not diagonally), then the gray disc takes one hit:
the first hit turns a solid disc into a cracked disc ;
the second hit reveals the number underneath, which is an ordinary
numbered disc from then on.
Hits are counted per wave of explosions, so a solid disc hit by
two clearing neighbours in the same wave opens immediately.
1. Before the move
2. The disc drops to the lowest empty cell
3. Wave 1: 1 disc match and clear (+7)
4. Cleared — and neighbouring gray discs take hits
5. Settled — ready for the next disc
Result: score +7 · 1 wave (wave 1: 1 × 7)
One hit cracks. The disc is still an obstacle, still counts toward runs, and still hides its number.
1. Before the move
2. The disc drops to the lowest empty cell
3. Wave 1: 1 disc match and clear (+7)
4. Cleared — and neighbouring gray discs take hits
5. Settled — ready for the next disc
Result: score +7 · 1 wave (wave 1: 1 × 7)
Two hits open a gray disc. Revealing is how the board gets new numbers, and how it gets new problems.
Those two hits do not have to come on different turns. In this position, a 3 clears by its row-run while a 2 beside it clears by its column-run. With a solid gray disc between them, both explosions hit it at once:
1. Before the move
2. The disc drops to the lowest empty cell
3. Wave 1: 2 discs match and clear (+14)
4. Cleared — and neighbouring gray discs take hits
5. Settled — ready for the next disc
Result: score +14 · 1 wave (wave 1: 2 × 7)
Two neighbours clearing in the same wave skip the cracked state. The gray disc never exists as a cracked disc on this board.
The same counting works when the two hits are not on opposite sides:
1. Before the move
2. The disc drops to the lowest empty cell
3. Wave 1: 2 discs match and clear (+14)
4. Cleared — and neighbouring gray discs take hits
5. Gravity: everything above falls
6. Settled — ready for the next disc
Result: score +14 · 1 wave (wave 1: 2 × 7)
Two hits in the same wave open a solid disc at once. Hits are judged on the board before the clear, so a disc that is about to be removed still counts as a neighbour.
A gray disc's number is always chosen uniformly at random from 1 to 7.
Gravity and chain reactions
When discs clear, everything above them falls straight down. If the changed
board creates a new match, those discs clear too. That is wave 2, and the
process can continue. Each successive wave is worth more than the last.
1. Before the move
2. The disc drops to the lowest empty cell
3. Wave 1: 1 disc match and clear (+7)
4. Cleared — and neighbouring gray discs take hits
5. Wave 2: 1 disc match and clear (+39)
6. Cleared — and neighbouring gray discs take hits
A two-wave chain. The second wave comes from a newly revealed 2 whose own run happens to match, which is why reveals can keep a cascade going.
Everything inside one move (however many waves) happens before the next disc
is offered, and the player has no decisions to make during it.
Scoring
Each disc cleared in chain wave d is worth floor(7 × d^2.5) points. The
curve is steep on purpose: a disc in wave 8 is worth 181 times a disc in wave 1.
Points per cleared disc, by chain wave — floor(7 × d^2.5)
table view
chain wave
points per disc
1
7
2
39
3
109
4
224
5
391
6
617
7
907
8
1,267
Per-disc value by wave. Multiply by the number of discs in the wave; a wave of three discs at depth 3 is 3 × 109 = 327.
Two bonuses sit on top of the wave points:
Event
Bonus
When
the board rises (every fifth drop)
17,000
awarded with every rise, on top of whatever the move scored
the board is completely empty after a move
70,000
awarded whenever a move ends with no discs on the board at all
Clearing the whole board. The 70,000 is awarded at the end of the move, after every wave has resolved.
Every fifth drop, the board rises
A clock counts down from 5. Each drop ticks it once. When it reaches zero, the
whole board shifts up one row and a new row of seven solid gray discs
appears along the bottom. The clock resets to 5 and play continues.
1. Before the move
2. The disc drops to the lowest empty cell
3. Fifth drop: the board rises (+17,000)
4. Settled — ready for the next disc
Result: score +17,000 · the board rose and the rise clock reset to 5
The rise happens after the move's cascade has finished. If the new row creates matches, they clear as part of the same move. The wave counter does not restart.
Two details of the rise matter for strategy. It happens after the cascade
of the move that triggered it, not before; and the seven new gray discs are
seven more unknown numbers and seven more occupied cells, which lengthens
every vertical run passing through them.
How a game ends
There are exactly two ways for a game to end, and both are about running out of
room:
The board cannot rise. When the clock reaches zero, every column must
have an empty top cell for the board to shift up. If any column is stacked
to the top, the rise is impossible and the game is over.
No column can take a disc. If every column is full, there is no legal
move, and the game is over.
1. Before the move
2. The disc drops to the lowest empty cell
3. Game over
Result: score +0 · the game is over
A blocked rise. A single full column ends the game even when six other columns have plenty of space, which is why height is the thing every strategy here watches most closely.
Nothing else ends a game: there are no timers, no move limits, and no way to lose points.
Vocabulary
Rule
Precisely
Board
7 columns × 7 rows.
A turn
You are shown the next disc; you choose a column whose top cell is empty; the disc falls to the lowest empty cell in that column.
Clearing
A numbered disc clears when the contiguous run of occupied cells through it, along its row or its column, has length exactly equal to its number. Gray discs count as occupied.
Waves
All matching discs clear simultaneously; gravity then pulls everything above them down; if new matches exist, the next wave clears them; repeat until nothing matches.
Gray discs
Might be a hidden gray disc or a cracked gray disc. An orthogonally adjacent disc clearing in the current wave, judged on the pre-clear board, gives the disc a hit. Solid + 1 hit = cracked. Cracked + 1 hit = revealed. Solid + 2 hits in one wave = revealed. The revealed number is uniform on 1-7, and this engine draws it at reveal time unless latent mode fixes it in advance.
Wave score
floor(7 × d^2.5) points per disc cleared in wave d: 7, 39, 109, 224, 391, 617, 907, 1,267, …
Rise
After every fifth drop (and after that move's cascade), the board moves up one row and a row of seven solid gray discs appears at the bottom. This gives a +17,000 survival bonus. A cascade caused by the new row might continue the move's wave count.
Board clear
A move that ends with an empty board earns +70,000.
Game over
The board must rise but some column's top cell is occupied; or no column can accept a disc.
Information
The player and any legal policy see only the board, the next disc, and the rise clock. Hidden gray values and future discs are unknown to the player and any legal policy.
Why the strategy is hard
A common pattern that human players naturally do in this game, that every computer
policy so far has not been able to perform, involves the long-term strategic thinking to
build up large chain reactions. If you review the computer games, you will see they tend
to play very efficiently but currently lose because of avoidable mistakes.