Connect 4 Board Sizes: What Changes on a 9x8 Grid vs the Classic 7x6

Updated 19 August 2026Exact counting, labelled estimates, measured engine output

Almost every four-in-a-row game you have played used the same board: seven columns by six rows. Line4 9x8 uses nine by eight. That sounds like a small tweak - two extra columns, two extra rows - but it changes the game measurably, not just cosmetically. Every claim below is tagged: Exact means provable counting, Estimate means first-order with its bounds stated, and Engine means measured output of our own engine - evidence, not perfect play.

Key findings

• 72 cells 71% more board than the classic 42 - and 30 extra discs before it fills.
• 153 lines 2.2x the classic 69 possible four-in-a-row lines.
• +29% average winning lines through a cell: 8.50 vs 6.57.
• Plateau the single peak column of 7x6 becomes three equally central columns.
• ~5 x 10²¹ estimated legal positions for 9x8 - about a billion 7x6s; still no exact count at this height.
• Unsolved 9x8 sits one column past the solved-board frontier at this height.

The numbers

Exact For a board w columns wide and h rows tall, the number of straight four-cell lines is L(w,h) = h(w-3) + w(h-3) + 2(w-3)(h-3): horizontals, verticals and the two diagonal directions. L(7,6) = 24 + 21 + 24 = 69, and L(9,8) = 48 + 45 + 60 = 153. Nothing here is taken on faith - recount it on a napkin.

The line count is the number that changes how the game feels. An average cell on 9x8 belongs to 8.50 possible four-in-a-row lines against 6.57 on 7x6 - about 29% more - and the busiest cells reach 16 against 13. The edges do not grow at all: a corner sits on exactly 3 lines on both boards. It is the middle that gets denser, which is exactly where threats hide.

One centre peak becomes a three-column plateau

On 7x6 the centre column is famously decisive: its cells cross more winning lines than any other column's, and the solved first-player win opens there. Count the lines through every cell and the classic board has a single peak - column 4 participates in 60 line-slots, its neighbours in 48:

On 9x8 the peak flattens into a plateau. Columns 4, 5 and 6 tie at 92 line-slots each, and the six busiest cells (16 lines each) form a block in the middle of the board rather than a single hot square:

Exact Both maps are pure counting - each number is how many of the board's winning lines pass through that cell, and the column sums total four times the line count, as they must. Equal participation is a geometric statement, not a strategic guarantee: gravity and tempo still make positions unequal. But the flat top changes the character of the opening. On 7x6 move one is "take the centre"; on 9x8 there is no single square to grab - the fight is for the middle band, and losing the exact centre is survivable in a way it never is on the classic board.

How big is the game?

Exact The classic 7x6 board has 4,531,985,219,092 legal positions - about 4.5 trillion, computed by Edelkamp and Kissmann (OEIS A212693). A tidy way to hold that number: it is 2^42.05, almost exactly one bit per cell.

Estimate Nobody appears to have published an exact count for 9x8 - OEIS A235610, which tabulates position counts by board size, runs out long before width 9 - though the width-9 column is no longer blank up to height 6, as the next section shows. If the one-bit-per-cell rate roughly holds, 72 cells lands near 2⁷² - about 5 x 10²¹ positions, a billion times the classic game. The naive upper bound of 3⁷² (every cell empty, yours or theirs) is about 2 x 10³⁴; legality eats roughly a third of the bits. First-order only, and we label it as such.

Exact There is also a concrete engineering reason 9x8 is harder to attack than it looks. Fast Connect Four solvers keep an entire position in one machine word, using (h+1) bits per column: 7x6 needs 49 bits, so it fits a 64-bit word with room to spare. 8x8 already needs 72 bits, and 9x8 needs 81 - the single-word bitboard trick that powers the classic solvers stops fitting before nine columns.

Exact position counts for width-9 boards

Exact Markus Boeck, whose solver produced the 2025 strong solve of 7x6 cited below, ran his BDD-based symbolic forward pass over width 9 and counted the legal positions exactly at heights 1 to 6. He has given permission to publish those counts here.

Exact The right-hand column is why this data bears on the estimate above. Information density per cell falls monotonically as the board gets taller, and by 9x6 it has reached 1.0009 bits per cell - against 1.0010 for 7x6, a board of different width and height. So the one-bit-per-cell regularity that the 2⁷² figure leans on is not a quirk of the classic board; it is roughly where the density lands once a board is reasonably tall.

Estimate That does not make 2⁷² exact, and it is worth being blunt about why. The series is still falling at 9x6, not flat, so carrying it two rows further is an extrapolation with a real error bar, and nothing on this page closes it. Width 9 at heights 7 and 8 remains uncounted - that computation has not been completed by anyone, as far as we know.

Counts computed by Markus Boeck (TU Wien) using Connect4-Strong-Solver, the solver behind Strongly Solving 7x6 Connect-Four on Consumer Grade Hardware (arXiv:2507.05267), and published here with his permission. The six runs above took 87.7 hours of compute in total. The counts were independently reproduced here for 9x1, 9x2 and the first ten plies of 9x3 with a from-scratch enumerator sharing no code with his pipeline: 40 per-ply values, 40 matches.

Is 9x8 Connect Four solved?

No - and as far as we can tell, nobody has published an attempt. The classic 7x6 game was solved in 1988, twice within fifteen days: first by James D. Allen, then independently by Victor Allis. With perfect play the first player wins, opening in the centre; in 2025 the board was even strongly solved on consumer hardware. John Tromp later solved a whole family of other sizes - his solved-sizes table is the frontier of what is known. At height 8 it reads:

Exact Two patterns in that table are worth staring at. Across every solved even-height board, the first player wins only at width 7 (7x6 and 7x8). And width 9 has been solved at two heights - 9x4 and 9x6 - with the second player winning both times. If that lean survived height 8, the blank cell would be a second-player win. That is a pattern in a table, not a theorem: we make no claim, and memorised 7x6 opening theory transfers to none of this. 9x8 sits exactly one step beyond the solved frontier.

What our engine thinks of the opening

Engine A learned evaluator cannot settle an open board, but its opinion is measurable, so here it is. The Champion's value head calls the empty 9x8 board dead even, a hair to the second player (-0.011 on a -1 to 1 scale). Its opening policy does not grab the exact centre: about 62% of the opening probability sits on the plateau columns either side of the centre and only 5.5% on the centre itself, and the move it actually plays is one right of centre. Facing that opening, its reply policy puts 96% on answering directly on top - the "follow-up" shape that, on an even-height board, hands the second player the even squares. A learned prior is evidence, not proof - but it rhymes with both the plateau geometry above and the second-player lean in the solved table. We took this much further in a 1,395-game self-play study: every opening mapped, the parity of every decisive win measured, raw data downloadable. How the Champion actually picks its moves is on the Champion AI page.

Double threats hide better

A single threat can always be blocked. Games are decided by double threats - two ways to complete a line, where your opponent can only stop one. The extra width gives both sides more room to prepare them, and the extra height means a diagonal can grow two rows further before it becomes obvious. In practice, most surprise losses on the 9x8 board come from a diagonal that quietly completed itself behind the front line.

• Immediate threat - a playable cell that wins on the very next move.
• Latent threat - a winning cell that gravity has not yet made reachable; it matters later, when its column fills.
• Double threat - one move that creates two immediate threats at once. This is what actually wins games.
• False double threat - looks like two lines, but one cell is unplayable or the opponent has a counter-threat in between.

Longer games, sharper endgames

72 cells instead of 42 means games last longer, and endgame parity matters more: every disc you drop lifts the landing row for the next one, so a move that looks safe can hand your opponent exactly the cell they were waiting for. Counting whose turn it will be when a key column fills up is a real skill on this board.

Why the AI was trained from scratch for this board

Position evaluation is board-specific: a network trained on 7x6 has learned which cells matter on that grid. The Champion in Line4 9x8 was trained with self-play on the 9x8 board from the start, which is why it plays the wider geometry naturally instead of applying 7x6 habits. More about how it picks moves is on the Champion AI page.

Try it

The quickest way to feel the difference is to play a game: open the 9x8 board and play against the Champion, pick a strength and see how far your 7x6 instincts get you. If you want to train the pattern recognition directly, the 9x8 Win-in-2 tactics puzzles are built for exactly that. New to the rules? Start with how to play four in a row.

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