Orange moves next. Can Orange avoid a forced Violet win over the next four plies (one player’s drop is one ply)?
Make a prediction before opening the reasoning.
Compare the predictions
- Yes: there is no immediate Violet win.
Not supported. Violet’s support move creates a diagonal threat whose block supplies the horizontal win above it.
- No: Violet has a forced four-ply win.
Supported. Every Orange first move and every later Orange reply is covered by the support-ladder proof.
- Yes: Orange can secure column 4 first.
Not supported. Violet waits in column 1; Orange still has to block R5C4 and thereby supports R4C4.
Predictions stay on this page; they are not saved or sent.
Test this exact position
Try the alternatives, then undo or reset before comparing another branch. The written argument below always starts from the original position. Played moves save locally in this browser; predictions do not.
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Use the column buttons to drop a token. Orange (O) and Violet (V) take turns. You control both sides here; there is no computer opponent. Test a reply, then undo to compare another.
Keyboard: Tab to an enabled control, then press Enter or Space. The study starts from the diagram shown; reload can restore your own saved moves.
Try the task before inspecting the answer.
The position and the question
Neither player currently has an immediate winning drop. That makes the board look less urgent than a visible three-in-a-row with an available landing square. The threat is hidden in the support cells that a player must fill before a higher square becomes playable.
Rows are numbered from the top, so the bottom square of column 4 is R6C4. Violet already occupies R6C3, R4C5 and R3C6: adding Violet at R5C4 would complete a diagonal. Violet also occupies R4C3, R4C5 and R4C6: adding Violet at R4C4 would complete a horizontal four.
Show the reasoning
If Orange plays away from column 4
For any initial Orange drop in column 1, 3, 5 or 7, Violet drops in column 4 at R6C4. This is a supporting move, not the win itself. It makes R5C4 playable on the next turn. Violet now threatens the diagonal R6C3–R5C4–R4C5–R3C6.
·R1C1OR1C2·R1C3·R1C4·R1C5OR1C6·R1C7·R2C1OR2C2·R2C3·R2C4·R2C5VR2C6·R2C7·R3C1VR3C2·R3C3·R3C4·R3C5VR3C6·R3C7·R4C1OR4C2VR4C3·R4C4VR4C5VR4C6·R4C7·R5C1VR5C2OR5C3·R5C4VR5C5OR5C6OR5C7OR6C1OR6C2VR6C3VR6C4OR6C5OR6C6VR6C7Example branch: Orange C1, Violet C4. Orange faces the R5C4 diagonal threat. Watch the forced block support another win
Orange has no immediate winning escape after that supporting move. If Orange plays outside column 4, Violet takes R5C4 and completes the diagonal. If Orange blocks by occupying R5C4, that token makes R4C4 playable. Violet then drops at R4C4 to complete the horizontal line R4C3–R4C4–R4C5–R4C6.
·R1C1OR1C2·R1C3·R1C4·R1C5OR1C6·R1C7·R2C1OR2C2·R2C3·R2C4·R2C5VR2C6·R2C7·R3C1VR3C2·R3C3·R3C4·R3C5VR3C6·R3C7·R4C1OR4C2VR4C3VR4C4VR4C5VR4C6·R4C7·R5C1VR5C2OR5C3OR5C4VR5C5OR5C6OR5C7OR6C1OR6C2VR6C3VR6C4OR6C5OR6C6VR6C7Orange blocked in C4, supporting Violet’s winning R4C4 drop. Check Orange’s remaining first move
Suppose Orange initially plays column 4, occupying R6C4 itself. Violet can wait by dropping in column 1. The same diagonal threat at R5C4 now demands Orange’s block. Playing elsewhere allows the diagonal; blocking R5C4 supports the horizontal win at R4C4. Starting in the critical column therefore does not escape the ladder.
·R1C1OR1C2·R1C3·R1C4·R1C5OR1C6·R1C7·R2C1OR2C2·R2C3·R2C4·R2C5VR2C6·R2C7·R3C1VR3C2·R3C3·R3C4·R3C5VR3C6·R3C7·R4C1OR4C2VR4C3·R4C4VR4C5VR4C6·R4C7·R5C1VR5C2OR5C3·R5C4VR5C5OR5C6OR5C7VR6C1OR6C2VR6C3OR6C4OR6C5OR6C6VR6C7Alternative start: Orange C4, Violet C1. Orange still faces the same stacked threats. Account for every defensive branch
The proof covers all five legal Orange first moves. After the selected Violet reply, all five legal Orange continuations were checked. Each of those 25 branches has a winning Violet drop, giving a forced win by the fourth ply from the start. This is a bounded tactical proof of this position, not a general claim that every pair of stacked threats wins.
The tempting shortcut
With no immediate opposing win, Orange can safely improve another part of the board.
Where the shortcut breaks
Violet can create a threat whose required defensive token supports a second winning square directly above it. An immediate-win scan does not see the complete sequence.
A better decision
Inspect the landing heights of future threats. Blocking a lower square can make a higher winning square playable for the opponent.
Changed conditions
In a constructed variation, change the bottom-row token R6C3 from Violet to Orange and keep Orange to move. Does the original four-ply loss still apply?
Check the changed-condition answer
No. Orange can drop in column 4 at R6C4 and immediately connect Orange tokens across R6C2–R6C6. That wins the game before Violet can build the support ladder. The original proof checked that Orange had no immediate winning escape; the changed token invalidates that condition. This is a supplied counterfactual board for reasoning, not a claim that the recorded opening history reaches it.
Take this back to your next game
Count the support beneath a threat as part of the tactic. Two threats in one column can work sequentially even when they cannot be played at the same height.
How the claim was checked
Replay the supplied 20-drop history; check no initial immediate wins; validate a complete four-ply winning certificate against every Orange reply.
- 5 legal Orange first moves
- No initial immediate winning drop for either side
- 25 defensive branches end with a Violet winning drop
- Constructed R6C3→Orange variation: only immediate Orange win is column 4
Read the fixed positions and supporting proof data. Computational checks establish only the claim and position stated here. They do not establish a player difficulty rating or make an unproved strategy optimal.
Playfield Arcade · Updated 4 October 2026 · Original case design, AI-assisted writing and code, with reproducible position checks. Our method · Report a correction