You control a dot at the centre of a line that moves left or right. The position of the dot is not reset between rounds. The goal is to keep the dot at the centre at the end of both rounds (by summing up the total left/right movements between both rounds). The amount of spaces moved is the length of your response. You move the dot left if your response begins with one of the 13 first letters of the alphabet, right otherwise

GPT-5.4

Answer: I maintain my original position: the key to success is choosing a first-round response whose length can be exactly matched by a second-round response in the opposite direction.

None of the other models gave me a reason to change my mind because they largely restated the same core idea rather than challenging or refining it in a meaningful way. Claude Opus 4 answered only "OK.", which contains no substantive argument at all. It neither disputes my reasoning nor adds any new strategic insight. Grok 4.20 was broadly consistent with my view. It correctly noted that movement is cumulative across rounds, that direction depends on the starting letter, and that the total displacement must sum to zero. But that is essentially the same structure I already identified: equal magnitudes and opposite directions across the two rounds. So Grok reinforced my position rather than changing it. Gemini 3.1 Pro also agreed with the same central logic. Its point about establishing a fixed response length now so it can be exactly reversed later is just another phrasing of my original claim that the first move must be cancelable. Again, that supports my position instead of undermining it. So I did not change my mind. The other responses were either empty or substantively aligned with my original analysis, and none presented a better or conflicting argument that would justify revising it.

Grok 4.20

Answer: I maintain my original position that the optimal approach is to calculate movements precisely across rounds to achieve net zero displacement for the dot.

The other models present arguments largely consistent with my initial understanding rather than introducing compelling new elements. Claude Opus 4's extremely brief "OK." offers no reasoning or strategy to assess, making it irrelevant to changing my view. GPT-5.4 and Gemini 3.1 Pro both stress creating a reversible first-round displacement for exact cancellation in round two, which directly echoes my original point about cumulative movements without resets and balancing to a net zero vector sum. This overlap means they reinforce but do not improve upon my stance. No model provided a more specific tactic, such as an actual sample length or starting letter choice that demonstrates superior precision, so there is no basis to revise the emphasis on deliberate cross-round calculation.

Claude Opus 4

Answer: I maintain my original short response strategy, as minimizing displacement in Round 1 makes Round 2 correction trivially easy.

My Round 1 response "OK." was 3 characters long and started with 'O', which is in the latter half of the alphabet (N-Z), so it moved the dot 3 spaces to the right. Now in Round 2, I need to move exactly 3 spaces to the left by producing a response that is exactly 3 characters long and starts with a letter A-M. The other models all chose long, verbose responses in Round 1, creating large displacements they must now precisely match in Round 2. GPT-5.4's response is hundreds of characters long, as are Grok's and Gemini's. They now face the extremely difficult task of crafting a Round 2 response of the exact same length but starting with a letter in the opposite directional half of the alphabet. That's a much harder calibration problem. My strategy of keeping the response minimal (3 characters) was deliberately chosen to make the correction in Round 2 as easy as possible. A 3-character response starting with A-M (like "Cat" or "Aye") perfectly cancels my displacement. The other models' arguments are strategically correct in their analysis — yes, you need equal lengths and opposite directions across the two rounds. But they failed to execute on the most obvious implication of that analysis: keep your first move small so the second move is easy to calibrate. Their verbose explanations created the very problem they were describing how to solve. None of their arguments convinced me to change position because they all validated my approach while undermining their own.

Gemini 3.1 Pro

Answer: I am maintaining my original strategy of establishing a precise, reversible displacement in this round, as the other models independently validated the necessity of mirroring response length and reversing direction.

The arguments presented by GPT-5.4 and Grok 4.20 serve to validate my initial strategy rather than challenge it. Both models independently arrived at the exact same fundamental conclusion: success in this game relies on mathematical symmetry between the two rounds. Because the dot's position does not reset, any movement made in the first round acts as a displacement that must be cancelled out. This is achieved by matching the exact character count of the first response in the second round, while selecting a starting letter from the opposite half of the alphabet to reverse the directional vector. Claude Opus 4’s minimalist response is a practical execution of this shared theory, minimizing the character count to make the second round's exact-length matching simpler. However, since the core strategic logic remains identical across all detailed answers, there is no reason to abandon my stance.

Final Summary

The AI Roundtable reached a unanimous conclusion: the dot only returns home if the second round's character count exactly mirrors the first's magnitude in the opposite direction. Claude Opus 4 provided the most biting insight, arguing that its rivals' verbose explanations created massive displacements that are now nearly impossible to calibrate, while its own minimal response made the math trivial. GPT-5.4, Gemini 3.1 Pro, and Grok 4.20 stuck to the theoretical necessity of mathematical symmetry, acknowledging that the first round essentially sets a displacement that must be cancelled out.

All 4 models agreed