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Can a language model plan a route of seventeen decisions, when a single wrong one loses the floor?

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This thesis tests that in Magic Tower, a puzzle game with no randomness and no undo.

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Every fight costs HP by one formula: attack lowers the number of strikes, defence lowers every strike.

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So order matters: a gem taken before a fight saves more than its face value.

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And nothing comes back: keys, HP and monsters are gone once used.

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Here is the first decision on the simple floor. Four actions are legal.

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The exact solver shows that only one, the Black Slime, still leaves a win. The other three have already lost the floor, though nothing shows it yet.

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In the re-run, nineteen of twenty episodes chose it.

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The agent splits the work: the engine computes reachability, exact damage and a lookahead; the model only picks a numbered action.

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An exact solver scores every state. It also corrected a published reference: the complex floor's optimum is 68 HP, not 22.

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Question one: what does the engine's observation contribute?

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Failed episodes kept citing lines that showed only one side of a trade-off: a saving, without the HP it costs to get there.

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Stating the missing side, with the model and the prompt unchanged, took the largest model from zero of five wins to ten of ten.

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Across both runs it won fifteen of fifteen, though always at 2 HP, where the optimum is 13.

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Two warnings. Every early win had contained a silent engine override; overrides are now mechanical only, and logged.

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And on the complex floor no model wins: twenty-nine of thirty losses fall at one cheap fight, long before the door a human would blame.

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Question two: does evolutionary prompt optimisation help? With the annotations present, its gains stay within the noise between two runs of one prompt.

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With a reasoning model, both search loops raised their training score and lost on held-out floors: the population search won 24 of 39 games, the plain rules prompt 32.

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Question three: react at every step, or commit to a plan?

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On the simple floor, reactive play won fourteen of twenty episodes; committed plans one of seventy. Plans match it with a fraction of the calls only when the order is given.

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On the full 24-floor tower, the rule-based heuristic stops at floor 8. The best model reached floor 18.

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Resumed there with blue keys for sale, as in the original game, it reached the normal ending.

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The lesson: put strategic knowledge into the engine's observation, with both sides of every trade-off, not into the prompt.

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Commit to a plan only when the order is known, and measure agents against an exact reference.

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Every episode, table and search is on this site. Try them.