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    \$\begingroup\$ By "expected" it seems you mean the average over all possible outcomes, not the single highest possible outcome (which would be achieved by hitting all blue pegs.) It looks like the strategy is to fill the central columns but it is not clear if this continues at high k. \$\endgroup\$ Commented Jan 11 at 7:20
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    \$\begingroup\$ Interesting; k=18 is like k=15: 12122222121. \$\endgroup\$ Commented Jan 13 at 12:27