In Puzzle 4, you should play KA d4 for 12, withholding the 2nd A. At first this play looks absolutely ridiculous: after all, KAE scores 18 more points, the A is a very bad tile for both duplication and rack balance, and your chances of drawing an N for AEONIAN aren’t very good. However, your opponent’s last play was MELD, which indicates that your opponent has at least 2 (probably 3) consonants on their rack: even though the play is obviously weak, it’s still almost inconceivable that their rack has 3 vowels.

Therefore, your chances of winning are abysmal, since you’ll never outscore your opponent unless you amazingly draw the last two consonants out of the bag. (And even then, you could easily lose.) An N draw will surely win you the game as AEONIAN plays in two spots and scores enough points to outrun your opponent. You might even get multiple chances to draw the N, as your opponent might leave one tile in the bag next turn.