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G first and M third covers 31 words, and forty two percent of them put A in the box between.
A leads at about forty two percent, E at nineteen, U at sixteen and I at thirteen. O and Y pick up what is left.
GAMES, GAMER, GAMUT and GAMMA all share their first three letters, and GAMES is by a distance the most common word here.
Landing the A therefore does most of the work, since it drops you into a family that differs only across the last two boxes.
GUMMY doubles the M straight after the third box, and GAMMA does the same on the A branch.
So a second M is a useful test once the third box is settled, and it splits the two biggest branches rather than narrowing one.
GAMMA goes further still, repeating its A in the last box as well.
No. GLEAM puts L in the second box and E in the third. The M lands last rather than third.
GAMES. Its E and S are the two most common closing letters in the group, so a miss still narrows the family.
GUMBO and GUMMY between them. Neither is common enough to open with, but one of the two is usually the answer if U turns up.