whoever does first win vs whoever does first wins

Some examples from the web:

• That way, whoever shot first wins.
• The point is, whoever dates first wins.
• Now, however, it seems that whoever comes first wins, whoever comes second loses, and the rest just take part.
• Yes, whoever wins gets first choice of what days to work.
• A force that cannot fail against whoever wins the first battle.
• Whoever figures out the bank robber's name first wins lunch for a week.
• Whoever figures out the bank robber's name first wins lunch for a week.
• Once again, whoever makes it across the pole first wins.
• The softball team's celebrating their first win.
• Also whoever does the typing gets a prize.
• [Martin] Way better looking than whoever does your taxes.
• I think whoever does the technological evaluation work will have to bear that in mind.
• With whoever does the most extraordinary thing.
• Whoever does it gets locked in.
• Whoever does not fear the truth I proclaim and acts accordingly can never die.
• You see, whoever does that gets loads of respect.
• Whoever doesn't get shot is q.B.-1.
• We must first win the will of the people.
• This is Homer Simpson's 13th raffle and first win.
• The one who strikes first wins.

Some examples from the web:

• That way, whoever shot first wins.
• The point is, whoever dates first wins.
• Now, however, it seems that whoever comes first wins, whoever comes second loses, and the rest just take part.
• Yes, whoever wins gets first choice of what days to work.
• A force that cannot fail against whoever wins the first battle.
• Whoever figures out the bank robber's name first wins lunch for a week.
• Whoever figures out the bank robber's name first wins lunch for a week.
• Once again, whoever makes it across the pole first wins.
• The softball team's celebrating their first win.
• Also whoever does the typing gets a prize.
• [Martin] Way better looking than whoever does your taxes.
• I think whoever does the technological evaluation work will have to bear that in mind.
• With whoever does the most extraordinary thing.
• Whoever does it gets locked in.
• Whoever does not fear the truth I proclaim and acts accordingly can never die.
• You see, whoever does that gets loads of respect.
• Whoever doesn't get shot is q.B.-1.
• We must first win the will of the people.
• This is Homer Simpson's 13th raffle and first win.
• The one who strikes first wins.