The person who set this puzzle didn't think this was the correct solution, but if JFC wants to argue the point I'll pass on his details. Here is the intended solution.

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Nearly at the end of the shoe the player might have, say, a 3% disadvantage. He has 16 vs Ace. He places a $1 insurance bet.

His chance of busting on 16 is over 50%; so is the chance of 'eating' an extra card (to be drawn by the dealer because of the insurance bet.)

Since a 3% disadvantage would mean a negative expectation of $15 per $500 bet (table minimum) each card 'eaten' would save over $2 in negative expectation, hence the $1 insurance bet would be justified.

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I'm posting a new and more difficult blackjack problem now, from the same source.