The interesting part of this question is that most know to insure at true 3.0 + (Hilo), but can't figure out the math behind it. Moses has given a ratio far higher than the 1 in 3 wins necessary to break even on an insurance bet.
So, for ease, use max bet of $100, think only of 41 hands insured, 18 winning, 23 losing, and the further inference that since all insured hands are crappy, no dealer blackjack still equates to a loss.
41 hands not insured at $100 equates to loss of $4100.
41 hands at $100 insured means $6150 at risk. 18 bj's recovers $2700. 23 non bj's los s $4050. Net loss is 1350 vs. $4100. WHEATHER to insure or not is really an easy de ision here.
The more interesting question would be win percentage at 3.0,3.5,4.0,4.5 etc etc. The answer to that allows one to make other types of decisions.
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