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The only relevant factor when deciding whether or not to take insurance is the probability that the dealer will get a T (a 10-valued card) to go with his Ace. Insurance is truly a proposition bet, which should be considered a completely independent event from whatever your two-card total happens to be. Since the insurance payoff is 2 to 1, it is an even-money situation only when exactly one-third ( 33.3%) of the undealt cards are T’s. Contrary to the BS edict that one should never take insurance, it is a smart choice for the player when more than a third of the cards remaining to be dealt are T’s.
Well-intentioned players and dealers alike will freely advise you to insure a hand of, say, T,T but not one of, say, 2,3. Insuring strong hands while not insuring weak hands makes no sense whatsoever. In fact, just the opposite is true. With a hand of 20, two extra T’s must be used up; therefore, the odds are even less likely that the dealer will also have a T in the hole, causing you to be all the more apt to lose your insurance wager.
If you have not been tracking the cards, you have to assume that the ratio of T’s to non-T’s is that of a freshly shuffled deck (16 to 36, or slightly over 30% T’s). Taking into account that the dealer must be showing an Ace to offer the insurance proposition, the ratio of available T’s to non-T’s climbs to just over 31% (sixteen out of a possible fifty-one), before considering the ranks of your first two cards or those of any other player. It would be necessary to see three more non-T’s and no additional T’s before the ratio would equal the even-money odds of 33.3% (sixteen out of forty-eight possible draws). But even if you see four more non-T’s than T’s per deck, the insurance wager is still not a winning one but merely a break-even proposition. Off the top of a fresh deck, there would have to be five or more non-T’s than T’s remaining to be dealt (bringing the ratio above 33.3%) in order to justify making the insurance wager. Only if you have been counting the cards and know that there are more than four non-T’s than T’s used up per deck should you consider insurance. Otherwise, join the noncounters and politely decline the offer.
Many players fail to realize that accepting “even money” for blackjacks is actually the same as taking insurance. Consider the following scenario: Three noncounters are all dealt blackjacks on $10 bets, but the dealer shows an Ace as her up-card. The dealer then asks, “Insurance anyone?” and player 1 slides $5 out into the insurance area of the layout. Player 2 says, “I’ll take the even money!” and the dealer immediately gives him $10. Player 3 sits pat as BS dictates. The dealer then flips over her hole card to reveal a non-T and proceeds to resolve the remaining payoffs. Player 1 loses his $5 insurance bet but is paid $15 for his blackjack, which nets him $10 on the hand. Player 2 has already received his $10 even money, netting the same as 1. Only player 3 gets the 3-to-2 payoff ($15 in this case) that a blackjack normally provides. Had the dealer obtained a blackjack as well, player 1 would have received $10 for taking insurance and a push, netting the same amount as player 2, who already pocketed $10 from his even money. Player 3 would push and neither win nor lose.
This example shows that insuring a blackjack and taking the even-money offer always works out to exactly the same result. Beginning players are always tempted to grab the even-money payoff, and often do, without realizing that by doing so they are actually accepting the insurance bet. They never take insurance while holding any other hands, since they are aware that the insurance proposition generally favors the house, but they cannot seem to resist the “sure win” when holding a blackjack. Without knowing the TC, they are unwittingly letting the casinos off the hook, by forfeiting their potential 3-to-2 payoffs, whenever they agree to settle for even money.