| Now, I understand that not all fundamentalism leads to violence. The Amish and Mennonites come to mind. But you see these people do not let their religion preclude or dictate political and economic policy. They live and work in our society and accept democracy and capitalism. Sure, they want to preserve their ways, but I assure you that the farms they run are there to make money for their families. Fine. Religion is a separate issue as well it should be. The same is true of many devout followers of Islam throughout the world and throughout our country in particular. For them religion is a separate issue. In their minds it is not a model for political and economic structure. They accept the separation of church and state. Any of you who play Blackjack know that there is a bet called Insurance in the game. By no means is this bet a 'Piece of the Rock'. For the few of you who are not familiar with Blackjack (if any) let me describe the bet to you. Each player in the game of Blackjack receives two cards, sometimes face up and sometimes face down; it doesn't matter. The dealer receives two cards as well, but the dealer's cards are dealt so that one is face down, the hole card, and one is face up. If the dealer's up card is an Ace, which counts as either one or eleven, then there is a reasonable possibility that the hole card is a ten, thus giving the dealer a two-card 21, a Blackjack. A Blackjack beats all other hands except another Blackjack, the latter case being a push. Whenever the dealer's up card is an Ace, the dealer offers the players the chance to 'Insure' their hand by making an Insurance bet. This wager allows each player to place a wager of up to one half of his or her original bet on the proposition that the dealer will indeed have a Blackjack. The bet pays 2 to 1. In other words, a player taking this bet is wagering that the hole card will indeed be a ten. For example, suppose the player's original wager was $10 and the dealer's up card is an Ace. The player makes a $5 Insurance wager. If the dealer's hole card is a ten then the player loses the original $10 wager but wins 2 to 1 on the $5 Insurance bet ($10) and the whole thing is a push. Well, there is an exception. If the player insured a Blackjack and the dealer had a ten in the hole, then the original wager is a tie and the player wins $10. If the dealer does not have a Blackjack, then the player loses the Insurance bet and play continues as usual. Whoever thought up the word 'Insurance' for this bet certainly had a wry sense of humor. Although there are times when the Insurance bet makes sense, and we will discuss this later, for the average player who is not counting cards this is a sucker bet. Let's see why. To begin with let us look at the composition of a full deck of 52 cards. There are 16 tens and 36 non-tens. The ratio of non-tens to tens is 2.25. This figure is the same for any number of decks. So, if one were playing against an infinite deck, that is, a deck in which the ratio does not change with card removal, it is clear that the player's expected return on the Insurance bet is: exp = 2 x 16/52 - 36/52 = -0.076923 (1) which is a house edge of around 7.69%. As we will see, as the number of decks drops, the Insurance bet improves but still remains in favor of the house. |
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