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In 1997 alone, Nevada casinos netted an estimated $6 billion, which works out to about $11,415 a minute throughout the entire year. These huge profits are possible because most players are true gamblers. They eagerly bet their money on various casino games that consistently pay off with unfavorable odds. They hope against hope that they will be one of the lucky few who walk away winners. Compare blackjack’s favourable playing odds of up to 10% for the player to the advantages that exist for the casino in some of these other popular games:
Keno (30%). People play keno, like bingo, for the fun of it, seldom expecting to actually win. They are merely having a “fling” with Lady Luck for the sheer excitement it offers.
Slot machines (3% to 25%). According to William Newcott (National Geographic, December 1996, page 73), Las Vegas casinos make more money from slots than all of the table games combined. There are over 115,000 machines in Clark county alone. Players beware: Casinos can set their machines to be “loose” or “tight.” Some video poker games, however, are purported to be beatable if played correctly long enough.
Craps (1.4% and up). This is the ultimate dice game. The low house advantage applies only to the “line bets”; all others take a larger bite out of your bankroll. Certain “odds bets” when combined with the line bets can offer even less than 1.4% casino advantage, and therefore are the best bets available to the player.
Roulette (1.35% and up). Most tables have two green numbers, 0 and 00, which increase the casino’s advantage to 5.26%, but the European style wheels have only one green zero, which lowers the house odds to 2.7%. Many European games offer en prison wagers on the six even-money outside bets. In this case, when the zero hits, a player’s bet is merely “imprisoned” until the next spin of the wheel. If the following spin results in a win for the player, he doesn’t lose the original wager after all, and the whole bet is returned. The en prison rule reduces the house odds to only 1.35%.
Baccarat (1.17% and up). Baccarat and mini-baccarat offer the lowest fixed casino percentage-advantage odds for single bets in any game. The player hand has losing odds of 1.37%, while the bank hand offers only 1.17% loss.

Proposition Bets
Proposition bets are merely proposals whose odds can be determined mathematically. Wagering that Beetle-Balm will show in the third race at Goose Downs is not a proposition bet, but betting that you can flip two heads or two tails in a row is. Unless you know how to figure the odds of such wagers, you are wiser to avoid them. However, as seen earlier in this chapter, being able to calculate the odds of a simple proposition bet like blackjack’s insurance is an important asset, and within the ability of most players.
Every roulette or craps bet placed is a proposition bet. The odds of any particular number hitting can be calculated precisely. For example, in roulette the house advantage is determined by the fact that the player wins only once out of thirty-eight tries (i.e., winning thirty-five chips while losing thirty-seven), which means that the casino is up two chips for every thirty-eight spins of the wheel on average (2/38 = 5.26%). Similarly, in craps every payoff is predetermined by the probability ratio of which dice total is most apt to appear. For example, 7 is produced by six possible combinations, but 4 by only three; therefore, the Point 4 odds-bet is paid off 2 to 1.
In blackjack the only true proposition wagers are the insurance and the over/under side bets. A few casinos offer a variation known as the “over and under 13″ proposition as follows: According to the total of the player’s first two cards, even money is paid if he has bet correctly. For this wager, Aces are counted as Is only. A total of exactly 13 is a loser, being neither over nor under 13. This is not a smart bet to make unless one is counting the cards and knows the TC is very positive or negative, since there is approximately a 9% chance of two cards totaling exactly 13; therefore, the casino’s advantage is a constant 9%. Knowing that the TC is extreme, however, can make this proposition bet a winner.
Think about the coin-flipping example mentioned above. Suppose some stranger offered you 2-to-l odds if you could obtain two similar results on your first two tosses. If you made two heads or two tails you would win $20, but if you didn’t you would lose $10. Would you accept the proposition? Before reading the answer below, try to calculate the odds for yourself.
Since the results of fair coin tosses are exactly even on the average, the chance of getting heads (or tails) for any particular toss is always the same, i.e., 50% or 1-to-l odds. If your first flip is heads, the odds that you will flip heads on the next toss is still dead even. Similarly, if your first toss is tails, there is a fify-fifty chance that your second toss will also be tails. Therefore, you would be wise to accept such a proposition bet, because the chance of your succeeding only warrants even money, while the stranger was prepared to give you 2-to-l odds.
The same stranger now suggests to you another proposition bet: he offers even money if you can pull two cards of the same color from a freshly shuffled full deck on your first two tries. Assuming a fair deck in which half the cards are red and half are black, should you accept the wager? As in the coin-flipping example above, it sounds like the chances of succeeding would be exactly even. Right? Wrong. Once you pull out a card, whether it is red or black, there are fewer of that color remaining in the deck than there are of the other color. Your second draw would no longer be a strictly fifty-fifty chance. By accepting such a wager you would be actually giving the stranger odds.
These two examples further illustrate why blackjack can be beaten while other table games cannot. The odds in roulette and craps always remain fixed in favor of the house, and there is nothing the player can do to change them. Blackjack’s odds are constantly changing. Sometimes they favor the house, and at other times they favor the player. By observing which cards have already appeared in a blackjack game and playing accordingly, the player can actually improve his chances of winning. Cards, in effect, do have a sort of “memory”; coins, bouncing balls, or rolling dice do not.
Here’s a proposition bet you can try on a friend. Suggest the following: “You’ll draw two cards from four Jacks and four Aces, and I’ll draw two cards from just three Jacks and only two Aces. At $1 a hand, we’ll give each other even money for blackjacks, and play until one of us is up $25. Okay?”
Being able to figure out exactly who would have the advantage in this kind of problem is a math skill worth remembering. It goes like this:
From eight cards, consisting of four Jacks and four Aces, there are 28 (8 X 7 / 2) possible two-card combinations. But only twelve of these are not blackjacks the six made up of only Jacks plus the six made up of only Aces. Therefore, the odds are 16-to-12, or 4-to-3, in favor of drawing a blackjack in this situation, over 57%.
From five cards, consisting of three Jacks and two Aces, there are 10 possible two-card combinations, but only three do not involve the Aces. Of the seven that do, only one combination consists of both Aces, so six combos must be blackjacks. Therefore, 6 out of 10 equals 60% Blackjacks in this case.
Maybe you should reconsider taking “advantage” of your friendship by offering such a proposition.