What casino games offer the best odds?
15-May-2007
Dear Straight Dope:
As a gambling degenerate, I've spent weeks trying to figure out what casino game gives the house the worst advantage. I assume all games are in the house's favor, but which game gives me the best odds? Is there any strategy to roulette, the game that makes me rich in ten minutes and broke in five? What about slot machines ? are some better than others? ?Sam
SDSTAFF Bricker responds:
As the WOPR computer in War Games says: ?The only way to win is not to play.?
Casino games are almost always designed to favor the house. The flashing lights, opulent penthouse suites, and big-name stage shows aren't paid for by a business that runs at a loss.
The odds for any bet on any table game can easily be computed mathematically. While no casino game played normally will make you a winner in the long run, there are several speeds at which you can lose. More about the ?played normally? caveat presently.
First some ground rules. I'll make no attempt to summarize all the possible variations in rules and payoffs at casinos around the world ? I could easily spend the next dozen paragraphs discussing rule variants and their effect on strategy for blackjack alone. Among the variables to be considered: does the house hit a soft 17? Is surrender (giving up your hand before the dealer plays his cards at the cost of one-half your bet) permitted? If so, is it early surrender (an option that can only be exercised before you hit) or late surrender? Double-exposure blackjack sounds like a no-brainer advantage for the player ? you get to see both dealer cards face up ? but typically is played with an even-money payoff on blackjack where ties go to the house, changes that actually increase the house edge.
Nonetheless, as a general principle, if you want to lose money at the slowest possible rate, play blackjack using what game experts call the "basic strategy." Tables summarizing correct play as dictated by basic strategy are widely available, and can even be generated using a calculator. An ordinary blackjack game played correctly using basic strategy typically provides an edge of less than one percent to the house.
In contrast, roulette, which you ask about, is a money-burner for you, and a license to print money for the casino. On a 38-space wheel, the odds for the most basic bets, red/black and odd/even, are even money. Yet there are only 18 odd and 18 even spots, and similarly 18 red and 18 black spots; the two green spots, zero and double-zero give the house a 5.26% edge. The individual numbers aren?t any better: you get a 36:1 payout for hitting the number ?22,? but have only a 1 in 38 chance of doing so. Unless you?re playing in Rick Blaine?s Café American and you?re married to a Bulgarian hottie, stay away from that bet.
Craps doesn?t help you either. The "pass line" bet, which wins for a new shooter who rolls a 7 or 11, loses on a 2, 3, or 12, and on any other number requires him to roll that number (his ?point?) again before rolling a 7, has an even money payoff that deliver a 1.41% edge to the house. The single-roll bets are just ridiculous: an ?any 7? bet pays 4:1 and gives the house a whopping 16% edge.
Slot machines are another story ? and not a good one. Slot machines can be adjusted to provide different odds; in Las Vegas and other gambling meccas, those percentages can vary dramatically, with venues vying for the reputation of having the ?loosest? slots in town. Payouts on slots in Vegas typically range between 90 and 97 percent, meaning that the house typically has a 3-10% edge. On the plus side, there?s no need to memorize complicated strategy tables; you merely insert your money, press a button, and lose a dime for every dollar you play.
Let?s take a moment here to discount a well-known gambling "system," the Martingale method, which refers to the practice of doubling your even-money bet after a loss. The idea here is that you?ll eventually guarantee yourself a win. Amble over to the roulette table and bet $5 on red ? if you win, you?re ahead $5. If you lose, bet $10. If it comes up red this time, you?ve recouped your lost $5 and won $5. If you lose, bet $20 on the next spin. Eventually, the system says, you?ll get a red and win all your lost money back, plus $5. Then start over with another $5 bet!
A moment?s analysis reveals two major flaws with this system. The first is that casino tables have upper and lower limits. Typically a roulette table that permits a $5 minimum bet will cap you out at, say, a $500 maximum bet. That means if you lose seven bets in a row (5+10+20+40+80+160+320), you're dead; you can?t bet the required $640 on the next round to recoup your losses. The second flaw: even if there were no limits, you?d need a gigantic bankroll to cover yourself in the event of sustained bad luck. After a streak of ten losses you?d be out $5,115 and obliged to risk $5,120 on the next spin ? if you lose again you've blown $10,235 and winning puts you up a lousy $5. Obviously, a string of ten blacks in a row is unlikely, but it?s by no means impossible, and in fact is pretty much guaranteed to happen over sufficiently long trials.
Having seen that the major difference between casino games isn't winning vs. losing but rather the speed at which you lose, let?s return to the tantalizing caveat from the introduction: ?played normally.?
Theoretically there's a way to play casino blackjack so the odds favor you rather than the house. That's because blackjack, unlike craps, roulette, and other table games, isn't a series of independent events. The odds of the roulette wheel paying off on "odd" are precisely the same for every spin; in contrast, the odds of being dealt a blackjack change slightly as cards are dispensed from the shoe. At the beginning of the shoe, we have six or eight complete decks of shuffled cards ready to be dealt. As the game progresses, if a disproportionately large number of high cards remains in the shoe, the player is favored; if more low cards are left, the house is favored. A savvy observer can keep track of cards as they?re dealt, and when the ratio temporarily favors the player, bet high. This is known as ?card counting.? The method was first shown definitively in the early 1960s by Edward Thorp, a professor of mathematics at MIT. Thorp developed a system to count cards, simulated his system on an IBM 704 in FORTRAN code, and ultimately went to Las Vegas to test his theory, winning over $11,000 in a single weekend. His subsequent book Beat the Dealer was the first take on the science of counting cards. Casinos responded by going to multiple-deck games and shuffling cards before the end of the shoe, blunting the card-counter?s ability to gather useful information. They also attempted to identify card counters and bar them from play.
A new generation of card counters responded to those countermeasures by disguising their counting using proxies. Ben Mezrich?s Bringing Down the House tells of a team of MIT students who were recruited in the mid-1990s to form card counting teams. One player would sit at a table placing the minimum bet every time ? but counting cards. When the count favored the player, he would surreptitiously signal a cohort to come over, sit down, and immediately start betting big. This tactic flew under the casinos? radar for detecting card counters, since their staffs were trained to look for people who studiously stayed at a table and bet big when the count was favorable. The team won millions before casinos caught on.
Today, high-limit blackjack tables are ready for the card counter with "continuous shuffle machines." After every hand the cards are immediately returned to the shuffle; each new hand is effectively dealt from a new deck, making counting useless. Lower-limit tables typically aren't worth such expensive countermeasures, especially when many would-be card counters have no idea what they?re doing. Undoubtedly among those reading this report will be one or two who think, ?That doesn?t sound so hard ? I can do that!? Casinos welcome the wishful-thinking, inexperienced card counter as a reliable profit maker.
So in the end, if you enjoy gambling, by all means gamble; you?re paying to participate in an enjoyable activity. But don?t think for a moment that there?s a reliable way to win money. The only way to win is not to play.
Sources
Snyder, A., The Big Book of Blackjack, 2006
Sklansky, D., Sklansky Talks Blackjack, 1999
Mezrich, B., Bringing Down The House, 2002
Thorp, E., Beat the Dealer, 1962
Discovery Channel series ?Breaking Vegas? ? "Professor Blackjack" episode, aired March 8, 2005
?SDSTAFF Bricker
LINK
15-May-2007
Dear Straight Dope:
As a gambling degenerate, I've spent weeks trying to figure out what casino game gives the house the worst advantage. I assume all games are in the house's favor, but which game gives me the best odds? Is there any strategy to roulette, the game that makes me rich in ten minutes and broke in five? What about slot machines ? are some better than others? ?Sam
SDSTAFF Bricker responds:
As the WOPR computer in War Games says: ?The only way to win is not to play.?
Casino games are almost always designed to favor the house. The flashing lights, opulent penthouse suites, and big-name stage shows aren't paid for by a business that runs at a loss.
The odds for any bet on any table game can easily be computed mathematically. While no casino game played normally will make you a winner in the long run, there are several speeds at which you can lose. More about the ?played normally? caveat presently.
First some ground rules. I'll make no attempt to summarize all the possible variations in rules and payoffs at casinos around the world ? I could easily spend the next dozen paragraphs discussing rule variants and their effect on strategy for blackjack alone. Among the variables to be considered: does the house hit a soft 17? Is surrender (giving up your hand before the dealer plays his cards at the cost of one-half your bet) permitted? If so, is it early surrender (an option that can only be exercised before you hit) or late surrender? Double-exposure blackjack sounds like a no-brainer advantage for the player ? you get to see both dealer cards face up ? but typically is played with an even-money payoff on blackjack where ties go to the house, changes that actually increase the house edge.
Nonetheless, as a general principle, if you want to lose money at the slowest possible rate, play blackjack using what game experts call the "basic strategy." Tables summarizing correct play as dictated by basic strategy are widely available, and can even be generated using a calculator. An ordinary blackjack game played correctly using basic strategy typically provides an edge of less than one percent to the house.
In contrast, roulette, which you ask about, is a money-burner for you, and a license to print money for the casino. On a 38-space wheel, the odds for the most basic bets, red/black and odd/even, are even money. Yet there are only 18 odd and 18 even spots, and similarly 18 red and 18 black spots; the two green spots, zero and double-zero give the house a 5.26% edge. The individual numbers aren?t any better: you get a 36:1 payout for hitting the number ?22,? but have only a 1 in 38 chance of doing so. Unless you?re playing in Rick Blaine?s Café American and you?re married to a Bulgarian hottie, stay away from that bet.
Craps doesn?t help you either. The "pass line" bet, which wins for a new shooter who rolls a 7 or 11, loses on a 2, 3, or 12, and on any other number requires him to roll that number (his ?point?) again before rolling a 7, has an even money payoff that deliver a 1.41% edge to the house. The single-roll bets are just ridiculous: an ?any 7? bet pays 4:1 and gives the house a whopping 16% edge.
Slot machines are another story ? and not a good one. Slot machines can be adjusted to provide different odds; in Las Vegas and other gambling meccas, those percentages can vary dramatically, with venues vying for the reputation of having the ?loosest? slots in town. Payouts on slots in Vegas typically range between 90 and 97 percent, meaning that the house typically has a 3-10% edge. On the plus side, there?s no need to memorize complicated strategy tables; you merely insert your money, press a button, and lose a dime for every dollar you play.
Let?s take a moment here to discount a well-known gambling "system," the Martingale method, which refers to the practice of doubling your even-money bet after a loss. The idea here is that you?ll eventually guarantee yourself a win. Amble over to the roulette table and bet $5 on red ? if you win, you?re ahead $5. If you lose, bet $10. If it comes up red this time, you?ve recouped your lost $5 and won $5. If you lose, bet $20 on the next spin. Eventually, the system says, you?ll get a red and win all your lost money back, plus $5. Then start over with another $5 bet!
A moment?s analysis reveals two major flaws with this system. The first is that casino tables have upper and lower limits. Typically a roulette table that permits a $5 minimum bet will cap you out at, say, a $500 maximum bet. That means if you lose seven bets in a row (5+10+20+40+80+160+320), you're dead; you can?t bet the required $640 on the next round to recoup your losses. The second flaw: even if there were no limits, you?d need a gigantic bankroll to cover yourself in the event of sustained bad luck. After a streak of ten losses you?d be out $5,115 and obliged to risk $5,120 on the next spin ? if you lose again you've blown $10,235 and winning puts you up a lousy $5. Obviously, a string of ten blacks in a row is unlikely, but it?s by no means impossible, and in fact is pretty much guaranteed to happen over sufficiently long trials.
Having seen that the major difference between casino games isn't winning vs. losing but rather the speed at which you lose, let?s return to the tantalizing caveat from the introduction: ?played normally.?
Theoretically there's a way to play casino blackjack so the odds favor you rather than the house. That's because blackjack, unlike craps, roulette, and other table games, isn't a series of independent events. The odds of the roulette wheel paying off on "odd" are precisely the same for every spin; in contrast, the odds of being dealt a blackjack change slightly as cards are dispensed from the shoe. At the beginning of the shoe, we have six or eight complete decks of shuffled cards ready to be dealt. As the game progresses, if a disproportionately large number of high cards remains in the shoe, the player is favored; if more low cards are left, the house is favored. A savvy observer can keep track of cards as they?re dealt, and when the ratio temporarily favors the player, bet high. This is known as ?card counting.? The method was first shown definitively in the early 1960s by Edward Thorp, a professor of mathematics at MIT. Thorp developed a system to count cards, simulated his system on an IBM 704 in FORTRAN code, and ultimately went to Las Vegas to test his theory, winning over $11,000 in a single weekend. His subsequent book Beat the Dealer was the first take on the science of counting cards. Casinos responded by going to multiple-deck games and shuffling cards before the end of the shoe, blunting the card-counter?s ability to gather useful information. They also attempted to identify card counters and bar them from play.
A new generation of card counters responded to those countermeasures by disguising their counting using proxies. Ben Mezrich?s Bringing Down the House tells of a team of MIT students who were recruited in the mid-1990s to form card counting teams. One player would sit at a table placing the minimum bet every time ? but counting cards. When the count favored the player, he would surreptitiously signal a cohort to come over, sit down, and immediately start betting big. This tactic flew under the casinos? radar for detecting card counters, since their staffs were trained to look for people who studiously stayed at a table and bet big when the count was favorable. The team won millions before casinos caught on.
Today, high-limit blackjack tables are ready for the card counter with "continuous shuffle machines." After every hand the cards are immediately returned to the shuffle; each new hand is effectively dealt from a new deck, making counting useless. Lower-limit tables typically aren't worth such expensive countermeasures, especially when many would-be card counters have no idea what they?re doing. Undoubtedly among those reading this report will be one or two who think, ?That doesn?t sound so hard ? I can do that!? Casinos welcome the wishful-thinking, inexperienced card counter as a reliable profit maker.
So in the end, if you enjoy gambling, by all means gamble; you?re paying to participate in an enjoyable activity. But don?t think for a moment that there?s a reliable way to win money. The only way to win is not to play.
Sources
Snyder, A., The Big Book of Blackjack, 2006
Sklansky, D., Sklansky Talks Blackjack, 1999
Mezrich, B., Bringing Down The House, 2002
Thorp, E., Beat the Dealer, 1962
Discovery Channel series ?Breaking Vegas? ? "Professor Blackjack" episode, aired March 8, 2005
?SDSTAFF Bricker
LINK
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