| Dutch Books A Dutch Book is a bet, or a series of bets, that appear to be fair to the gambler but are actually constructed so that the gambler will always lose. The classic casino example of this is American Roulette, since its wheel contains "00" in addition to the "0". An addition which, over the long haul, guarantees a win for the house. Why? The wheel contains the numbers 1 through 36, plus the 00 and the 0. This means that there are 38 spots. The odds pay 35 to 1. Consequently, if you placed $1 on every spot, although you would be guaranteed to win, you would lose $3 every single time. For this reason, the house advantage can range from 5.26% to 7.29%. Although there are all kinds of supposed "systems" and books out there on how to beat the Roulette wheel, trust us, it cannot be beaten in the long run. You can trust our mathematics on this. WANT TO KNOW ABOUT OTHER DUTCH BOOKS? Click Here |
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| Casino Odds, Probabilities, and the House Any discussion of casino gambling eventually breaks down into a discussion of odds and probabilities. This essential branch of mathematics is well-suited to betting analysis, and subsequently, an understanding of basic probability will help any player improve their chances of winning. So, what exactly are probabilities, and how does the house use them to their advantage? Probability measures the likelihood of how often something will occur. Therefore, since gambling games involve structures of which we know all of the possible outcomes, we can make predictions with a high level of accuracy. Take, for example, a 52 card deck. We can figure out the likelihood of picking a Spade by using the following ratio: Pr (X) = Number of ways to get X = 13 = 1 = .25 Number of all possible outcomes 52 4 From this we can further deduce that there is a 1 in 4 chance that X will occur, with Odds of 3 to 1. Basic Probability Rules 1) The probability of a single event occurring will have a value between 0 and 1, with 0 being impossible and 1 being certain. 2) The probability of an event occurring plus the probability of it not occurring will equal 1. 3) The probability of the occurrence of a series of independent events equals the product of the individual probabilities. If you want to calculate the probability of rolling snake eyes, or two ones, you would utilize the rule. The probability of rolling the first one is 1/6. The probability of rolling the second one is 1/6. So, the probability of snakes eyes is: 1/6 x 1/6=1/36 The Odds Once we have figured out the probability of an event, we can figure out the odds. Casino odds are generally construed as the 'odds against' something happening. If we take another look at our previous Spade example, we know that the probability of picking a Spade is 1/4. There is one chance in four of success, and conversely, there are three chances to fail. Therefore the true odds of this event occurring are 3 to 1. This is the same as saying 39 (number of non-spades) to 13 (number of Spades). The fraction has just been reduced. So, the odds against an event X occurring are "Y-X" to "X", in which Y is all possible outcomes and X is the desired outcome. Expected Value Expected value tells you how much you can expect to win or lose on a bet. We can derive this information from the casino's odds. This information will further give us an indication of both the fairness of the bet, and how the house conceives its edge. So, expected Value can be calculated in the following way: In this equation, the odds are represented as b:a (b is the loss, a is the payout) and the event is represented as q: EV= {(a x Pr(q) - b x Pr(-q)} The House Edge then is simply the conversion of the EV into a percentage. So, if 5 cents of every dollar bet goes to the house over the long run, the house edge is 5%. In the rare instances in which this number is negative, the advantage is tilted toward the gambler. WANT TO KNOW WHICH GAMES ARE TO THE PLAYERS ADVANTAGE? Click Here |
| Poker This is a game of skill, luck, and psychological warfare. So, it is a complex! Importantly, this is not because of its rules and probabilities, but rather due to the human variable. As such, in Poker, there are basically two ways to win- having the best hand at the end of a round of play, or by psychologically forcing everyone else to fold. And, since almost all games involve a single deck of 52 cards, our probability rules can be applied. First let's look at a ranking of poker hands: Royal Flush: A,K,Q.J,10 all in the same suit Straight Flush: Five cards of the same suit in sequence Four of a Kind: Four cards of the same rank Full House: A three of a kind coupled with a pair Flush: Any five cards of the same suit Straight: Any five cards in sequence Three of a Kind: Three cards of the same rank Two Pair: Two cards of one rank coupled with two cards of a second rank One Pair: Two cards of the same rank High card: The highest card wins, with Ace being the highest, and so on Successful Poker players must have an understanding of the odds and of the expected value (based on the pot), which can shift with each hand. If the card odds are larger than the pot odds, you should fold. If the pot odds of winning are equal to or greater than the true odds, you should see it through. As an example, if you have a 25 to 1 chance of getting a flush, you should fold. Consequently, the biggest mistake most players make is playing too many hands. This may seem counter intuitive, but you will win more by folding more. Best Flop Cards On average, the best players see the flop, or starting hands (depending on game), in one in three hands. As such, here are the best hands to play: Seven Card Stud Three of a kind: Obviously an excellent start. However you will only see this hand 1 in every 425 hands. High Pairs: 10's or better. Even if they don't improve with play, they have a good chance of winning. Small or Medium Pairs: Dangerous. It will depend on the kicker, or the third card dealt. Drawing Hands: Starting hands that need improvement. A three card open-ended straight, or flush, should be played dependent upon expected value. For this reason, probabilistically, drawing hands play better at a full table. Also, check to see if the cards you need are showing on the table. If they are, you should fold. Texas Hold'em High Pairs: 10's or better. Even if they don't improve with play, they can have a good chance of winning Small or Medium Pairs: Dangerous. In this game they are drawing hands. The odds of improving this pair to a three of a kind on the flop is 8 to 1 against. Remember, in this game five cards are shared. Want to Know More About Poker? Click Here |
| Sports Books It can be said that wherever sports goes, the money follows. Unlike casino games, however, the house does not have a built-in mathematical advantage when it comes to sports betting. When you bet on a game you are not betting against the casino. As such, sporting events are independent events that are not strictly ruled by mathematical probability theory. They are, however, based on the epistemic probabilities of a professional handicapper or bookie. So, if you know sports, and you understand handicapping, this is one of the best bets in the house. By far and large, the most popular sports books are focused on college and pro football. So, lets use football to describe the various types of bets that can be made. Here is an example bet: Bet # Team Line Total Money Line 146 Giants -4 +150 147 Vikings 42 -170 Bet Number You use this # to make your bet with the ticket writer. So, for example, if you said "I want Number 147 for $20." it would mean that you wanted to bet twenty dollars on the Vikings. Team The home team is always listed under the visiting team. Line The line is the point spread, which is the main wager of sports betting. In our example, the Giants are a four point favorite. So, if you bet on the Giants, they would have to win by more than 4 points in order to cover the spread. In other words, you would have to subtract 4 points from their final score to see if you won your bet. Conversely, if you bet on the Vikings, they must win outright or be fewer than four points short of the Giants score, in order for you to win your bet. Point spreads can often change after you have placed your bet. The listed spread at the time you place your bet is yours irregardless. Totals This is the second most common bet after the point spread. It is basically a bet on whether the combined points scored by both teams will be more or less than the posted number. Money Line This bet is an option on which team will win outright without factoring in a point spread. This bet is more common for baseball, hockey, and boxing. The Numbers The house has around a 4.5% advantage on a standard point spread bet. You must win 52.4% of your point spread bets to come out ahead. Want to Know More About Sports Betting? Click Here |
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| Craps This is undoubtedly the fastest and most thrilling game in the casino. Played with a pair of dice, the table layout is complex and the betting jargon incomprehensible. If you stick with the simplest bets, however, you can do well- as the simplest bets have the best odds! The Dice The easiest way to be at ease at the Craps table is to become comfortable with a pair of dice. There are six possible outcomes for the roll of a single die. Thus, there are 36 possible outcomes for a pair of dice: 6 x 6= 36. Since only one combination of the dice can give you a total of twelve- 6 and 6- the probability of this occurring is 1 in 36. Conversely, you have six ways in which to achieve a total of seven- 1 and 6; 2 and 5; 3 and 4; 4 and 3; 5 and 2; 6 and 1- so, this gives you a probability of 6 in 36, or 1 out of six occurrences. Everything in Craps is symmetric around the number seven. An eight is as likely to occur as a six, and a nine is as likely as a five. By pairing off the numbers in this way, we can figure out the odds quickly. As an example, the odds of rolling a ten are 33 to 3 since there are 3 ways in which to achieve the number ten. This further reduces to 11 to 1. The Play The action begins when a shooter is offered five or six dice by the stickman. She then chooses two and generates the play that all of the other players will bet on. The shooter MUST make a line bet. There are two- the pass line or the don't pass line. The payout on both of these bets is even money. The other players also place bets at this time. When the shooter rolls the dice, in order for the roll to be considered legal, it must rebound off of the opposite wall. The shooter's first roll is referred to as the come-out roll. If the shooter rolls a 7 or an 11, the pass line wins (the don't pass line losses) and the round is over. If the shooter rolls a 2, 3, or 12 (these numbers are craps), the don't pass line wins (the pass line losses) or ties if its a twelve (sometimes two), and the round is over. If the shooter rolls a 4, 5, 6, 8, 9, or 10, then the number rolled becomes the point. At this time, the dealer will move a button to the point. It will remain there as a reminder until the round is ended by either the shooter rolling a 7 or the point number again. The Bets In addition to the aforementioned pass and don't pass bets, Craps, like any good dice game, offers a multitude of good and bad odds. Let's start dissecting them by looking at the come bet. The bet allows you to make a pass line bet after the point has been made. So, this bet turns the next roll into a come-out roll, and starts a separate and new round of play for the bettor that makes this bet. This bet has a house edge of 1.41%. The don't come bet is the exact opposite of the come bet. A place bet can be made on any of the point numbers- 4,5,6,8.9,10- at any time during the round of play. If your number rolls prior to a 7 you win. If a 7 rolls prior to your number, you lose. The worst place bet is 4 or 10 to win- the house advantage is 6.67%. The best is 6 or 8 to win- the house edge here is 1.52%. The field bet is a box with a slew of numbers in it, and also the worst possible bet you can make at the Craps table. Even though you get to bet on seven out of twelve numbers that pay even money or more, it is a classic Dutch Book bet- so don't play the field! Taking Odds This is the best way to increase your chances of winning. Casinos allow you to take odds on pass, don't pass, come, and don't come wagers after the point has been established. These bets can be made at any time, once the point is established, as long as you made an original wager. Additionally, you may remove your odds bet at any time. This is not surprising since the casino pays true odds on these bets. No house advantage- no restrictions! Most casinos allow you to take double odds, and our advice to you is to take them. |
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