The rules vary slightly from one casino to another, but the expected value of several bets is only slightly negative (the most favorable bets with the most favorable rules offer a house advantage of as little as 0.18%). All bets have a negative expectation except for the “free odds” bet that the player is allowed to make after a point is established on a flat (line) bet (this bet has a long-term expected value of 0). However, the “free odds” bet cannot be made independently, so the expected value of the entire bet, including odds, is still negative. Since there is no correlation between die rolls, there is no possible long-term winning strategy. While experienced blackjack players who learn to count cards can gain a small mathematical advantage over extended playing sessions by diligent study, there is no comparable strategy for craps.

Occasionally, players win several bets in a row; such players are said to be “on a roll.” Those who increase their bets during a winning series can rapidly win substantial sums. On the other hand, money can be lost back just as quickly, as there is no statistical likelihood of a “hot streak” continuing for any given duration. To counter this, experienced players take full advantage of “free odds” — bets on which there is zero house advantage. Maximizing the size of your odds bet in relation to your line bet will minimize but never eliminate the house edge. Many casinos have limitation on how large the odds bet can be in relation to the flat bet, with single, double, and five times odds common. Some casinos offer 3-4-5 odds, referring to the maximum multiple of the line bet a player can place in odds for the points of 4 and 10, 5 and 9, and 6 and 8, respectively. During promotional periods, a casino may even offer 100x odds bets, which renders the house edge to almost nothing but dramatically increases volatility. Horseshoe Casino founder Benny Binion once quipped that if every player took the 100x odds, the house “wouldn’t be able to keep the lights on,” referring to the overhead required to run casino games.

The only casino currently in Las Vegas to offer 100x odds is the Casino Royale located next to Harrah’s on the strip. The Stratosphere offers 10x odds and most of the other casinos such as MGM and Bellagio offer 3x4x5. Some casinos such as the Riviera, Orleans and Gold Coast offer 2x odds which is considered an anathema to craps players, in equal footing with 6:5 payouts on single-deck blackjack. Most downtown casinos offer 5x (Binions) or 10x odds (Plaza and Main Street Station, with the Golden Nugget offering the unusual 6x8x10 odds), while a handful of downtown casinos offer the horrible 2x odds (Sam Boyd’s Fremont).

There are numerous middle market casinos whose income from gaming is negligible due to minimal chip size, and whose business model focuses on generating revenue primarily through the sale of alcohol. At such institutions, craps will often be rigged mildly in favor of guests, allowing the house to serve drinks to the large number of onlookers a winning table generates. Low limit Craps is also known to be used as a loss leader via the same odds to give the impression that a casino which derives its profits from gambling (almost all in Las Vegas) is full of winners and fun place to be, causing guests to play other, house favored games.

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Sportsbook at Wynn Las Vegas, during Super Bowl XLII, February 2008

A sportsbook (sometimes abbreviated as book) or a race and sports book is a place where a gambler can wager on various sports competitions, including football, basketball, baseball, hockey, soccer, horse racing and boxing. The method of betting varies with the sport and the type of game. The more prominent the event, the more wagering options that are made available.

Winning bets are paid when the event finishes, or if not finished, when played long enough to becomes official; otherwise all bets are returned. This policy can cause some confusion since there can be a difference between what the sportsbook considers official and what the sports league consider official. Customers should carefully read the sportsbook rules before placing their bets.

The betting volume at sportsbooks varies throughout the year. Bettors have more interest in certain types of sports and increase the money wagered when those sports are in season. Likewise the interest in sports varies by country since the level of interest in the various sports is not constant the world over. Some major sporting events that don’t follow a specific schedule, like boxing, can create peaks of activity for the sportsbooks.

Word origin

A sportsbook is a portmanteau, French for “jacket holder,” meaning a suitcase with two storage spaces. Sportsbook combines two meanings into one word for a sports gambling operation, in this case SPORTS and BOOK which is short for bookmaking.

Odds

In the mid 1930s, Leo Hirschfield started a company in Minneapolis, Minnesota called Athletic Publications, Inc., that published and distributed odds to bookies across the country by telephone and telegraph. He had a team of handicappers analyzing the matchups who also studied newspapers across the country. The company was a major provider of odds and prices until it finally disbanded, under fear of prosecution from the Federal Wire Act of 1961.

Today most sportsbooks get their opening prices from other sportsbooks as well as private companies like Las Vegas Sports Consultants. They adjust prices based on the bets coming in, news, injury, and weather information, and the price movement by other sportsbooks.

Nevada sportsbooks

Today there are roughly 150 licensed sportsbooks in the United States, all located in Nevada casinos. Now that many casinos share the same parent company, they offer the exact same wagering choices and odds, which is a disadvantage to the astute gambler who in the past could do more shopping for better prices.

In the 1950s the first Nevada sportsbooks, called turf clubs, opened. They were independent from the casinos, and had an informal agreement with the hotels that they would stay out of the casino business as long as the hotels stayed out of the sportsbook business. The sportsbooks had to pay a 10% tax so they charged a high vigorish to gamblers, but they still brought in a lot of business.

In 1974 the tax was lowered to 2%, (and in 1983 lowered to 0.25%), and in 1975 Lefty Rosenthal, who ran the Stardust Casino, convinced legislators to allow them in the casinos, and soon nearly all of the casinos added them. The turf clubs were no longer able to compete and eventually all closed.

In Nevada casino sportsbooks you will find:

• Betting Windows
• Numerous big screen televisions
• Places to sit and watch
• Interactive betting stations
• Odds boards, usually computerized

UK sportsbooks

Betting shops are common in the United Kingdom. Companies like Ladbrokes and William Hill have offered walk-in betting shops for decades.

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Betting odds slang is a series of words used to describe particular common fractional odds.

• Evens – Levels, Scotch
• 2/1 – Bottle
• 3/1 – Carpet, Gimmel
• 4/1 – Rouf
• 5/1 – Hand
• 5/2 – Face
• 6/1 – X’s
• 7/1 – Nevs
• 8/1 – T.H.
• 9/1 – Enin
• 10/1 – Cockle, Net
• 11/10 – Tips
• 33/1 – Double Carpet
• 100/30 – Burlington Bertie

Some outs for a hand require drawing an out on both the turn and the river—making two consecutive outs is called a runner-runner. Examples would be needing two cards to make a straight, flush, or three or four of a kind. Runner-runner outs can either draw from a common set of outs or from disjoint sets of outs. Two disjoint outs can either be conditional or independent events.

Common outs

Drawing to a flush is an example of drawing from a common set of outs. Both the turn and river need to be the same suit, so both outs are coming from a common set of outs—the set of remaining cards of the desired suit. After the flop, if x is the number of common outs, the probability P of drawing runner-runner outs is

P = (x/47) x ((x – 1)/46).

Since a flush would have 10 outs, the probability of a runner-runner flush draw is (10/47) x (9/46) = (90/2162) ~ 0.04163. Other examples of runner-runner draws from a common set of outs are drawing to three or four of a kind. When counting outs, it is convenient to convert runner-runner outs to “normal” outs. A runner-runner flush draw is about the equivalent of one “normal” out.

The following table shows the probability and odds of making a runner-runner from a common set of outs and the equivalent normal outs.

.00093080 : 1.02.0027859 : 1.07.0055679 : 1.13.0092507 : 1.22.013881.1 : 1.33.019430.5 : 1.46.025907.6 : 1.61.033309.0 : 1 .78 0 .04163 3.0 : 1 .98

Likely drawing to	Common outs	Probability	Odds	Equivalent outs
Four of a kind (with pair) Inside-only straight flush
Three of a kind (with no pair)
Two pair or three of a kind (with no pair)
Flush

, J} or {

}. The number of outs for the second card is conditional on the first card—a Q or

, respectively) for the second card, while a J or

(8 cards) for the first card leaves 8 outs ({Q,

} or {J,

P = ((8/47) x (4/46)) + ((8/47) x (8/46)) = 96/2162 ~ 0.0444.

The following table shows the probability and odds of making a runner-runner from a disjoint set of outs for common situations and the equivalent normal outs.

.044401.5 : 1 .04 .029602.8 : 1.70.014806.6 : 1 .35.0027859 : 1.07.0018540 : 1.04

Drawing to	Probability	Odds	Equivalent outs
Outside straight
Inside+outside straight
Inside-only straight
Outside straight flush
Inside+outside straight flush

The preceding table assumes the following definitions.

Outside straight and straight flush

Drawing to a sequence of three cards of consecutive rank from

-4-5 to 0-J-Q where two cards can be added to either end of the sequence to make a straight or straight flush.

Inside+outside straight and straight flush

Drawing to a straight or straight flush where one required rank can be combined with one of two other ranks to make the hand. This includes sequences like -7-8 which requires a

plus either a or as well as the sequences J-Q-K, which requires a 0 plus either a or A, and

-3-4 which requires a plus either an A or

.

Inside-only straight and straight flush

Drawing to a straight or straight flush where there are only two ranks that make the hand. This includes hands such as -7-9 which requires a

and an as well as A-2-3 which requires a and a .

Compound outs

The strongest runner-runner probabilities lie with hands that are drawing to multiple hands with different runner-runner combinations. These include hands that can make a straight, flush or straight flush, as well as four of a kind or a full house. Calculating these probabilities requires adding the compound probabilities for the various outs, taking care to account for any shared hands. For example, if P_s is the probability of a runner-runner straight, P_f is the probability of a runner-runner flush, and P_sf is the probability of a runner-runner straight flush, then the compound probability P of getting one of these hands is

P = P_s + P_f − P_sf.

The probability of the straight flush is subtracted from the total because it is already included in both the probability of a straight and the probability of a flush, so it has been added twice and must therefore be subtracted from the compound outs of a straight or flush.

The following table gives the compound probability and odds of making a runner-runner for common situations and the equivalent normal outs.

.083261.0 : 1.98.069383.4 : 1.65.055507.0 : 1.30

Drawing to	Probability	Odds	Equivalent outs
Flush, outside straight or straight flush
Flush, inside+outside straight or straight flush
Flush, inside-only straight or straight flush

Some hands have even more runner-runner chances to improve. For example, holding the hand J♠ Q♠ after a flop of 0♠ J♥ 7♦ there are several runner-runner hands to make at least a straight. The hand can get two cards from the common outs of {J, Q} (5 cards) to make a full house or four of a kind, can get a J (2 cards) plus either a

or 0 (6 cards) to make a full house from these independent disjoint outs, and is drawing to the compound outs of a flush, outside straight or straight flush. The hand can also make {

,

} or {0, 0} (each drawing from 3 common outs) to make a full house, although this will make four of a kind for anyone holding the remaining 7 or 10 or a bigger full house for anyone holding an overpair. Working from the probabilities from the previous tables and equations, the probability P of making one of these runner-runner hands is a compound probability

P = 0.08326 + 0.00925 + (2×6)/1081 + (0.00278 x 2) ~ 0.1092

and odds of 8.16 : 1 for the equivalent of 2.59 normal outs. Almost all of these runner-runners give a winning hand against an opponent who had flopped a straight holding , ^[3], but only some give a winning hand against A♠ 2♠ (this hand makes bigger flushes when a flush is hit) or against K♣ Q♦ (this hand makes bigger straights when a straight is hit with 9). When counting outs, it is necessary to adjust for which outs are likely to give a winning hand—this is where the skill in poker becomes more important than being able to calculate the probabilities.

Notes

1. ^{^} In the example, if the opponent is holding either 8♥ 9♥ or 8♦ 9♦, then the opponent wins with a flush if the player makes a straight using two hearts or two diamonds, respectively. If the opponent is holding 8♦ 9♦, then the opponent wins with a straight flush if the player makes a full house with 10♦ J♦.

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The value of a starting hand can change dramatically after the flop. Regardless of initial strength, any hand can flop the nuts—for example, if the flop comes with three 2s, any hand holding the fourth 2 has the nuts. Conversely, the flop can undermine the perceived strength of any hand—A♣ A♥ would not be happy to see

♠ 9♠ 10♠ on the flop because of the straight and flush possibilities.

There are

(50/3) = 19,600

possible flops for any given starting hand. By the turn the total number of combinations has increased to

(50/4) = 230,300

and on the river there are

(50/5) = 2,118,760

possible boards to go with the hand.

The following are some general probabilities about what can occur on the board. These assume a “random” starting hand for the player.

Board consisting of	Making on flop		Making by turn		Making by river
	Prob.	Odds	Prob.	Odds	Prob.	Odds
Three or more of same suit	0.05177	18.3 : 1	0.13522	6.40 : 1	0.23589	3.24 : 1
Four or more of same suit			0.01056	93.7 : 1	0.03394	28.5 : 1
Rainbow flop (all different suits)	0.39765	1.51 : 1	0.10550	8.48 : 1
Three cards of consecutive rank (but not four consecutive)	0.03475	27.8 : 1	0.11820	7.46 : 1	0.25068	2.99 : 1
Four cards to a straight (but not five)			0.03877	24.8 : 1	0.18991	4.27 : 1
Three or more cards of consecutive rank and same suit	0.00217	459 : 1	0.00869	114 : 1	0.02172	45.0 : 1
Three of a kind (but not a full house or four of a kind)	0.00235	424 : 1	0.00935	106 : 1	0.02128	46 : 1
A pair (but not two pair or three or four of a kind)	0.16941	4.90 : 1	0.30417	2.29 : 1	0.42450	1.36 : 1
Two pair (but not a full house)			0.01037	95.4 : 1	0.04716	20.2 : 1

An interesting fact to note from the table above is that more than 60% of the flops will have at least two of the same suit—you’re likely to either be drawing to a flush or worried about one.

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Many lotteries have a “powerball” (or “bonus ball”). If the powerball is drawn from a different pool of numbers from the main lottery, then simply multiply the odds by the number of powerballs. For example, in the 6 from 49 lottery we have been discussing in this article, if there were 10 powerball numbers, then the odds of getting a score of 3 and the powerball would be 1 in 56.66 x 10, or 566.6 (the probability would, of course, be divided by 10, to give an exact value of 8815/4994220).

Where more than 1 powerball is drawn from a separate pool of balls to the main lottery (e.g. the Euromillions game), the odds of the different possible powerball matching scores should be calculated using the method shown in the “other scores” section above (in other words, treat the powerballs like a mini-lottery in their own right), and then multiplied by the odds of achieving the required main-lottery score.

If the powerball is drawn from the same pool of numbers as the main lottery, then, for a given target score, one must calculate the number of winning combinations which includes the powerball. For games based on the Canadian lottery (e.g. Lotto, the UK lottery), after the 6 main balls are drawn, an extra ball is drawn from the same pool of balls, and this becomes the powerball (or “bonus ball”), and there is an extra prize for matching 5 balls + the bonus ball. As described in the “other scores” section above, the number of ways one can obtain a score of 5 from a single ticket is c(6,5)*c(43,1), or 258. Since the number of remaining balls is 43, and your ticket has 1 unmatched number remaining, 1/43 of these 258 combinations will match the next ball drawn (the powerball) – so there are 258/43 = 6 ways of achieving it. Therefore, the odds of getting a score of 5 + powerball are c(49,6)/6 = 1 in 2,330,636.

Of the 258 combinations that match 5 of the main 6 balls, in 42/43 of them the remaining number will not match the powerball, giving odds of c(49,6)/(258*(42/43)) = 166474/3 (approx 55491.33) for obtaining a score of 5 without matching the powerball.

Using the same principle, to calculate the odds of getting a score of 2 + powerball, calculate the number of ways to get a score of 2 as c(6,2)*c(43,4) = 1,851,150 then multiply this by the probability of one of the remaining four numbers matching the bonus ball – which is 4/43. 1,851,150*(4/43) = 172,200, so the probability of obtaining the score of 2 + bonus ball is 172,200/c(49,6) = 1025/83237. This gives approximate decimal odds of 81.2.

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The fundamental bet in craps is the pass line bet, in which one bets that the dice will pass (that is, roll the point number before rolling a 7). A pass line bet is also won if the come-out roll is a 7 or 11. The following discussion assumes that the shooter, as is usually the case, is betting on the pass line.

If a 4,5,6,8,9, or 10 is thrown on the come-out roll (i.e., if a point is set), most casinos allow pass line bettors to take odds by placing from one to five times (and at some casinos, up to 100 times) the pass line bet behind the line. This additional bet wins if the point is rolled again before a 7 is rolled (the point is made) and pays at the true odds, 2-to-1 if 4 or 10 is the point, 3-to-2 if 5 or 9 is the point, and 6-to-5 if 6 or 8 is the point. While the house has a small (1.4%) advantage on pass line bets, the house has no advantage at all on odds bets. Therefore, taking the maximum odds (which vary by casino) can lower the house percentage for any given bet down to as low as 0.5%.

Odds bets in craps are one of the few bets offered at a casino that are completely free of any house advantage. Another such bet is the “double-up” option offered to the player in some forms of video poker after winning a hand.

Let’s see why that is. There are 36 possible permutations (ways to roll a pair of 6-sided dice):

          1-1              = 1 way to make a 2
        1-2 2-1            = 2 ways to make a 3
      1-3 2-2 3-1          = 3 ways to make a 4, true odds pays 2-1
    1-4 2-3 3-2 4-1        = 4 ways to make a 5, true odds pays 3-2
  1-5 2-4 3-3 4-2 5-1      = 5 ways to make a 6, true odds pays 6-5
1-6 2-5 3-4 4-3 5-2 6-1    = 6 ways to make a 7
  2-6 3-5 4-4 5-3 6-2      = 5 ways to make an 8, true odds pays 6-5
    3-6 4-5 5-4 6-3        = 4 ways to make a 9, true odds pays 3-2
      4-6 5-5 6-4          = 3 ways to make a 10, true odds pays 2-1
        5-6 6-5            = 2 ways to make an 11
          6-6              = 1 way to make a 12

There are a total of 36 possible combinations. So on the come-out roll there are 8 ways to win, 4 ways to lose and (36-12=) 24 ways to start a point.

The odds of making the point are the ratio of the number of ways to make a 7 to the number of ways to make the point. For example, there are five ways to make a 6 or 8, so the odds of making a point of 6 or 8 are 6-5. Therefore an odds bet of $5 on 6 or 8 pays out $6.

Many experienced craps players only make pass line and odds bets since the odds are much more favorable to the player than any other bets in craps, and in fact most casino games. The pass line and odds bet is one of the best wagers you can make in gambling, and a lot of the excitement and fortunes of craps can be experienced with this simple bet.

The rules for the come wagers are the same as for the pass line except that they can only be made after the come-out roll. Effectively, they represent starting a new game using the same stream of numbers being generated by the existing (pass line) game.

Because of the come bet, if the shooter makes their point, a player can find themselves in the situation where they have a come bet with odds on it, and yet be rooting for the shooter to roll a 7 on their next come-out roll. Because of this, it is usual that odds bets on come wagers are presumed to be not working. That means that if the shooter rolls a 7 on the come-out roll, any players with active come bets lose their initial wager but will have their odds money returned to them, unless they tell the dealer that they want their odds working. Conversely, if the shooter rolls a number that matches an active come bet, the original bet is paid off at even money and the odds money is returned to the player (unless they told the dealer that they wanted their odds working, in which case they are paid at the true odds).

There is also a don’t come box in which one can place bets that the dice will not pass on the next sequence starting with the immediate roll as a virtual come-out roll; even the shooter may bet that he or she will miss out. Don’t pass and don’t come bets are basically the opposite of pass and come bets; the player is betting that a 7 will be rolled before the point. On the come-out roll a 7 or an 11 is a loss, whereas a 2, 3, or 12 is a win. Casino craps layouts bar either 2 or 12 on the don’t pass and don’t come bets. This means that if 2 is barred and the shooter rolls a 2 on the come-out roll, the wager is a stand off and the player’s money is returned.

When betting against the shooter, the bettor must put up the long side of the bet. Thus a don’t pass bettor who bets $10 when the point is a 4 could place an odds bet of $20 behind the line. If the shooter rolls a 7 before achieving their point, the bettor would receive $10 for the don’t pass bet plus $10 for their odds bet. Even though the house advantage on the don’t pass and don’t come bets are almost identical to the pass line and come bets, for most players the disadvantage of putting up the long side of the bet makes the don’t pass line less desirable. Additionally, many craps players consider don’t pass and don’t come bets to be in poor taste, or even “taboo”.

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• There are 12,994,800 scoring hands in Cribbage (52c5 x 5, 5 cards then any of those 5 as the turn up card).
• Approximately 8.5% of randomly drawn four-card hands will score 0 (not including pegging).
• The highest score is 29 (555J in hand with the turn-up 5 of the same suit as the Jack).
• The second highest score is 28 (any 10/J/Q/K+5555 in hand and turn-up excepting the above 29 hand) and the third highest is 24 (A7777, 33339, 36666, 44447, 44556, 44566, 45566, 67788, 77889).
• All scores between 0 and 29 are possible, with the exception of 19, 25, 26 and 27. Players will sometimes refer to a 0-scoring hand as having a score of 19, which can confuse new players.
• The odds of getting a 28 hand in a 2 player game are 1 in 15,028.
• The odds of getting a perfect 29 hand in a 2 player game are 1 in 216,580.
• The odds of getting a perfect 29 hand in a 3 or 4 player game are 1 in 649,740.
• The dealer will always peg at least one point in 2 player, 6 card cribbage (unless opponent pegs out before all the cards are played).
• The most points that can be pegged by playing one card are 15. This is accomplished by completing a double pair royale, while making the count 15 on the last card (12 for Double Pair Royale, 2 for 15, 1 for last card). Although this is rare, players declare it as “15 for 15.”
• The highest score as a dealer is 53. The turn-up must be a 5, and one hand must have J555 while the other has 4466. The first being a 29 (With the right Jack) and the second being 24.

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One must calculate the total number of lottery combinations (c(49,6) = 13,983,816, as explained in the section above), and divide it by the number of those combinations which give the desired result – which equates to the number of ways one can select the winning numbers multiplied by the number of ways one can select the losing numbers.

For a score of n (e.g. if 3 of your numbers match the 6 balls drawn, then n=3), there are c(6,n) ways of selecting the n winning numbers from the 6 drawn balls. For one’s losing numbers, there are c(43,6 – n) ways to select them from the 43 losing lottery numbers. The total number of combinations giving that result is, as stated above, the first number multiplied by the second. The expression is therefore c(49,6)/(c(6,n)*c(43,6-n)). This gives the following results (remember that odds are the reciprocal of probability):

References

• This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.

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In probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1 − p), where p is the probability of the event or proposition. The logarithm of the odds is the logit of the probability.Odds have long been the standard way of representing probability used by bookmakers, though the method of presenting odds varies by location.

Taking an event with a 1 in 5 probability of occurring (i.e. 0.2 or 20%), then the odds are 0.2 / (1 − 0.2) = 0.2 / 0.8 =

.25. If you bet 1 at fair odds and the event occurred, you would receive back 4 plus your original 1 stake. This would be presented in fractional odds of 4 to 1 against (written as 4 : 1 or 4/1), in decimal odds as 5.0 to include the returned stake, in craps payout as 5 for 1, and in moneyline odds as +400 representing the gain from a 100 stake.

By contrast, for an event with a 4 in 5 probability of occurring (i.e. 0.8 or 80%), then the odds are 0.8 / (1 − 0.8) = . If you bet 4 at fair odds and the event occurred, you would receive back 1 plus your original 4 stake. This would be presented in fractional odds of 4 to 1 on (written as 1 : 4 or 1/4), in decimal odds as 1.25 to include the returned stake, in craps as 5 for 4, and in moneyline odds as −400 representing the stake necessary to gain 100.

The odds are a ratio of probabilities; an odds ratio is a ratio of odds, that is, a ratio of ratios of probabilities. Odds-ratios are often used in analysis of clinical trials. While they have useful mathematical properties, they can produce counter-intuitive results: in the example above an 80% probability is four times the chance of a 20% probability but the odds are 16 times higher.

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Pocket Aces refers to a starting poker hand that contains two Aces. The most common context is a game of Texas Hold’em.Other names for Ace-Ace include American Airlines, bullets, and rockets.

In a conventional game of hold’em, Ace-Ace is the best possible starting hand. It is the best hand before the flop, is the hand most likely to form the best hand after the flop, and in the long run shows the most earning potential of any starting hand. The second-best starting hand is King-King.

It is also possible to have pocket aces in a game of seven-card stud, if the two hole cards are aces.

The odds against being dealt pocket aces are 220:1.

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In gambling a Dutch book or lock is a set of odds and bets which guarantees a profit, no matter what the outcome of the gamble. It is associated with probabilities implied by the odds not being coherent.In economics a Dutch book usually refers to a sequence of trades that would leave one party strictly worse off and another strictly better off. Typical assumptions in consumer choice theory rule out the possibility that anyone can be Dutch-booked.

Gambling

In one example, a bookmaker has offered odds and attracted bets that make the result irrelevant; in this case the implied probabilities will add up to a number greater than 1.

In this case, whichever horse wins, the bookmaker will pay out 200 (including returning the winning stake) and so make a profit of 10.

If for some reason Horse 4 was withdrawn and the bookmaker was foolish enough not to adjust the other odds, the implied probabilities would add up to 0.95 and a gambler could lock in a profit of 10, by betting 100, 50 and 40 on the remaining three horses respectively.

Other forms of Dutch books can exist when incoherent odds are offered on exotic bets such as forecasting the order in which horses will finish. With competitive fixed-odds gambling being offered electronically, gamblers can sometimes create a Dutch book by selecting the best odds from different bookmakers, in effect by undertaking an arbitrage operation. The bookmakers should react by adjusting the offered odds in the light of demand, so as to remove the potential profit.

In Bayesian probability, Frank P. Ramsey and Bruno de Finetti required personal degrees of belief to be coherent so that a Dutch book could not be made against them, whichever way bets were made. Necessary and sufficient conditions for this are that their degrees of belief satisfy the axioms of probability.

Economics

In economics the classic example of a situation in which a consumer X can be Dutch-booked is if he or she has intransitive preferences. Suppose that for this consumer, A is preferred to B, B is preferred to C, and C is preferred to A. Then suppose that someone else in the population, Y, has one of these goods. Without loss of generality, suppose Y has good A. Then Y can first sell A to X for B + ε; then sell B to X for C + ε; then sell C to X for A + ε, where ε is some small amount of the numeraire. After this sequence of trades, X has given 3·ε to Y for nothing in return. Y will have exploited an arbitrage opportunity by taking advantage of X’s intransitive preferences.

Economists usually argue that people with preferences like X’s will have all their wealth taken from them in the market. If this is the case, we won’t observe preferences with intransitivities or other features that allow people to be Dutch-booked. However, if people are somewhat sophisticated about their intransitivities and/or if competition by arbitrageurs drives epsilon to zero, non-”standard” preferences may still be observable.

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Online casinos, also known as virtual casinos or internet casinos, are online versions of traditional (“brick and mortar”) casinos. Online casinos enable gamblers to play and wager on casino games through the Internet.Online casinos generally offer odds and payback percentages that are comparable to land-based casinos. Some online casinos claim higher payback percentages for slot machine games, and some publish payout percentage audits on their websites. Assuming that the online casino is using an appropriately programmed random number generator, table games like blackjack have an established house edge. The payout percentage for these games are established by the rules of the game.

Reliability and trust issues are commonplace and often questioned. Many online casinos lease or purchase their software from well-known companies like Wager Works, Microgaming, Realtime Gaming, Playtech and Cryptologic in an attempt to “piggyback” their reputation on the software manufacturer’s credibility. These software companies either use or claim to use random number generators to ensure that the numbers, cards or dice appear randomly.

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Video: Poker Room Review and Online Casinos to Avoid

Equipment

The primary piece of equipment used to play modern Russian roulette is a toy gun that has a 1/6 probability of activating when the trigger is pulled. The gun may be a dedicated device, or it could be a video game light gun connected to a computer programmed for Russian roulette simulation.

Play

All players put money in the pot. Each player in turn points the gun at their head and pulls the trigger. If the gun activates, the person holding the gun is eliminated from the game. The last player remaining wins the pot.

Odds

Assuming a six-shot revolver and that each hole is equally likely to be under the hammer, the probability of losing in the first round is 1 in 6 and the probability increases with each trigger pull. On the 6th trigger pull the probability of losing is 1 in 1 (100%).

If the cylinder is spun after every shot, the odds of losing remain the same, 1/6 each time the trigger is pulled; in this case, in a two-person to-the-death game, it is better to go second (if the first person loses, the second person wins, even if he would have lost on his next move — this is equivalent to the house advantage in blackjack, where the house wins if the player busts, even if the dealer himself also is going to bust).

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Video: Russian Roulette

Betting odds slang is a series of words used to describe particular common fractional odds.

• Evens – Levels, Scotch
• 2/1 – Bottle
• 3/1 – Carpet, Gimmel
• 4/1 – Rouf
• 5/1 – Hand
• 5/2 – Face
• 6/1 – X’s
• 7/1 – Nevs
• 8/1 – T.H.
• 9/1 – Enin
• 10/1 – Cockle, Net
• 11/10 – Tips
• 33/1 – Double Carpet
• 100/30 – Burlington Bertie

An Asian Handicap is a sports betting term used to describe spread betting in football (soccer). Described as Asian because of its Eastern origins, the phrase has little else to do with the region. This form of soccer betting has gained increased popularity over the last few years and is now offered by a variety of mainstream bookmakers.Football bets can be made using a few different formats. From a gambler’s standpoint, Asian handicap odds provide many benefits. For starters, the Asian handicap system eliminates any chance for loss due to a tie, which increases the gamblers chances of success. Secondly, bookmakers typically charge less Vigorish than with other bets.

Description

Soccer is one of the few sports in the world where a tie is a fairly common outcome. With traditional fixed odds, ties are treated as an additional outcome to the game. In other words, bettors lose when they place a wager on either team to win and the game ties. With Asian Handicaps, however, the chance for a tie is eliminated by use of a handicap that forces a winner. This creates a situation where each team has a 50-50 chance of winning; similar to the odds for a basketball or baseball game where a tie is impossible.

This system works in a straight-forward manner. The bookmakers’s goal is to create a handicap or “line” that will make the chance of either team winning (considering the handicap) as close to 50% as possible. Since the odds are as close to 50% as possible, bookmakers offer payouts close to even money, or 1.90 to 2.00. Asian Handicaps start at a quarter goal and can go as high as 2.5 or 3 goals in matches with a huge disparity in ability. What makes Asian Handicaps most interesting is the use of quarter goals to get the “line” as close as possible. Taken in conjunction with the posted total for the game, the handicap essentially predicts the game’s final score. Take a look at this example:

Example

Match: Everton vs. Newcastle United

Handicap: 0 : 1 1/2

Explained: This handicap states that Everton is “giving” Newcastle one and one half goal for the match.

This means is that Newcastle is starting the game with a 1.5-0 lead. If the final score of the game is 2-1, then a bet on Newcastle wins the with the final score (considering handicap) as 2-2.5.

Quarter Handicaps

Subsequently, many matches are handicapped in 1/2 and 1/4 intervals; both of which eliminate the possibility of a tie since no one can score a half-goal. Quarter (1/4) handicaps split the bet between the two next closest 1/4 intervals. For instance, a $1000 bet with a handicap of 1 3/4 is the same as betting $500 at 1 1/2 and $500 at 2. With 1/4 handicap bets, you can win and tie (win 1/2 of wager) or lose and tie (lose 1/2 wager).

Whole Handicaps and Ties

Handicaps that are whole numbers still allow for the possibility of a tie. Sportsbooks will refund both bets in the event of a game tied by the handicap.

Reference & Payout Charts

• Asian Handicap Betting Article from DragonBets.com
• See their Asian Handicap article for quarter handicap payout charts.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

Video: How To Score Goal in Soccer Match

Lottery jackpot records are a matter of some interest to both participants and observers of this form of gambling.It is often said that the annual Christmas lottery in Spain, dubbed El Gordo (The Fat One), is the largest in the world. In 2003 its prize fund reached (converting euros to approximate dollars) $2,200,000,000 with a first prize of $470,000,000 and second prize of $235,000,000. However, every number entered in this lottery is on 170 tickets which are often sold in fractions (usually tenths). Thus, the El Gordo prize is usually split, and is not comparable to the winner-take-all style drawings popular elsewhere.

U.S.A. lotteries

The largest draw prize in a lottery was US $365 million Powerball on February 18, 2006 won by a group of eight meat processing workers in Nebraska. The 2nd largest draw prize in a lottery was the US $363 million Big Game jackpot of May 9, 2000, split between two winners. This game was relaunched as Mega Millions, with odds lengthened to 135 million to one, in May 2002, and the odds further lengthened to 175 million to one in June 2005, but the jackpot record has not been broken. The largest single Big Game or Mega Millions winner has been Geraldine Williams of Lowell, Massachusetts, USA, with the $294 million annuity-value jackpot of the July 2, 2004 drawing. The Mega Millions jackpot of November 15, 2005, divided by seven employees of a medical center who shared one winning ticket, had an annuity value of $315 million, but the lump sum value was a record $187.1 million.

The largest single winner of any lottery prize was Andrew J. Whittaker Jr. of West Virginia, who won $314.9 million in the Powerball drawing of December 25, 2002. Opting as most large prize winners in the U.S. do for the lump sum, his after-tax prize has been variously reported as $111,681,349 and $113,386,407.77. Because of different tax rates, the $168 million lump sum opted for by Mega Millions winner Geraldine Williams (see previous paragraph) was reported as $117.6 million after taxes. Harold and Helen Lerner of New Jersey also claimed a higher after-tax lump sum than Whittaker in the Mega Millions of September 16, 2005 as New Jersey has no state tax on lottery prizes. The October 19, 2005 Powerball drawing won by nine members of the West and Chaney families of Medford, Oregon was for a larger annuity ($340 million) but a smaller lump sum than Whittaker’s.

State lotteries in the United States

The record annuity-value prizes in the largest state lottery games in the United States have been:

California: $193 million to three tickets February 16, 2002; to single winner, $141 million to Alcario Castellano on June 23, 2001
New York: $130 million in special Millennium Millions game November 4, 2000, shared by two winners; to single winner, $100 million to Johnnie Ely in Millennium Millions of December 31st 1999; in regular New York Lotto, $72 million to four tickets May 31, 1997; single-ticket record for New York Lotto is $58 million
Pennsylvania: $115.6 million shared among fourteen winning tickets in April 1989, in Super 7 game later discontinued after a scandal; in subsequent Super 6 game $86,192,222.20 in December 1999, claimed by Shemonski family in March 2000
Florida: $106.5 million to six tickets in September 1990
Texas: estimated $145 million June 19, 2004
Ohio: $75 million April 13, 2002.

The ratio between lump sum and annuity value varies over time with interest rates and possible alterations in the length of the period for which payments are made.

European lotteries

Unlike in the United States, where lottery wins are taxed, and the full winnings are paid by an annuity over a period of many years or a reduced lump-sum amount is offered, European lotteries are generally tax-free and the winning jackpot is paid out immediately in one lump sum.

EuroMillions is a pan-European lottery, with odds of 1 in 76,275,360. In July 2005, Irish woman, Dolores McNamara won a tax-free €115,436,126 ($139m) jackpot. On February 3, 2006, EuroMillions had a prize of €183 million ($219m), which was shared between three winning tickets, two in France and one in Portugal, each winning €61,191,026.

The largest win on the British National Lottery, established in 1994, is currently £22,590,829 (US$40 million) won on 10 June 1995 by Paul Maddison and Mark Gardiner. The oldest person made a sterling millionaire by the lottery was Gracie Vera Coulson, who was 87 when she won £1,090,387 in December 1999. Two 16 year olds and two 17 year olds have also won between £1 and £2 million.

The Irish National Lottery, established in 1987 and replacing the Irish Sweepstakes which had run since 1930, has a guaranteed jackpot of €1,500,000 for each of its twice-weekly draws. The largest ever win was €7,892,753 won in May 1997 by an anonymous winner from Cork.

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Betting strategies or betting systems are approaches to gambling intended to increase the odds of winning.

Independent Events

The following betting strategies have been recorded as being applied to games which operate on independent events. For such games, the odds of a particular outcome are identical for every bet played. No such strategy can beat the house edge (if any) in the long run, and all of them trade off many small wins for a big loss or vice versa.

• Martingale – doubling bet after each loss until a win is achieved (or fails when the amount of the bet becomes excessive).
• Kelly criterion;

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Jueteng (pronounced wet-teng) is an illegal numbers game played in the Philippines. Jueteng came from China and it means flower (jue) and bet (teng). Although illegal, it is a widely popular game with participation that crosses most, if not all social and economic boundaries, played by rich and poor alike. With long odds and no limits on minimum or maximum bets, the lure of quick riches through a lucrative payout is by far its strongest appeal.The game relies heavily on having a large number of wagers, and there is no limit to the amount of the bet(s). Usually the gambler selects two numbers from 1 through 37, and the winning number is determined by selecting a pair of numbers from a set of 37 numbered balls. Thus the theoretical odds of winning on any one play are one in ₃₇C₂, or 1/666. This is unlike the numbers games in the U.S. during the early part of the 20th century, where the last digit of the winning pay out or the number of the winning horse for three consecutive races determined the winning combination.

Although much has been done to curtail or eradicate this form of unregulated gambling by government and community leaders, it appears that such efforts have fallen by the wayside due to its vast popularity, and the poverty which cripples the country.

Scandals

Jueteng was brought to notoriety in 2000 during the impeachment proceedings of deposed Philippine President Joseph Estrada, who was accused of receiving illegal payoffs from gambling profits. Another political scandal erupted in June 2005 involving allegations that relatives of Gloria Macapagal-Arroyo received payouts from jueteng operators.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.