bet line
BET theory is a well-known rule for the physical adsorption of gas molecules on a solid surface, that is basis for an important analysis technique for the measurement of the specific surface area of a material. In 1938, Stephen Brunauer, Paul Hugh Emmett, and Edward Teller published an article about the BET theory in a journal[1] for the first time; “BET” consists of the first initials of their family names.
The concept of the theory is an extension of the Langmuir theory, which is a theory for monolayer molecular adsorption, to multilayer adsorption with the following hypotheses: (a) gas molecules physically adsorb on a solid in layers infinitely; (b) there is no interaction between each adsorption layer; and (c) the Langmuir theory can be applied to each layer. The resulting BET equation is expressed by (1):
P and P0 are the equilibrium and the saturation pressure of adsorbates at the temperature of adsorption, v is the adsorbed gas quantity (for example, in volume units), and vm is the monolayer adsorbed gas quantity. c is the BET constant, which is expressed by (2):
E1 is the heat of adsorption for the first layer, and EL is that for the second and higher layers and is equal to the heat of liquefaction.
BET plotEquation (1) is an adsorption isotherm and can be plotted as a straight line with 1 / v[(P0 / P) − 1] on the y-axis and φ = P / P0 on the x-axis according to experimental results. This plot is called a BET plot. The linear relationship of this equation is maintained only in the range of 0.05 < P / P0 < 0.35. The value of the slope A and the y-intercept I of the line are used to calculate the monolayer adsorbed gas quantity vm and the BET constant c. The following equations can be used:
The BET method is widely used in surface science for the calculation of surface areas of solids by physical adsorption of gas molecules. A total surface area Stotal and a specific surface area S are evaluated by the following equations:
Aside from simple wagers--betting a friend that one's favorite baseball team will win its division, for instance, or buying a football "square" for the Super Bowl--sports betting is commonly done through a bookmaker. Legal sports bookmakers exist throughout the world (perhaps most notably in Las Vegas). In areas where sports betting is illegal, bettors usually make their sports wagers with illicit bookmakers (known colloquially as "bookies") and on the Internet, where thousands of online bookmakers accept wagers on sporting events around the world. (In the United States, the legality of Internet wagering is ambiguous, due to the fact that online bookmakers generally operate outside of the U.S. Some online bookmakers do not accept wagers from the U.S. due to these unresolved legal questions.) The bookmaker earns a commission or "vigorish" by regarding the money at risk as less than the size of the bet placed. A common line is a $110 bet on a fair coin which pays $210 to win and $0 to lose. On this line, it costs $220 to bet both sides of the same coin simultaneously, but the combined bet always pays $210. The $10 loss constitutes the vig. There are opposing positions on whether the winner or loser can be construed as paying the vig, but this debate is not especially meaningful. If you view $110 to win $210 on a fair coin as $100 at risk, then it will appear as if the loser pays the vig; if you view the same line as $110 at risk, then it will appear as if the winner pays the vig. It happens that standard practice among bookies is to adjust odds so the amount at risk remains constant from the winning side of the proposition, hence the common perception that the loser pays the vig. Vigs expressed as percentages suffer from the same perceptual bias. On the line as given in this example, for a fair coin, the bookie has an expectation of making $5 for each $110 bet placed, which is often divided out and expressed as 4.5% Odds on teams or adversaries are quoted in terms of the favorite (the team that is expected to win, thus requiring a riskier wager) and the underdog.
Bookmakers generally offer two types of wagers on the winner of a sporting event: a straight-up or money line bet, or a point spread wager. Moneylines and straight-up prices are used to set odds on sports such as association football, baseball and hockey (the scoring nature of which renders point spreads impractical) as well as individual vs. individual matches, like boxing. For these sports, bookmakers in Europe and Asia generally use straight-up odds, which are quoted based on a payout for a single bet unit; for example, a 2-1 favorite would be listed at a price of 1.50, whereas an underdog returning twice the amount wagered would be listed at a price of 3.00.
American bookmakers generally use moneylines, which are quoted in terms of the amount required to win $100 on a favorite, or the amount paid for a $100 bet on an underdog. The amount "won" in a bet is the net amount over and above the initial bet. If a person wins $200 on a bet of $100, the bookmaker actually pays the winner $300 (i.e. $200 plus the initial bet of $100).
For example, a baseball game between the St. Louis Cardinals and Chicago Cubs might have a moneyline on St. Louis (the favorite) at -200 and Chicago (the underdog) at +180. A bettor looking to take St. Louis must risk $200 for every $100 he wishes to win over and above the initial $200 bet. A person wagering on Chicago will win $180 for every $100 he bets.
The +180 moneyline on Chicago includes a 20 cent "dime line". Bookmakers generally use a "dime line" with moneylines to calculate the vigorish they receive on losing wagers. Without the 20 cent dimeline in the example above, the Chicago moneyline would be +200.
For favorites of -120 to -150, the difference between the favorite and underdog is 10 cents; i.e., the underdog to a -120 favorite is priced at +110. The discrepancy between prices rises for favorites of -160 or higher.
Unlike point spread bets, a moneyline wager requires only that the team wagered upon win the match. In sports such as baseball, where certain teams can be heavy favorites against weaker opponents (sometimes as much as -350 or higher), the moneyline system requires that a hefty sum be risked on the favorite, while enticing underdog players with a higher payout.
In sports such as basketball or American football, betting on the point spread is more popular, although money line odds are usually offered as well. A point spread wager typically requires a bettor to risk $110 to win $100, the extra $10 being the bookmaker's vigorish if the wager loses. However, bettors backing the favorite collect only if their team wins by more than a specific victory margin, which is set at the time of the wager. This is called "covering the spread". Similarly, underdog bettors can collect even when their team loses, as long as they win against the point spread by losing by fewer points than were quoted by the bookmaker. For example, suppose that a college football game between Oklahoma and Kansas had Oklahoma as a 27 point favorite (quoted as Oklahoma -27, or Kansas +27):
If Oklahoma defeats Kansas by more than 27 points, they have covered the spread and bettors on Oklahoma would receive $100 on a $110 bet. Kansas bettors lose the $110 they wagered. If Kansas defeats Oklahoma, bettors on Kansas would receive $100 on a $110 bet. Oklahoma bettors lose the $110 they wagered. If Kansas loses by less than 27 points, they have won against the spread. Bettors on both sides are then treated exactly as if Kansas had won the game. If Oklahoma wins by exactly 27 points, the wager is called a "push", and neither side wins. Standard practice by U.S. bookmakers is to return the stakes of all bettors on the game in full. To prevent pushes and ensure that they receive their commission on losing wagers, bookmakers often set point spreads that include a half-point. Another common wager available for sporting events involves predicting the combined total score between the competing teams in a game. Such wagers are known as "totals" or "over/unders." For example, the Oklahoma/Kansas football game described above might have a total of 55 points. A bettor could wager that both teams will combine for over 55 points, and play the "over." Or, he could predict that the score will fall under this amount, and play the "under." As with point spreads, bookmakers frequently set the totals at a number involving a half-point (i.e., 55.5), to reduce the occurrence of pushes.
http://www.enterbet.com
amounts that may be wagered per bet, as well as the odds allowed ... These are the bets where a player can bet against a particular number from rolling'
A common line is a $110 bet on a fair coin which pays $210 to win and $0 to lose. On this line, it costs $220 to bet both sides of the same coin simultaneously
You cannot place a Money Line and a Point Spread bet on the same team. ... Money Lines posted with a minus sign "-" require a bet equal to the amount shown
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