Kuhn poker

Kuhn poker is a simplified form of poker developed by Dr. Harold W. Kuhn. It is a zero sum two player game. The deck includes only three playing cards, for example a King, Queen, and Jack. One card is dealt to each player, then the first player must bet or pass, then the second player may bet or pass. If any player chooses to bet the opposing player must bet as well "call" in order to stay in the round. After both players pass or bet the player with the highest card wins the pot. Kuhn demonstrated that there are many game theoretic optimal strategies for the first player in this game, but only one for the second player, and that, when played optimally, the first player should expect to lose at a rate of −1/18 per hand.

In more conventional poker terms:

Each player antes 1
Each player is dealt one of the three cards, and the third is put aside unseen
Player One can check or raise 1
If Player One checks then Player Two can check or raise 1
If Player Two checks there is a showdown for the pot of 2
If Player Two raises then Player One can fold or call
If Player One folds then Player Two takes the pot of 3
If Player One calls there is a showdown for the pot of 4
If Player One raises then Player Two can fold or call
If Player Two folds then Player One takes the pot of 3
If Player Two calls there is a showdown for the pot of 4

Casino security refers to the measures that are taken at casinos to protect the establishment's money and property and the patrons. The security protects the casino and its customers from violent crime, theft, and other inappropriate behavior.

Given the relatively large amounts of currency that are handled within a casino, the temptation exists for both patrons and staff to commit crimes. Many casinos take security measures to prevent theft and other crime. The most basic level of security today consists of cameras located throughout the property operated by highly trained individuals who attempt to locate cheating and stealing by both players and employees.

While casino security of the past was nothing more than a muscle man, today's security is a multi-million dollar investment that is as complex as a police department. Modern casino security is usually divided between a physical security force and a specialized surveillance department that operates the casino's closed circuit television system known in the industry as the eye in the sky in an effort to detect any misconduct by both guests and employees alike. Both of these specialized casino departments work very closely with each other to ensure the safety of both guests as well as the casino's assets, and have been quite successful in preventing crime. Some casinos also have catwalks in the ceiling above the casino floor. These catwalks allow surveillance personnel to look directly down, through one-way glass, on the activities at the tables and/or slot machines.

In addition to cameras and other technological measures, casinos also enforce security through rules of conduct and behavior; for example, players at card games are usually required to keep their hands visible at all times.

The amount of security that is used at a casino is determined based on local laws and ordinances and what the prosecutors in the region are willing to act upon.

Betting arbitrage, miracle bets, sure bets, sports arbitraging is a particular case of arbitrage arising on betting markets due to bookmakers’ different opinions on either event outcomes or plain errors. By placing one bet per each outcome with different betting companies, the bettor can make a profit. In the bettors' slang an arbitrage is often referred to as an arb; people who use arbitrage are called arbers. A typical arb is around 2 percent, often less; however 4-5 percent are occasionally seen and during some special events they might reach 20 percent. Arbitrage betting involves relatively large sums of money stakes are bigger than in normal betting.

Bookmakers generally disapprove of arbers, and restrict or close the accounts of those who they suspect of engaging in arbitrage betting. Although arbitrage betting has existed since the beginnings of bookmaking, the rise of the Internet, odds-comparison websites and betting exchanges have enabled the practice to be easier to perform. On the other hand, these changes also made it easier for bookmakers to keep their odds in line with the market.

The best way of generating profit, which has been established in Britain via sports arbitrage, consists of 'key men' employing others to place bets on their behalf, so as to avoid detection and increase accessibility to bookmakers. This allows the financiers or key arbers to stay at a computer to keep track of market movement.

While often claimed to be risk-free, this is only true if an arb is successfully completed; in reality, there are several threats to this:

Arbs in online sports markets have a median lifetime of around 15 minutes, after which the difference in odds underpinning them vanishes through betting activity. Without rapid alerting and action, it is possible to fail to make all the legs of the arb before it vanish, thus transforming it from a risk-free arb into a bet. High street bookmakers however, offer their odds days in advance and rarely change them once they have been set. These Arbs can have a lifetime of several hours.

Making errors: In the excitement of the action and due to the high number of bets placed, it is not uncommon to make a mistake like traders on financial markets. For example the appropriate stakes may be incorrectly calculated, or be placed on the wrong legs of the arb, locking in a loss, or there may be inadequate funds in one of the accounts to complete the arb. Those errors might temporarily have an important impact. In the long term, the benefit will depend on the odds. For example one could actually make more money by placing the wrong bet where the outcome happens to be beneficial, though not justified by the arbitrage calculation. However, this stroke of luck being repeated is unlikely, assuming the bookies have calculated the odds so they make a profit.

Bet cancellation: If a bettor places bets so as to make an arbitrage and one bookmaker cancels a bet, the bettor could find himself in a bad position because he is actually betting with all the risks implied. The bettor can repeat the bet that has been cancelled so as minimize the risk, but if he cannot get the same odds he had before he may be forced to take a loss. In some cases the situation arises when there are very high potential payouts by the bookie, perhaps due to an unintentional error made while quoting odds. Many jurisdictions allow bookmakers to cancel bets in the event of such a palpable [obvious] error in the quoted odds This is often loosely defined as an obvious mistake, but whether a palp in fact has been made is often the sole discretion of the bookmaker.

Other problems: Bookmakers who suspect arbing can set very low maximum stake limits, making arbing insufficiently profitable. Capital diffusion is serious; many bookmakers make it very easy to deposit funds and difficult to withdraw them. Making a return involves many bets spread over typically many bookmakers so keeping track is a considerable challenge, and requires excellent record-keeping.