Betting on team sports has become an important service industry in many countries. For example, millions of Britons play the football pools every week. At sports betting, players may beat the bank.
Most jurisdictions in Canada and the United States regard sports betting as illegal (Nevada offers full sports betting and the Canadian provinces offer Sport Select – government-run sports parlay betting). However, millions engage in sports betting despite its illegality.
In Canada and the United States the most popular sports bets include:
against the spread – the bettor wagers either that the favoured team will win by a specified number of points or that it will not. Giving the points involves betting the favourite, and taking the points means betting the underdog. See point spread. A team covers the spread if it wins the game with the score modified by the spread. If Dallas and Washington are playing and the spread is (Dallas -7), then Dallas has to win by at least 8 points to cover. Half-point spreads are also possible and the spread may not change.
against odds – the most popular types of bets against odds comprise simple bets that a team will win and over-under (bets on the total points, runs, or goals scored by both teams). In making an over-under bet, the bettor wagers that the total will exceed or fall short of a total specified by the bookmaker.
against a combination of odds and spread
In sports betting, a parlay involves a bet that two or more teams will win. In the United States gamblers have made the parlay card one of the most common forms of sports betting: here bettors wager on the outcomes of two or more games. If all their picks win, they collect. Most such betting occurs in workplaces.
In some casinos, the rule that placing chips equal to or greater than half the normal bet amount beyond the amount required to call constitutes a commitment to raise the normal amount. For example, in a game with a $4 fixed limit, a player facing a $4 opening bet who places $6 in the pot is deemed to have raised, and must complete his bet to $8. The alternative is the “full bet rule”.
half kill
A kill for less than double the normal limits. For example, a $6 game may have a kill for $9 rather than the usual $12.
half-pot limit
A betting structure resembling pot limit, but which allows maximum raises of half the amount in the pot rather than the full amount.
hammer
To bet and raise aggressively. Nora kept hammering, so I folded.
“Having the hammer” is being in last position, especially head up. You’ve got the hammer; I check to you.
A “hammer lock” refers to a player with an almost 100% chance of winning the pot.
In Texas Hold’em, The Hammer refers to a starting hand consisting of a 7-2 offsuit.
hand
The set of cards played by one player.
A single instance of a game of poker, begun by shuffling the cards and ending with the award of a pot. Also called a “deal” (though both terms are ambiguous).
hand for hand
In tournament play, the act of equalizing the number of hands played at two or more tables by waiting for slower tables to finish each hand before beginning the next hand on every table. This is usually done to ensure an accurate finishing order to distribute prize money.
hard
Aggressive and uncompromising, said of one’s play. Jim played me hard all night; I could never get a break.
Chips, as opposed to paper money. I gave the floorman $100 for $50 hard and $50 soft.
head up, heads up
Playing against a single opponent. After Lori folded, Frank and I were head up for the rest of the hand.
here kitty kitty
A conspicuously small bet made with a very powerful hand in the hope of getting a call from one or more opponents who would otherwise fold to a normal-sized bet.
high, high hand
The best hand using traditional poker hand values, as opposed to lowball. Used especially in high-low split games.
high card
A no pair hand, ranked according to its highest-ranking cards.
To defeat another player by virtue of high-ranking cards, especially kickers.
To randomly select a player for some purpose by having each draw one card, the highest of which is selected (for example, to decide who deals first). When all the players get here, we’ll high card for the button. Often high card by suit is used for this purpose.
high-low, high-low split
Any of several games in which the pot is divided between the player with the best conventional poker hand and the best lowball hand.
high society
Large-denomination chips. Also “society”.
$10,000 worth of chips. “Give me three stacks of high society.”
hit and run
To play for a short time, make money, and leave. Also called “chopping” a game.
hog, hogger
To win all of the pot in a split-pot game, for example, by having both the best high hand and best low hand simultaneously. Also called “scooping” the pot.
hole, hole card
Face-down cards. I think Willy has two more queens in the hole.
A seat, often preceded by a number relative to the button. Sara opened from the 2-hole.
Hollywood
Overt acting to deceive other players. Karl had a big smile when he bet, but it seemed too Hollywood to me, so I called anyway.
home game
A game played at a private venue (usually the home of one of the players), as opposed to a casino.
hop the fence
The enter the pot with a cold call.
horse
A player financially backed by someone else. I lost today, but Larry was my horse in the stud game, and he won big.
H.O.R.S.E.
A combination game with five games played in rotation: Texas hold ‘em, Omaha hold’em, razz, seven-card stud, and eight-or-better seven-card stud high-low. Other combinations of the letters are often seen as well: S.H.O.E., H.O.E., etc.
hunt
Looking further into the deck after the hand is over to see what cards would have come next (see also: fox hunt, rabbit hunt).
The World Series of Poker is the most prestigious set of poker tournaments in the world.
Origins
The original World Series of Poker was started by Tom Morehead of the Riverside casino in Reno and was an invitational event. The set of tournaments the World Series of Poker (WSOP) would evolve to was the brainchild of Las Vegas legend, casino owner, and poker player Benny Binion as well as his two sons Jack and Ted.
Johnny Moss, Becky Binion, and Puggy Pearson at the 1974 World Series of Poker
The Binion family not only nurtured the WSOP, but poker in general. Prior to the 1970s, poker was not found at many casinos because of the difficulty of keeping cheaters out. Through better security techniques as well as the Binion’s tireless promotion through events like the WSOP, poker became a very popular game.
In 1970 the first WSOP at Binion’s Horseshoe took place with seven players. The winner, Johnny Moss was elected by his peers as the first World Champion of Poker and received a silver cup as a prize.
Caribbean stud poker is a casino table game with rules similar to five card stud poker. However, unlike standard poker games, Caribbean stud is played against the house rather than against other players (and, like most such games, it cannot be beaten in the long run). There is no bluffing or other deception. For these reasons, most poker players do not consider it to be a form of poker. (They do not necessarily feel that it should not be called poker, but means merely that they will not refer to it as simply “poker”. For instance, a gambler might say “I played poker” if he played seven card stud, but probably would not if he played Caribbean stud.)
The following rules are typical of U.S. casinos, but some of the details (the payouts and limits) vary from casino to casino.
To play, every player places his ante on the layout where indicated; all ante wagers must be placed prior to the dealer announcing “No more bets“. Each player and the dealer will then receive 5 cards, face down. The dealer will turn over one of his cards, then push the cards toward the players, after which the players may look at their cards. They may only look at their own cards, and may not discuss what they have with any other player at the table.
Players have the option to play or fold; if they choose to play, they place their bets (twice the amount of their respective ante) in the bet box. If they choose to fold, they forfeit their ante. After all the players have made their decisions, the dealer reveals his hole cards. The dealer only plays with an ace/king or higher; he then compares his cards to the players’ cards (individually, right to left), and the best poker hand wins.
There are some major rules in Caribbean Stud Poker that must be observed at all times while playing:
Only one hand per player. Players cannot hold or wager on multiple hands at the table.
Players choosing to play the Progressive Payout feature are responsible for ensuring their $1 wager has been inserted into slot and the “Indicator Light” is ON.
Players may not exchange or communicate information regarding their hands to other players or the dealer. Player violation will result in a dead hand and forfeiture of all wagers.
Incorrect amount of cards to the player constitutes a dead hand (or push) for that player only.
The decision of the table/casino supervisor is final.
If the dealer is dealt four cards of the five-card hand, the dealer shall deal an additional card to complete the hand. Any other misdeal to the dealer shall result in all hands being void and the cards shall be reshuffled.
Each player shall be required to keep the five cards in full view of the dealer at all times. Once each player has examined his or her cards and placed them face down on the layout, they may not touch the cards again.
If a hole card is exposed prior to the dealer announcing No More Bets, all hands shall be void.
If a player’s cards beat the dealer’s cards, the player will receive even money (1-1) on the ante, and the following on his bet (with a maximum payout of $5,000 U.S. Dollars per hand on each bet wager):
Royal flush
100 to 1
Straight flush
50 to 1
Four of a kind
20 to 1
Full house
7 to 1
Flush
5 to 1
Straight
4 to 1
Three of a kind
3 to 1
Two pair
2 to 1
One pair or less
1 to 1
If the dealer does not have at least ace/king, all bet wagers will be void, and players will receive even money on their ante bet only. If the dealer’s cards beat a player’s cards, the dealer collects both the ante and bet.
In addition, in Caribbean stud poker, players can also bet on their poker hands and win the “progressive feature”; this is done by dropping a 1.00 dollar gaming chip into the chip acceptor on the table after placing the ante. Players with a flush or higher win, regardless of the outcome of their table bets:
Royal Flush
100% of Progressive Meter
Straight Flush
10% of Progressive Meter
Four-of-a-Kind
$500
Full House
$100
Flush
$50
Winning progressive payout hands are paid in accordance with the amount on the meter when it is the player’s turn to be paid. However, if more than one player at a table has a royal flush progressive payout hand, each player shares equally in the amount on the meter when the first player with a royal flush is to be paid.
A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric. Many of the commonly studied 2×2 games are symmetric. The standard representations of Chicken, the Prisoner’s Dilemma, and the Stag hunt are all symmetric games. [1]
Most commonly studied asymmetric games are games where there are not identical strategy sets for both players. For instance, the Ultimatum game and similar the Dictator game have different strategies for each player. It is possible, however, for a game to have identical strategies for both players, yet be asymmetric. For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players.
Zero sum and non-zero sum
A Zero-Sum Game
A
B
A
2, -2
-1, 1
B
-1, 1
3, -3
In zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero (or more informally put, a player benefits only at the expense of others). Poker exemplifies a zero-sum game, because one wins exactly the amount one’s opponents lose. Other zero sum games include Matching pennies and most classical board games including Go and Chess. Many games studied by game theorists (including the famous Prisoner’s Dilemma) are non-zero-sum games, because some outcomes have net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another.
It is possible to transform any game into a zero-sum game by adding an additional dummy player (often called “the board”), whose losses compensate the players’ net winnings.
Simultaneous and sequential
Simultaneous games are games where both players move simultaneously, or if they do not move simultaneously, the later players are unaware of the earlier players’ actions (making them effectively simultaneous). Sequential games (or dynamic games) are games where later players have some knowledge about earlier actions. This need not be perfect knowledge about every action of earlier players; it might be very little information. For instance, a player may know that an earlier player did not perform one particular action, while she does not know which of the other available actions the first player actually performed.
The difference between simultaneous and sequential games is captured in the different representations discussed above. Normal form is used to represent simultaneous games, and extensive form is used to represent sequential ones.
Perfect information and imperfect information
A game of imperfect information (the dotted line represents ignorance on the part of player 2)
An important subset of sequential games consists of games of perfect information. A game is one of perfect information if all players know the moves previously made by all other players. Thus, only sequential games can be games of perfect information, since in simultaneous games not every player knows the actions of the others. Most games studied in game theory are imperfect information games, although some interesting games are games of perfect information, including the Ultimatum Game and Centipede Game. Many popular games are games of perfect information including Chess, Go, and Mancala.
Perfect information is often confused with complete information, which is a similar concept. Complete information requires that every player know the strategies and payoffs of the other players but not necessarily the actions.
Infinitely long games
For obvious reasons, games as studied by economists and real-world game players are generally finished in a finite number of moves. Pure mathematicians are not so constrained, and set theorists in particular study games that last for infinitely many moves, with the winner (or other payoff) not known until after all those moves are completed.
The focus of attention is usually not so much on what is the best way to play such a game, but simply on whether one or the other player has a winning strategy. (It can be proved, using the axiom of choice, that there are games—even with perfect information, and where the only outcomes are “win” or “lose”—for which neither player has a winning strategy.) The existence of such strategies, for cleverly designed games, has important consequences in descriptive set theory.
Notes
^ Some scholars would consider certain asymmetric games as examples of these games as well. However, the most common payoffs for each of these games are symmetric.
Just as Oxford stud is a mixed stud/community card version of Texas hold ‘em, Billabong is a mixed version of Manila. Each player is dealt two downcards and one upcard. Low upcard starts the betting with a Bring-in if you are playing with one, otherwise high card starts the betting. Next, two community cards are dealt, followed by a second betting round, beginning with the player with the best exposed partial poker hand (counting the community cards, as in Oxford stud). Then a third community card is dealt, followed by a third betting round. Finally a fourth community card and fourth betting round and showdown. Each player plays the best five-card hand he can make from the three in his hand plus the four on the board in any combination.
Shanghai is the same game with an extra hole card, but no more than two hole cards play. That is, the game begins with each player being dealt three downcards and one upcard; each player must discard one of his hole cards at some point during the game as determined ahead of time. The most common variation is to discard immediately as in Pineapple; the second most common is to discard just before showdown as in Tahoe.
A freeroll is a situation that arises during poker play (usually when only two players remain) before the last card has been dealt, in which one player is guaranteed to at least split the pot with his opponent no matter what the final cards are, but where there is some chance he can win the whole pot if certain final cards are dealt. This most commonly occurs in a high-low split game where one player knows that he has a guaranteed low hand made, his opponent cannot make a better low no matter what the last card is, but the player who is low might possibly catch a lucky card that gives him a straight or flush, winning high as well.
Here’s an example from Texas hold’em: Angie holds K♣ 10♣, and Burt holds K♥ 10♥. After round three, the board is A♣ Q♠ J♥ 4♣. Both players have an ace-high straight, the current nut hand, and so they will most likely split the pot. But if the final card happens to be a club, Burt’s straight will lose to Angie’s flush. There is no other possible final card that will give Burt more than a split; only Angie can improve, so she is freerolling Burt.
If a player knows he has a freeroll, he can raise the pot with impunity, and often a less-skilled opponent with a good hand who does not realize that he is on the wrong end of the freeroll will continue to put in raises with no possible hope of gain.
In Hold’em, it is possible to know you have a freeroll without seeing your opponents cards. After the turn if the board has two aces and two kings all of separate suits, and you hold hold AK, you are guaranteed a minimum of a split. However, there is a possibility of you getting the nuts, with a guaranteed winning hand, if an Ace or a King hits on the river.
The term is also used to describe a tournament with no entry fee.
A transformation playing card from the 1895 Vanity Fair deck
In early games the kings were always the highest card in their suit. However, as early as the late 1400s special significance began to be placed on the nominally lowest card, now called the Ace, so that it sometimes became the highest card and the Two, or Deuce, the lowest. This concept may have been hastened in the late 1700s by the French Revolution, where games began being played “ace high” as a symbol of lower classes rising in power above the royalty. The term “Ace” itself comes from a dicing term in Anglo-Norman language, which is itself derived from the Latin as (the smallest unit of coinage). Another dicing term, trey (3), sometimes shows up in playing card games.
Corner and edge indices appeared in the mid-1800s, which enabled people to hold their cards close together in a fan with one hand (instead of the two hands previously used). Before this time, the lowest court card in an English deck was officially termed the Knave, but its abbreviation (“Kn”) was too similar to the King (“K”). However, from the 1600s on the Knave had often been termed the Jack, a term borrowed from the game All Fours where the Knave of trumps is termed the Jack. All Fours was considered a low-class game, so the use of the term Jack at one time was considered vulgar. The use of indices changed the formal name of the lowest court card to Jack.
This was followed by the innovation of reversible court cards. Reversible court cards meant that players would not be tempted to make upside-down court cards right side up. Before this, other players could often get a hint of what other players’ hands contained by watching them reverse their cards. This innovation required abandoning some of the design elements of the earlier full-length courts.
The joker is an American innovation. Created for the Alsatian game of Euchre, it spread to Europe from America along with the spread of Poker. Although the joker card often bears the image of a fool, which is one of the images of the Tarot deck, it is not believed that there is any relation. In contemporary decks, one of the two jokers is often more colorful or more intricately detailed than the other, though this feature is not used in most card games. The two jokers are often differentiated as “Big” and “Little,” or more commonly, “Red” and “Black.” In many card games the jokers are not used. Unlike face cards, the design of jokers varies widely. Many manufacturers use them to carry trademark designs.
In the twentieth century, a means for coating cards with plastic was invented, and has taken over the market, producing a durable product. An example of what the old cardboard product was like is documented in Buster Keaton’s silent comedy The Navigator, in which the forlorn comic tries to shuffle and play cards during a rainstorm.
Playing cards have been used as vehicles for political statements. Here, a playing card of the French Revolution symbolising freedom of cult and brotherhood.
Betting limits apply to the amount a player may open or raise, and come in four common forms: no limit, pot limit (the two collectively called big bet poker), fixed limit, and spread limit.
All such games have a minimum bet as well as the stated maximums, and also commonly a betting unit, which is the smallest denomination in which bets can be made. For example, it is common for a games with $20 and $40 betting limits to have a minimum betting unit of $5, so that all bets must be in multiples of $5, to simplify game play. It is also common for some games to have a bring-in that is less than the minimum for other bets. In this case, players may either call the bring-in, or raise to the full amount of a normal bet, called completing the bet.
Outside of the United States, pot limit and no limit games are the most common. Most American home games are played with a spread limit, while casino games are played with spread or fixed limits, though larger casinos may have a high-stakes pot limit or no limit game as well. Fixed limit and spread limit games emphasise the skill of estimating odds, whereas pot limit and no limit games emphasize the skills of game theory and psychology. Almost all poker players believe that pot and no limit poker involve more skill than fixed limit play. A few prominent players, most notably Mason Malmuth, believe that the richer tactics make fixed limit more skilled. Although the main event at the World Series of Poker is played no limit, most high stakes cash games are fixed limit, so it is unclear which format is the experts’ choice.
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Johnny Moss, Becky Binion, and Puggy Pearson at the 1974 World Series of Poker
A game of imperfect information (the dotted line represents ignorance on the part of player 2)
A transformation playing card from the 1895 Vanity Fair deck
Playing cards have been used as vehicles for political statements. Here, a playing card of the French Revolution symbolising freedom of cult and brotherhood.