Second dealing is a method of illegally influencing the outcome of a poker game by way of dealing the second, rather than the top, card of the deck. Generally, a second dealer will sneak a peek at the second or first card of the deck just after or during the cut. With the knowledge of that (or those two) card(s) in mind, he can deal the second or first card to himself or a confederate to help his or his buddy’s hand, or deal it to someone else if he knows the card will not help the opponent (thereby preventing the opponent from improving his hand). The identity of the top card can also be determined by using marked (or pegged) cards.
Card sharps who specialize in this cheat are known as “second dealers.”
Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. First developed as a tool for understanding economic behavior, game theory is now used in many diverse academic fields, ranging from biology to philosophy. Game theory saw substantial growth during the Cold War because of its application to military strategy, most notably to the concept of mutually assured destruction. Beginning in the 1970s, game theory has been applied to animal behavior, including species’ development by natural selection. Because of interesting games like the Prisoner’s dilemma, where mutual self-interest hurts everyone, game theory has been used in ethics and philosophy. Finally, game theory has recently drawn attention from computer scientists because of its use in artificial intelligence and cybernetics.
In addition to its academic interest, game theory has received attention in popular culture. An important figure in game theory, John Nash was the subject of the 2001 film A Beautiful Mind. Several game shows have adopted game theoretic situations, including Friend or Foe and Deal or No Deal. [1]
Although similar to decision theory, game theory studies decisions that are made in an environment where various players interact. In other words, game theory studies choice of optimal behavior when costs and benefits of each option are not fixed, but depend upon the choices of other individuals.
Notes
^ GameTheory.net has an extensive list of references to game theory in popular culture.
References
Textbooks and general reference texts
Gibbons, Robert (1992) Game Theory for Applied Economists, Princeton University Press ISBN 0691003955 (readable; suitable for advanced undergraduates. Published in Europe by Harvester Wheatsheaf (London) with the title A primer in game theory)
Ginits, Herbert (2000) Game Theory Evolving Princeton University Press ISBN 0691009430
Osborne, Martin and Ariel Rubinstein: A Course in Game Theory, MIT Press, 1994, ISBN 0-262-65040-1 (modern introduction at the introductory graduate level)
Fudenberg, Drew and Jean Tirole: Game Theory, MIT Press, 1991, ISBN 0262061414 (the definitive reference text)
Historically important texts
Fisher, Ronald (1930) The Genetical Theory of Natural Selection Clarendon Press, Oxford.
Luce, Duncan and Howard Raiffa Games and Decisions: Introduction and Critical Survey Dover ISBN 0486659437
Maynard Smith, John Evolution and the Theory of Games, Cambridge University Press 1982
Morgenstern, Oskar and John von Neumann (1947) The Theory of Games and Economic Behavior Princeton University Press
Nash, John (1950) “Equilibrium points in n-person games” Proceedings of the National Academy of the USA 36(1):48-49.
Poundstone, William Prisoner’s Dilemma: John von Neumann, Game Theory and the Puzzle of the Bomb, ISBN 038541580X
Other print references
Camerer, Colin (2003) Behavioral Game Theory Princeton University Press ISBN 0691090394
Gauthier, David (1987) Morals by Agreement Oxford University Press ISBN 0198249926
Grim, Patrick, Trina Kokalis, Ali Alai-Tafti, Nicholas Kilb, and Paul St Denis (2004) “Making meaning happen.” Journal of Experimental & Theoretical Artificial Intelligence 16(4): 209-243.
Kavka, Gregory (1986) Hobbesian Moral and Political Theory Princeton University Press. ISBN 069102765X
Lewis, David (1969) Convention: A Philosophical Study
Maynard Smith, J. and Harper, D. (2003) Animal Signals. Oxford University Press. ISBN 0198526857
Quine, W.v.O (1967) “Truth by Convention” in Philosophica Essays for A.N. Whitehead Russel and Russel Publishers. ISBN 0846209705
Quine, W.v.O (1960) “Carnap and Logical Truth” Synthese 12(4):350-374.
Skyrms, Brian (1996) Evolution of the Social Contract Cambridge University Press. ISBN 0521555833
Skyrms, Brian (2004) The Stag Hunt and the Evolution of Social Structure Cambridge University Press. ISBN 0521533929.
Sober, Elliot and David Sloan Wilson (1999) Unto Others: The Evolution and Psychology of Unselfish Behavior Harvard University Press. ISBN 0674930479
Some poker games just don’t fit neatly into the categories of draw poker, stud poker, or community card poker, and some have features of more than one of these categories.
Stud Horse poker
Stud Horse poker is mentioned in the California law books as one of the gambling games prohibited in California’s card rooms. There is no definition for it under the law, however. It appears not to be Stud poker, which is not prohibited and is offered in several variations in California card rooms.
Blind Man’s Bluff
Blind Man’s Bluff is a version of poker in which a player sees the cards that would generally be visible to the other players, but does not see his own. It can be played with just one card (“Indian Poker”), as a community card poker game, or as five-card stud.
Probably starting about the time of World War II, many modern poker games used community cards (also called “shared cards” or “widow cards”), which are cards dealt face up to the center of the table and shared by all players. In these games, each player is dealt privately an incomplete hand (“hole cards”), which is then combined with the community cards to make a complete hand. The set of community cards is called the “board” or the “widow”, and may be dealt in a simple line or arranged in a special pattern; rules of each game determine how they may be combined with each player’s private hand.
The canonical community card game today is probably Texas hold ‘em (and variants thereof), originating sometime in the 1920s. That game is described in great detail in its own article, while most of the descriptions below are brief and refer to that more detailed article (a few other games merit their own article as well, such as Omaha hold’em).
In home games, it is typical to use antes, while casinos typically use only blinds for these games. Fixed limit games are most common in casinos, while spread limit games are more common in home games. No limit and pot limit games are less common, but some games play particularly well with those structures. As with stud poker, later betting rounds often have a higher limit than earlier betting rounds. Each betting round begins with the player to the dealer’s left (when blinds are used, the first round begins with the player after the big blind), so community card games are generally positional games.
Most community card games do not play well with lowball hand values, though some do play very well at high-low split, especially with ace-to-five low values, making it possible to win both halves of a pot. When played high-low split, there is generally a minimum qualifying hand for low (often 8-high), and it is played cards speak.
Stud poker is any of a number of poker variants in which each player receives a mix of face-down and face-up cards dealt in multiple betting rounds. Stud games are also typically non-positional games, meaning that the player who bets first on each round may change from round to round (it is usually the player whose face-up cards make the best hand for the game being played). The cards dealt face down to each individual player are called hole cards (which gave rise to the common English expression ace in the hole, which suggests that one has something valuable that is hidden from view).
Five-card stud first appeared during the American Civil War, and became very popular. In recent years, Seven-card stud has become more common, both in casinos and in home games. These two games form the basis of most modern stud poker variations.
The number of betting rounds in a game influences how well the game plays with different betting structures. Games with four or fewer betting rounds, such as five-card stud and Mississippi stud (described below), play well with any structure, and are especially well suited to no limit and pot limit play. Games with more betting rounds are more suited to fixed limit or spread limit. It is common (and recommended) for later betting rounds to have higher limits than earlier ones. For example, a “$5/$10 Seven-card Stud” game in a Nevada casino allows $5 bets for the first two rounds and $10 bets for subsequent rounds. Also common is to make the final round even higher: a “$5/$10/$20″ game would allow $20 bets on the last round only. Another common rule is to allow the larger bet on the second round if there is an “open pair” (that is, at least one player’s upcards make a pair). Some casinos (typically in California) use the smaller limit on the first three rounds rather than just the first two.
It is a common convention in stud poker to name the betting rounds after the number of cards each player holds when that betting round begins. So the bet that occurs when each player has three cards is called “third card” or “third street”, while the bet that occurs when each player has five cards is “fifth street”. The final round, regardless of the number of betting rounds, is commonly called the “river” or simply the “end”.
The variations described below assume that you are already familiar with five-card stud and seven-card stud, and with the game play of poker in general.
Draw poker is any poker variant in which each player is dealt a complete hand before the first betting round, and then develops the hand for later rounds by replacing cards.
The descriptions below assume that you are familiar with the general game play of poker, and with hand values (both high and low variations). They also make no assumptions about what betting structure is used. In home games, it is typical to use an ante, and betting always begins with the player to the dealer’s left. In casino play, it is more common to use blinds; the first betting round thus begins with the player to the left of the big blind, and subsequent rounds begin with the player to the dealer’s left, thus draw games are very positional.
Some sample deals below will assume that a game is being played by four players: Alice, who is dealing in the examples, Bob, who is sitting to her left, Carol to his left, and David to Carol’s left.
Standard five-card draw
This is often the first poker variant learned by most players, and is very common in home games although it is now quite rare in casino and tournament play. When played skillfully, it can become monotonous. The lowball variations described later are more interesting games. Two to eight players can play.
Play begins with each player being dealt five cards, one at a time, all face down. The remaining deck stub is placed aside, often protected by placing a chip or other marker on it. Players pick up the cards and hold them in their hands, being careful to keep them concealed from the other players. The first betting round occurs at this point, starting with the player to the dealer’s left. If more than one player remains after this round, the “draw” phase begins. Each player specifies how many of his cards he wishes to replace, and discards that many from his hand. The deck stub is retrieved, and after a burn card is dealt, each player in turn is dealt the same number of cards he discarded, so that each player again has five cards. It is important that each player discards the cards he wishes to replace before he takes any replacements, and that he take the same number of replacements as he discarded. A second betting round occurs after the draw phase, followed by a showdown if more than one player remains.
A common “house rule” in some places is that a player may not replace more than three cards, unless he draws four cards while keeping an ace (or wild card). This rule is only needed for low-limit social games where many players will stay for the draw, and will help avoid depletion of the deck stub. In more serious games such as those played in casinos it is unnecessary and generally not used. A rule that is used by many casinos is that a player is not allowed to draw five consecutive cards from the deck. In this case, if a player wishes to replace all five of his cards, he is given four of them in turn, the other players are given their draws, and then the dealer returns to that player to give him his fifth replacement (if no later player drew, it is necessary to deal a burn card first).
Another common house rule is that the bottom card of the deck is never given as a replacement, to avoid the possibility of someone who might have seen it during the deal using that information. If the deck stub is depleted during the draw before all players have received their replacements, the last players can receive cards chosen randomly from among those discarded by previous players. For example, if the last player to draw wants three replacements but there are only two cards remaining in the deck stub, the dealer gives the player the one top card he can give, then shuffles together the bottom card of the deck, the burn card if any, and the earlier players’ discards (but not the three discards of the last player!), and finally deals two more replacements to the last player.
Example: Alice deals five cards to each player and places the deck stub aside. Bob opens the betting round by betting $1. Carol folds, David calls, and Alice calls, closing the betting round. Bob now declares that he wishes to replace three of his cards, so he removes those three cards from his hand and discards them. Alice retrieves the deck stub, deals a burn card, and then deals three cards directly to Bob, who puts them in his hand. David discards one card, and Alice deals one card to him from the deck stub. Alice now discards three of her own cards, and replaces them with three from the top of the deck stub. Now a second betting round begins. Bob checks, David bets $3, Alice calls, and Bob folds, ending the second betting round. David shows a flush, and Alice shows two pair, so David takes the pot.
Anaconda is a variety of the card game poker. It is played like five-card draw, but with 3 significant alterations: No more than 6 people can play at one time.
Each player is dealt 8 cards at the beginning (best 5 card hand wins)
After looking at their cards, each player chooses 3 cards that they do not want. These cards will get passed to the player to their left. (Make sure it is understood that you pass your 3 cards BEFORE looking at the three cards that were passed to you, which prevents players from getting an unfair advantage.)
After looking at their 8 cards, which include the three received from the other player, players now pass 2 unwanted cards to the person on their left.
After looking at their cards, players pass 1 unwanted card to their left.
The passing is done, and players pick their best 5 card hand. The three unwanted cards are removed from the hand and placed in a discard pile.
Betting begins now, if you are betting.
(optional). A betting variation is available to anaconda. Each player places their 5 cards in front of them. One card is turned over and a round of betting then follows. This happens until one card is left. After that, players turn over their final card and decide who wins.
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The origin of playing cards is obscure, but it is almost certain that they began in China after the invention of paper. Ancient Chinese “money cards” have four “suits”: coins (or cash), strings of coins (which may have been misinterpreted as sticks from crude drawings), myriads of strings, and tens of myriads. These were represented by ideograms, with numerals of 2-9 in the first three suits and numerals 1-9 in the “tens of myriads”. Wilkinson suggests in The Chinese origin of playing cards that the first cards may have been actual paper currency which were both the tools of gaming and the stakes being played for. The designs on modern Mahjong tiles and dominoes likely evolved from those earliest playing cards. The Chinese word p’ai is used to describe both paper cards and gaming tiles.
The time and manner of the introduction of cards into Europe are matters of dispute. The 38th canon of the council of Worcester (1240) is often quoted as evidence of cards having been known in England in the middle of the 13th century; but the games de rege et regina there mentioned are now thought to more likely have been chess. If cards were generally known in Europe as early as 1278, it is very remarkable that Petrarch, in his dialogue that treats gaming, never once mentions them. Boccaccio, Chaucer and other writers of that time specifically refer to various games, but there is not a single passage in their works that can be fairly construed to refer to cards. Passages have been quoted from various works, of or relative to this period, but modern research leads to the supposition that the word rendered cards has often been mistranslated or interpolated.
It is likely that the ancestors of modern cards arrived in Europe from the Mamelukes of Egypt in the late 1300s, by which time they had already assumed a form very close to those in use today. In particular, the Mameluke deck contained 52 cards comprising four “suits”: polo sticks, coins, swords, and cups. Each suit contained ten “spot” cards (cards identified by the number of suit symbols or “pips” they show) and three “court” cards named malik (King), nā’ib malik (Viceroy or Deputy King), and thānī nā’ib (Second or Under-Deputy). The Mameluke court cards showed abstract designs not depicting persons (at least not in any surviving specimens) though they did bear the names of military officers. A complete pack of Mameluke playing cards was discovered by L.A. Mayer in the Topkapi Sarayi Museum, Istanbul, in 1939; this particular complete pack was not made before 1400, but the complete deck allowed matching to a private fragment dated to the twelfth or thirteenth century. There is some evidence to suggest that this deck may have evolved from an earlier 48-card deck that had only two court cards per suit, and some further evidence to suggest that earlier Chinese cards brought to Europe may have travelled to Persia, which then influenced the Mameluke and other Egyptian cards of the time before their reappearance in Europe.
It is not known whether these cards influenced the design of the Indian cards used for the game of Ganjifa, or whether the Indian cards may have influenced these. Regardless, the Indian cards have many distinctive features: they are round, generally hand painted with intricate designs, and comprise more than four suits (often as many as twelve).
The act of making the first non-zero bet in a betting round is called opening the round. On the first betting round, it is also called opening the pot. Some games may have special rules about opening a round that may not apply to other bets. For example, they may have a betting structure that specifies different allowable amounts for opening than for other bets, or they may require a player to hold certain cards to open.
Call
To call is to make the total amount of one’s bet equal to the amount of the immediately preceding bet (which will be the largest bet made in that round). All players must eventually call an equal amount for the betting round to end, or else one player must bet an amount that no one calls, thus ending the entire deal and awarding him the pot.
The second and subsequent calls of a particular bet amount are sometimes called overcalls.
A player calling a raise before he or she has invested money in the pot in that round is cold calling. For example, if in a betting round, Jerry bets, Sally raises, and Eric calls, Eric “calls two bets cold”.
A player calling instead of raising with a strong hand is smooth calling, a form of slowplay. Smooth calling is generally done in early betting rounds and against only one or two opponents; otherwise at least one opponent may have too good a chance of drawing out on the smooth caller and the trap backfires.
In public card rooms and casinos where verbal declarations are binding, the word “call” is such a declaration. In particular, the practice commonly seen in poker games on television and in movies of saying “I call, and raise $100″ is considered a string raise and is not allowed in a serious poker game. Saying “I call” commits you to the action of calling, and only calling.
Check
When no one has yet opened the betting round, one may check, which is equivalent to calling the current bet of zero. The player declines making a bet; indicating that he does not choose to open, but that he wishes to keep his cards and retain the right to call or raise later in the same round if some other player opens. A common way to signify checking is to tap the table with a fist or an open hand.
A player with a live blind who chooses not to take advantage of his right to raise is said to check his option, which can be signified the same way.
Raise
To raise is to make the amount of one’s bet greater than the amount of the immediately preceding bet, forcing all subsequent players to call the new amount. If the current bet amount is nothing, this action is considered the opening bet. A player making the second (not counting the open) or subsequent raise of a betting round is often said to reraise.
Except in the case of a live blind, a player may not raise the current bet amount if he is the one who first set it. If it is that player’s turn to act who first set the current amount, the betting round is closed and no further betting may take place in this round. This occurs when all other players have either called the amount or folded. All remaining players will have bet an equal total amount (except for some rare cases covered by table stakes rules).
A universal rule in casinos in the United States, and common in home games as well, is that any raise must at least equal the amount of the previous raise. For example, if a player in a spread limit or no limit game bets $5, the next player may raise by another $5 or more, but he may not raise by only $2, even if that would otherwise conform to the game’s betting structure. The primary purpose of this rule is to avoid game delays caused by “nuisance” raises (small raises of large bets that do not affect the bet amount much but that take time). This rule is often overridden by table stakes rules, so that a player may in fact raise a $5 bet by $2 if that $2 is his entire remaining stake.
In many casinos, for fixed-limit or spread-limit games, there is a limit to the total number of raises allowed in a single betting round (typically three or four, not including the opening bet of a round). For example in a casino with a three-raise rule, if one player opens the betting for $5, the next raises by $5 making it $10, a third player raises another $5, and a fourth player raises $5 again making the current bet $20, the betting is said to be capped at that point, and no further raises beyond the $20 level will be allowed on that round. It is common to suspend this rule when there are only two players betting in the round (called being heads-up). Pot-limit and no-limit games do not have a limit on the number of raises.
Fold
Although not specifically a betting action, to fold is to discard one’s hand and forfeit any further interest in the hand or the current pot. Also called “drop” or “pass” (the latter term is ambiguous, because it can also mean check). This can be done verbally, or simply signalled by discarding one’s hand into the pile of other discards called the muck. In stud poker played in the United States, it is customary to signal folding by turning all of your cards face down. In casinos in the United Kingdom, a player folds by giving his hand as is to the “house” dealer, who will spread the hand’s upcards for the other players to see before mucking them.
It is a serious breach of etiquette to fold out of turn, that is, when it is not the folding player’s turn to act, because this can harm other players. For example, if there are three players remaining and the first player in turn bets, the third player folding out of turn now would give valuable strategic information to the second player (who is in turn at this point), to the detriment of the bettor. In some games, even folding in turn when you are entitled to check (because there is no bet facing you) is considered an out of turn fold since it gives away information to which players would otherwise not be entitled. Finally, if a player folds out of turn in a stud poker game, the player in turn may demand that his upcards remain exposed until he has completed his turn.
Deuce-to-seven low is a method for evaluating low hands in poker. It is often called “Kansas City” low or just “low poker”. It is almost the direct opposite of standard poker: high hand loses. It is not as commonly used as the ace-to-five low method.
As in all lowball games, pairs and trips are bad: that is, any hand with no pair defeats any hand with a pair; one pair hands defeat two pair or trips, etc. No-pair hands are compared starting with the highest ranking card, just as in high poker, except that the high hand loses. In deuce-to-seven low, straights and flushes count for high (and are therefore bad). Aces are always high (and therefore bad).
For example, the hand 8-5-4-3-2 defeats 9-7-6-4-3, because eight-high is lower than nine-high. The hand 7-6-5-4-2 defeats both, because seven-high is lower still. The hand 7-6-5-4-3 would lose, because it is a straight. Aces are high, so Q-8-5-4-3 defeats A-8-5-4-3. In the rare event that hands with pairs tie, kickers are used just as in high poker (but reversed): 3-3-6-4-2 defeats 3-3-6-5-2.
A special rule is that a wheel is not considered a straight: A-5-4-3-2 is simply ace-high no pair (it would therefore lose to any king-high, but would defeat A-6-4-3-2.
It’s called deuce-to-seven low because the best possible hand is 7-5-4-3-2, followed by 7-6-4-3-2, 7-6-5-3-2, 7-6-5-4-2, 8-5-4-3-2, 8-6-4-3-2, etc.
When speaking, low hands are referred to by their highest ranking card or cards. Any nine-high hand can be called “a nine”, and is defeated by any “eight”. Two cards are frequently used: the hand 8-6-5-4-2 can be called “an eight-six” and will defeat “an eight-seven” such as 8-7-5-4-2.
Another common notation is calling a particular low hand “smooth” or “rough.” A smooth low hand is one where the remaining cards after the highest card are themselves very low; a rough low hand is one where the remaining cards are high. For instance, 8-7-6-4-2 would be referred to as a “rough eight,” but 8-5-4-3-2 would be referred to as a “smooth eight.”
Wild cards are rarely used in deuce-to-seven games, but if used they play as whatever rank would make the lowest hand. Thus, in 7-6-Joker-3-2, the joker plays as a 4, while in Joker-5-4-3-2 it would play as a 7 (a six would make a straight, and an ace would make ace-five high).
High-low split games with deuce-to-seven low are usually played with a declaration.
