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.

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Tracking poker play in a B&M casino is very difficult. You can easily monitor your winnings, but tracking any detailed statistics about your game requires a player to take notes after each hand, which is cumbersome and distracting.

Conversely, tracking poker play online is easy. Most online poker rooms support “Hand Histories” text files which track every action both you and your opponents made during each hand. The ability to specifically track every single played hand has many advantages. Many third-party software applications process hand history files and return detailed summaries of poker play. These not only include exact tallies of rake and winnings, which are useful for tax purposes, but also offer detailed statistics about the person’s poker play. Serious players use these statistics to check for weaknesses or “leaks” (mistakes that leak money from their winnings) in their game. Such detailed analysis of poker play was never available in the past, but with the growth of online poker play, it is now commonplace among nearly all serious and professional online poker players.

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One of the most widespread forms of gambling involves betting on horse races, most commonly on races between thoroughbreds or between standardbreds.

Wagering may take place through parimutuel pools; or bookmakers may take bets personally. Parimutuel wagers pay off at prices determined by support in the wagering pools, while bookmakers pay off either at the odds offered at the time of accepting the bet; or at the median odds offered by track bookmakers at the time the race started.

In Canada and the United States, the most common types of bet on horse races include:

• win – to succeed the bettor must pick the horse which wins the race.
• place – the bettor must pick a horse which finishes either first or second.
• show – the bettor must pick a horse which finishes first, second, or third.
• exacta, perfecta, or exactor –the bettor must pick the two horses which finish first and second and specify which will finish first
• quinella or quiniela – the bettor must pick the two horses which finish first and second, but need not specify which will finish first.
• trifecta or triactor – the bettor must pick the three horses which finish first, second, and third and specify which will finish first, second and third.
• superfecta – the bettor must pick the four horses which finish first, second, third and fourth, and specify which will finish first, second, third and fourth.
• double – the bettor must pick the winners of two successive races; most race tracks in Canada and the United States take double wagers on the first two races on the program (the daily double) and on the last two (the late double).
• triple – the bettor must pick the winners of three successive races; many tracks offer rolling triples, or triples on any three successive races on the program. Also called pick three.
• sweep – the bettor must pick the winners of four or more successive races. In the US, this is usually called pick four and pick six, with the latter paying out a consolation return to bettors correctly selecting five winners out of six races, and with “rollover” jackpots accumulating each day until one or more bettors correctly picks all six winners.

Win, place and show wagers class as straight bets, and the remaining wagers as exotic bets. Bettors usually make multiple wagers on exotic bets. A box consists of a multiple wager in which punters bet all possible combinations of a group of horses in the same race. A key involves making a multiple wager with a single horse in one race bet in one position with all possible combinations of other selected horses in a single race. A wheel consists of betting all horses in one race of a bet involving two or more races. For example a 1-all daily double wheel bets the 1-horse in the first race with every horse in the second.

People making straight bets commonly employ the strategy of an ‘each way’ bet. Here the bettor picks a horse and bets it will win, and makes an additional bet that it will show, so that theoretically if the horse runs third it will at least pay back the two bets. The Canadian and American equivalent is the bet across (short for across the board): the bettor bets equal sums on the horse to win, place, and show.

In Canada and the United States punters make exotic wagers on horses running at the same track on the same program. In the United Kingdom bookmakers offer exotic wagers on horses at different tracks. Probably the Yankee occurs most commonly: in this the bettor tries to pick the winner of four races. This bet also includes subsidiary wagers on smaller combinations of the chosen horses; for example, if only two of the four horses win, the bettor still collects for their double. A Trixie requires trying to pick three winners, and a Canadian or Super Yankee trying to pick five; these also include subsidiary bets. The term nap identifies the best bet of the day.

A parlay (US) or accumulator (UK) consists of a series of bets in which bettors stake the winnings from one race on the next in order until either the bettor loses or the series completes successfully.

(Similarly, greyhound racing offers a popular betting alternative to horse racing in many countries.)

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garbage

1. The muck.
2. A worthless hand.

gretzky

In games like Texas hold ‘em to have pocket 9′s. A reference to hockey player Wayne Gretzky’s number 99.

grinder

A player who earns a living by making small profits over a long period of consistent, conservative play.

guts, guts to open

1. A game with no opening hand requirement; that is, where the only requirement to open the betting is “guts”, or courage.
2. Any of several poker variants where pots accumulate over several hands until a single player wins.

gutshot

An inside straight draw (“gutshot draw”)

gypsy

To enter the pot cheaply by just calling the blind rather than raising.

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A chip race is an event that takes place in poker tournaments, especially those with an escalating blinds (such as Texas hold ‘em), in which chips of denominations that are no longer needed (as the current and upcoming blinds are more easily played with larger chip values) are removed from play. This has the effect of reducing the number of physical chips in front of any player, and makes it easier for the players to count their stacks and their bets.

In a typical chip race:

1. All players color up their lesser-valued chips into greater denominations. For example, if the blinds have increased to a level where $5 chips are no longer needed to post blinds, each five $5 chips will be exchanged for a $25 chip. Players will temporarily keep any leftover chips that cannot be fully colored up to larger chips (less than 5 $5 chips in the above example).
2. All leftover chips are counted, and equivalent chips in the larger denomination are presented to the table. Continuing the example, if there are 15 $5 chips remaining among 6 players, 3 $25 chips are prepared. In the event the remaining smaller chips do not add up to a whole larger chip, an extra larger chip should be added as long as the leftover smaller chips total more than half a single larger chip.
3. Each player with leftover chips in the smaller denomination will receive one card for each chip. The cards are typically dealt face up, starting from the small blind position for the upcoming hand. Each player due to receive cards will receive all of his cards before the next player, rather than a “traditional” card deal; the player on the little blind, for example, who is due to receive three cards for his three chips, will receive all three of his cards before the big blind receives any.
4. The larger chips are issued to the players with the highest single cards showing (poker hands do not count). No player is issued more than one chip. Ties (cards of the same rank) are broken by suit, using the same bridge (ascending alphabetical) order of the suits: Spades are highest, followed by Hearts, Diamonds, and Clubs. All remaining lesser-value chips are removed from play.

A chip race cannot eliminate a player from the game. In the event a player’s last smaller-denomination chips are removed from play as part of the chip race, he automatically gets one colored up chip if one is available. Any leftover colored up chips go to the winner(s) of the chip race as described above.

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When certain pay schedules are offered by a video poker machine, players using perfect or near perfect strategy can obtain greater than 100% payback over a sufficiently long period of play. These machines are referred to as “full pay” machines. Casinos place full pay machines alongside other machines with pay schedules that offer a negative return, so it is up to the player to properly identify which video poker machines offer the full pay schedules.

Most full pay machines are configured with a pay schedule that is only full pay when the maximum amount of credits is bet. (See the pay schedule tables later in this article for details.)

Deuces Wild

One variation of video poker, called “Deuces Wild”, can be found with pay schedules that offer up to a theoretical return of 100.762%, when played with perfect strategy. It is also available with other pay schedules that have lesser theoretical returns:

• *Notice the gap between the payoff for a Natural Royal Flush played with 4 credits vs. one with 5 credits. The payoff schedule for most video poker machines has a gap like this, such that players who do not play with the maximum number of credits at a time are playing with a negative theoretical return.

Double Bonus

Another variation of video poker, called “Double Bonus”, can be found with pay schedules that offer up to a theoretical return of 100.1725%, when played with perfect strategy. It is also available with other pay schedules that have lesser theoretical returns:

• *Notice the gap between the payoff for a Royal Flush played with 4 credits vs. one with 5 credits. Players who do not play with the maximum number of credits at a time are playing with a negative theoretical return.

Double Double Bonus

Another variation of video poker, called “Double Double Bonus”, can be found with pay schedules that offer up to a theoretical return of 100.067%, when played with perfect strategy. It is also available with other pay schedules that have lesser theoretical returns:

• *Notice the gap between the payoff for a Royal Flush played with 4 credits vs. one with 5 credits. Players who do not play with the maximum number of credits at a time are playing with a negative theoretical return.

Other Full Pay Games

Other kinds of video poker only have positive theoretical returns when the progressive jackpot is high enough. Many establishments advertise with a billboard when the progressive jackpot is high enough.

Locating Full Pay Games

Although full pay video poker machines are found in many “locals” casinos (located off the Strip) in the Las Vegas market (and in a few Reno casinos), most Strip casinos and casinos in other markets only offer video poker pay schedules with a negative theoretical return.

The maximum bet size is kept fairly small on video poker machines with a full pay schedule (one dollar or less), which makes it impractical to win a large amount of money over any reasonable period of time.

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The games studied by game theory are well-defined mathematical objects. A game consists of a set of players, a set of moves (or strategies) available to those players, and a specification of payoffs for each combination of strategies. There are two ways of representing games that are common in the literature.

Normal form

The normal (or strategic form) game is a matrix which shows the players, strategies, and payoffs (see the example to the right). Here there are two players; one chooses the row and the other chooses the column. Each player has two strategies, which are specified by the number of rows and the number of columns. The payoffs are provided in the interior. The first number is the payoff received by the row player (Player 1 in our example); the second is the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays top and that Player 2 plays left. Then Player 1 gets 4, and Player 2 gets 3.

When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other. If players have some information about the choices of other players, the game is usually presented in extensive form.

Extensive form

Extensive form games attempt to capture games with some important order. Games here are presented as trees (as pictured to the left). Here each vertex (or node) represents a point of choice for a player. The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action for that player. The payoffs are specified at the bottom of the tree.

In the game pictured here, there are two players. Player 1 moves first and chooses either F or U. Player 2 sees Player 1′s move and then chooses A or R. Suppose that Player 1 chooses U and then Player 2 chooses A, then Player 1 gets 8 and Player 2 gets 2.

Extensive form games can also capture simultaneous-move games as well. Either a dotted line or circle is drawn around two different vertices to represent them as being part of the same information set (i.e., the players do not know at which point they are).

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Another variant of Texas hold ‘em that is quite popular and complex is Omaha hold’em. Briefly, each player is dealt four cards to his private hand instead of two. The betting rounds and layout of community cards are identical. At showdown, each player’s hand is the best five-card hand he can make from exactly three of the five cards on the board, plus exactly two of his own cards. Unlike Texas hold ‘em, a player cannot play only one of his cards with four of the board, nor can he play the board, nor play three from his hand and two from the board, or any other combination. Each player must play exactly two of his own cards with exactly three of the community cards.

The most popular form of the game is high-low split, called “Omaha/8 or better”, or just “Omaha/8″. Each player, using the above rules, makes a separate five-card high hand and five-card low hand, and the pot is split between the high and low (which may be the same player). To qualify for low, a player must be able to play an 8-7-6-5-4 or lower. A few casinos play with a 9-low qualifier instead, but this is rare. This game is generally played at fixed limit.

When high hands only are used, the game is generally called “Omaha high” to avoid ambiguity. This game plays particularly well at pot limit, called “PLO”.

Another variant is to deal each player five cards instead of four. The same rules apply for showdown: each player must use two of his cards with three of the community cards.

In the game of “Courcheval”, popular in Europe, instead of betting on the initial four cards and then flopping three community cards for the second round, the first community card is dealt before the first betting round, so that each player has four private cards and the single community card on his first bet. Then two more community cards are dealt, and play proceeds exactly as in Omaha.

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Though called “stud”, this is a combination stud/community card game that was popular at MIT in the 1960s, in which players receive individual downcards, individual upcards, and community cards. Many variations on this are possible by changing what kinds of cards and how many are dealt in various rounds.

One difficulty with such a combination is deciding the betting order: in stud games, the player with the best upcards showing bets first in each round (except sometimes the first, where the worst upcard is forced to begin the betting with a Bring-in). In community card games, each betting begins with the same player (because there generally are no upcards), making it more positional. Oxford stud chooses to use the players’ individual upcards for determining order, which makes it play more like stud.

First, each player is dealt two downcards and one upcard as in seven-card stud, followed by a first betting round. Like stud, the game is usually played with a Bring-in, the lowest upcard being forced to pay it, and betting follows after that. After the first round is complete, two community cards are dealt to the table, followed by a second betting round, beginning with the player with the highest-ranking incomplete poker hand (as in stud) made from his upcard plus the two community cards. For example, if one player has a K upcard, and a second player has a 7 upcard, and the community cards are T-7 (T = 10), the second player bets first (since he has a pair of 7s, and the other player only has K-high). Then a second upcard is dealt to each player, followed by a third betting round, again beginning with the player who can make the best partial hand with his two upcards and the board. Finally, a third community card is dealt to table, followed by a fourth betting round and showdown. Note that as with Mississippi stud, each player has five cards of his hand exposed at this point (two of his own plus three on the board), so it is possible for a flush or straight to be the high hand for the purpose of first bet. At showdown each player makes the best five-card hand he can from the four cards he is dealt plus the three community cards, in any combination. This game is usually played High-low split.

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This is the most popular community card game today. Each player is dealt two private cards, after which there is a betting round. Then three community cards are dealt face up (in no particular order or pattern), followed by a second betting round. A fourth community card is followed by a third betting round, a fifth community card and the fourth and final betting round. At showdown, each player plays the best five-card hand he can make using any five cards among the two in his hand and the five on the board.

Texas hold ‘em does not play well high-low split (Omaha hold’em is probably the best high-low community card game). It plays very well at no limit, and in fact the “main event” of the World Series of Poker, the tournament generally considered to be the world championship of the game of poker, is the $10,000 entry no limit Texas hold ‘em event.

Pineapple (and Crazy Pineapple, Tahoe)

These are variants of Texas hold ‘em in which each player is initially dealt three cards instead of two. In Pineapple, each player then immediately discards one of the three cards he is dealt, and the game proceeds exactly as in Texas hold ‘em. In Crazy Pineapple, the players discard their third card after the second betting round, before the fourth community card is dealt. In Tahoe, players keep all three cards through showdown, but may not use all three of them to make a hand—each player may use none, one, or two cards from his hand, combined with those on the board, to make his final five-card hand.

Crazy Pineapple and Tahoe are often played high-low split, and play reasonably well that way, though plain Pineapple does not.

Double-board hold’em

A split-pot variant that can be applied to many games (but that is generally only applied to normal hold’em) is “double-board”. For double-board hold’em, two separate five-card boards are dealt, and the high hand using each board takes half of the pot. For example, after the first betting round, three community cards are dealt to each of two separate boards; after the second round, another community card is dealt to each board; and before the final round, a fifth community card is dealt to each board (so there will be in total ten community cards, comprising two separate five-card hold’em boards).

This variant of Texas Hold’em is sometimes called “double-flop hold’em”, which is a bit of a misnomer, since there are not just two flops, but also two turns and two rivers.

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