Card Poker

Poker, card game, played in various forms throughout the world, in which a player must call (i.e., match) the bet, raise (i.e., increase) the bet, or concede (i.e., fold).Its popularity is greatest in North America, where it originated.It is played in private homes, in poker clubs, in casinos, and over the Internet.Poker has been called the national card. Three Card Poker is played with a single 52-card deck and is actually two games in one. First, the Pair Plus game allows players to wager on whether they will be dealt a Pair or better, or not. Secondly, the Play/Ante game allows players to wager against the house (dealer) to see who has the highest hand.

Here are the rules of the game: you and the computer each get one cardand ante $1. You bet first, either $0 or $1. Then the computergets a chance to match you (if you bet $1) or raise you (if you bet$0). If you bet $0 and the computer raised you, you get a chanceto call. Betting $0 when your opponent has already bet $1 meansyou fold and lose your ante. If no one folds before the end ofbetting, the higher card wins the pot; that results in a net gain ofeither $1 or $2, equal to the other player's ante plus the bet of $0or $1.

One-card poker is a simple game; nonetheless it has many of theelements of more complicated games, including incomplete information,chance events, and multiple stages. And, optimal play requiresbehaviors like randomization and bluffing. The biggest strategicdifference between one-card poker and larger variants such as draw,stud, or hold-em is the idea of hand potential: while 45679 and 24679are almost equally strong hands in a showdown (they are both 9-high),holding 45679 early in the game is much more valuable becausereplacing the 9 with either a 3 or an 8 turns it into astraight. In other words, hands need to be evaulated accordingto both their current value and the possibility that they might becomemore valuable.

Even the simple game of one-card poker is difficult to solveoptimally: the first efficient solution that I know of is presented in[Kollerand Pfeffer, 1995]. That paper applies the sequencerepresentation of extensive form games to one-card poker. Beforethe invention ofthe sequence form, the standard algorithm was to convert the game toits normal form, which is exponentially large in the size of thedeck.

For this page, we are using a single-suit (13-card) deck. Withthis deck size, the normal form has 2^26 (about 67 million) purestrategies per player. By contrast, the sequence form has only26 information states and 52 sequences per player. Real-worldpoker variants are much larger, with many more information states thancould possibly fit in memory. Even so, modern techniques(which include trickslike grouping together sets of similar hands and ignoring some of thecoupling between very early and very late rounds of betting) can nowfind approximately-optimal solutions for games like two-player Texashold-em.

If you play optimally, you should be able to keep your losses down toabout 6.4 cents per deal on average. To limit your performanceto this level, the computerized second player plays according to thebetting tables below. By contrast, if the computer decidedwhether to bet by flipping a coin without looking at its card, youcould win up to 50 cents per deal on average. These tables werecomputed in Matlab by solving a small linear program generated fromthe sequence form of the game tree. (Getthe source.) The tables are not unique; theanswer we compute depends on the details of the linear programmingsolver we use. (SamGanzfried pointsout, interestingly, that there are other equilibrium strategies thatweaklydominate this one (perform better against some opponents withoutperforming worse against any): e.g., in the tables we calculated,player 1 never bets first holding a 5-8. So when we are decidingwhether to call a bet, our hands 5-8 are completelyequivalent—the opponent must have something lower than a 5 orhigher than an 8. Because of this equivalence, the LP solverchose arbitrarily how to distribute the bets we make on thesehands. But we can take any bets we'd make on a low hand like a 5and move them to happen on a higher hand like an 8; doing so doesn'tchange our performance against this particular opponent, but strictlyimproves our performance against any opponent who happens to bet firstholding 5-8. In particular, since we can only improve ourpayoff, the new strategy is still an equilibrium; and since there aresome opponents where we actually do improve our payoff, the newstrategy weakly dominates the current one.)

Here is the betting table for player 2. To use it, look upplayer 2's card in the column headers. Then choose a rowaccording to whether player 1 bet or passed. The correspondingentry says how often to bet: for example, 0.632 means bet 63.2% of thetime.

In case you're interested, here is the analogous betting table forplayer 1. You can play optimally using just this table and a1000-sided die. The first row says how often to bet in thefirst round; the second row says how often to bet if you passed in thefirst round and the computer raised to $1.

Here are the betting tables plotted as graphs:

Notice that these strategies contain interesting behaviors such asbluffing (for example, player 2 always bets holding a 2 if player 1passes) and slow-playing (for example, player 1 doesn't always bet onthe first round even if he holds an ace).

Poker, or five card draw

Five card draw is one of the oldest forms of poker, which emerged in New York salons with the outbreak of the Civil War. Today, it remains popular with all on the internet, thanks to our version of 5 card draw online, recommended especially for novice poker players.

Five card draw is only up to two hands

Some admit that the short duration of an entire game now means that they play five card draw extremely rarely in casinos. Some other poker games have probably contributed to a reduction in the number of players and fans of the game. However, nothing is lost! The younger brother of these cult card games has moved to another more fertile and progressive ground of online games. Fans from all over the world constantly return to play the game. Short games are in this case the advantage of five card draw online, because many people are looking for uncomplicated fun, and have no time to play an extended an nerve-wracking game of ordinary poker. Five card draw is simpler than today's popular poker variations and known to many people in the amateur game, from playing at the table in their homes with family or friends.

One-card poker is a simple game; nonetheless it has many of theelements of more complicated games, including incomplete information,chance events, and multiple stages. And, optimal play requiresbehaviors like randomization and bluffing. The biggest strategicdifference between one-card poker and larger variants such as draw,stud, or hold-em is the idea of hand potential: while 45679 and 24679are almost equally strong hands in a showdown (they are both 9-high),holding 45679 early in the game is much more valuable becausereplacing the 9 with either a 3 or an 8 turns it into astraight. In other words, hands need to be evaulated accordingto both their current value and the possibility that they might becomemore valuable.

Even the simple game of one-card poker is difficult to solveoptimally: the first efficient solution that I know of is presented in[Kollerand Pfeffer, 1995]. That paper applies the sequencerepresentation of extensive form games to one-card poker. Beforethe invention ofthe sequence form, the standard algorithm was to convert the game toits normal form, which is exponentially large in the size of thedeck.

For this page, we are using a single-suit (13-card) deck. Withthis deck size, the normal form has 2^26 (about 67 million) purestrategies per player. By contrast, the sequence form has only26 information states and 52 sequences per player. Real-worldpoker variants are much larger, with many more information states thancould possibly fit in memory. Even so, modern techniques(which include trickslike grouping together sets of similar hands and ignoring some of thecoupling between very early and very late rounds of betting) can nowfind approximately-optimal solutions for games like two-player Texashold-em.

If you play optimally, you should be able to keep your losses down toabout 6.4 cents per deal on average. To limit your performanceto this level, the computerized second player plays according to thebetting tables below. By contrast, if the computer decidedwhether to bet by flipping a coin without looking at its card, youcould win up to 50 cents per deal on average. These tables werecomputed in Matlab by solving a small linear program generated fromthe sequence form of the game tree. (Getthe source.) The tables are not unique; theanswer we compute depends on the details of the linear programmingsolver we use. (SamGanzfried pointsout, interestingly, that there are other equilibrium strategies thatweaklydominate this one (perform better against some opponents withoutperforming worse against any): e.g., in the tables we calculated,player 1 never bets first holding a 5-8. So when we are decidingwhether to call a bet, our hands 5-8 are completelyequivalent—the opponent must have something lower than a 5 orhigher than an 8. Because of this equivalence, the LP solverchose arbitrarily how to distribute the bets we make on thesehands. But we can take any bets we'd make on a low hand like a 5and move them to happen on a higher hand like an 8; doing so doesn'tchange our performance against this particular opponent, but strictlyimproves our performance against any opponent who happens to bet firstholding 5-8. In particular, since we can only improve ourpayoff, the new strategy is still an equilibrium; and since there aresome opponents where we actually do improve our payoff, the newstrategy weakly dominates the current one.)

Here is the betting table for player 2. To use it, look upplayer 2's card in the column headers. Then choose a rowaccording to whether player 1 bet or passed. The correspondingentry says how often to bet: for example, 0.632 means bet 63.2% of thetime.

In case you're interested, here is the analogous betting table forplayer 1. You can play optimally using just this table and a1000-sided die. The first row says how often to bet in thefirst round; the second row says how often to bet if you passed in thefirst round and the computer raised to $1.

Here are the betting tables plotted as graphs:

Notice that these strategies contain interesting behaviors such asbluffing (for example, player 2 always bets holding a 2 if player 1passes) and slow-playing (for example, player 1 doesn't always bet onthe first round even if he holds an ace).

Poker, or five card draw

Five card draw is one of the oldest forms of poker, which emerged in New York salons with the outbreak of the Civil War. Today, it remains popular with all on the internet, thanks to our version of 5 card draw online, recommended especially for novice poker players.

Five card draw is only up to two hands

Some admit that the short duration of an entire game now means that they play five card draw extremely rarely in casinos. Some other poker games have probably contributed to a reduction in the number of players and fans of the game. However, nothing is lost! The younger brother of these cult card games has moved to another more fertile and progressive ground of online games. Fans from all over the world constantly return to play the game. Short games are in this case the advantage of five card draw online, because many people are looking for uncomplicated fun, and have no time to play an extended an nerve-wracking game of ordinary poker. Five card draw is simpler than today's popular poker variations and known to many people in the amateur game, from playing at the table in their homes with family or friends.

In five card draw online, strategy counts

Card Poker Rules

Another advantage of five card draw is the emphasis on strategy. Here you can forget about the myth of lucky cards, and count only on your skills and mental acuity. It is possible to win chips from the table with a weak hand, or to lose holding a strong one. Therefore it is worth familiarizing yourself with the basics of poker variants, for against more experienced opponents there would be no chance of winning. However, any beginner is recommended to play five card draw as often as possible. After all, as the well-known saying goes, 'practice makes perfect', and tricks gleaned from better players can help you to win. Contrary to appearances the rules themselves are not that difficult, and the action takes place very quickly, so even the most demanding five card draw online player will not be bored. In addition, online practice is the best opportunity to learn to play poker safely, without the risk or fear of losing your money.

How to play five card draw?

The key to winning is to have five cards that make up the best combination among all the players, known as the best hand. The trick to playing five card draw is to have a good strategy alongside the ability to bluff perfectly. It is not only the person with the best cards who can win – but also the player who can confuse their opponent effectively.

Before the cards are dealt the player on the immediate left of the dealer is required to pay the the small blind, and the next player the big blind. This determines the stakes on a given table. For example, if the small blind is $1, the big blind will be $2. Once each player in the game has been dealt five cards, the first round of betting starts. Each player from the big blind onwards must bet a higher amount to stay in the hand, call, or fold. The player who posted the big blind makes the last move. Later, everyone has the opportunity to exchange up to four cards. After betting, the players who remain at the table reveal their hands. The winning hand consists of the strongest cards. In the hierarchy of poker hands, the royal flush is the highest. This is made up of five cards: ten, jack, queen, king and ace of the same suit, for example diamonds.

Try your hand at five card draw online

Card Poker Games

Interested in the game? On GameDesire, don't be a fish – a well-known term in the poker world for a beginner, just starting their adventure in card games. Experience in five card draw can bring you a lot of respect from other players, as well as sizeable winnings.