Poker Hand Ranking

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Mathematics of Poker (Part 1)

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In high-low split games, both the highest-ranking and lowest-ranking hands win, though different rules are used to rank the high and low hands. Each hand falls into a hand-ranking category determined by the patterns formed by its cards.

Hands in a higher-ranking category always rank higher than hands in a lower-ranking category. Hands in the same category are ranked relative to each other by comparing the ranks of their respective cards.

There are nine hand-ranking categories when using a standard card deck , except under ace-to-five low rules where straights, flushes and straight flushes are not recognized. An additional category, five of a kind, is introduced when using one or more wild cards. The fewer hands a category contains, the higher its rank.

It ranks above a straight flush but is only possible when using one or more wild cards, as there are only four cards of each rank in a standard card deck. Each five of a kind is ranked by the rank of its quintuplet. Under high rules, an ace can rank either high e. There are 40 possible straight flush hands and 10 distinct ranks of straight flush under high rules when using a standard card deck.

It ranks below a straight flush and above a full house. There are possible four of a kind hands and distinct ranks of four of a kind when using a standard card deck. There are 3, possible full house hands and distinct ranks of full house when using a standard card deck.

There are 5, possible flush hands and 1, distinct ranks of flush under high rules when using a standard card deck. It ranks below a flush and above three of a kind. There are 10, possible straight hands and 10 distinct ranks of straight under high rules when using a standard card deck. It ranks below a straight and above two pair. There are 54, possible three of a kind hands and distinct ranks of three of a kind when using a standard card deck.

In community card games, such as Texas hold 'em, three of a kind is called a set only when it comprises a pocket pair and a third card on the board. For a detailed explanation of the video poker scene in Macau, please visit my companion site, Wizard of Macau. Often Internet casinos will match a deposit with free money.

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The only casino in southern Nevada that I know of to still offer table 1 is the Pioneer in Laughlin. Bovada offers pay table 1 in its online casino. In some casinos added a "Mini Royal" to the pay table. The following two pay tables show the house edge of various Pairplus pay tables, both with and without the Mini Royal.

In case you're wondering, tables 9 and 10 can be found at Internet casinos using Gamesys N. The lower left cell shows an expected loss of -.

So the house edge of the combined bet would be -. Overall betting equally on the Ante and Pairplus on the pay tables stated above the probability of a win is I have seen two versions of the progressive side bet in Three Card Poker. Both versions also feature an envy bonus if another player gets a royal flush. All wins are on a "for one" basis, in other words the player does not get back his original wager, even if he wins.

The return depends on the jackpot amount and number of other players. To be specific, it is The most notable difference compared to version 1 is that version 2 pays for a straight as well. It is based on the player's three cards and two other cards. I am not sure which other two cards are used, as the table was closed at the time I saw it. The following table shows the pay table. Wins are on a "for one" basis. The "6 Card Bonus" is a side bet based on the highest five-card poker hand that can be composed out of the player's and dealer's three cards.

It is most likely to be found at Caesars Entertainment casinos. I've seen or heard of three possible pay tables. The lower right cell shows a house edge of Millionaire Maker is a six-card side bet that I have seen at lots of casinos owned by Caesars Entertainment, beginning about

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