Poker Hand Matchups

Buy poker hand histories from HHSmithy. The best network coverage, super fast downloads, 6 download mirrors, and ridiculously low pricing. Some hands will only have two determining factors, like a straight. The first value would be a straight's spot in the rank of the poker hands (greater than 3 of a kind, less than a flush), and the second value would be the top card in the straight (7, jack, king, etc.).

1. Poker Hand Matchup Odds
2. Poker Hand Matchup Calculator
3. Poker Hand Matchups
4. Poker Hand Matchups

Rummoli is a family card game for 2 to 8 people. This Canadianboard game, first marketed in 1940 by the Copp Clark Publishing Company of Toronto^[1] requires a Rummoli board, a deck of playing cards (52 cards, no jokers), and chips or coins to play. The game is usually played for fun, or for small stakes (e.g. Canadian Dimes). Rummoli is one of the more popular versions of the Stops Group of matching card games^[2], in particular it falls into a subgroup of stops games based on the German Poch^[3] and falls into a family of Poch variants such as the French Nain Jaune(Yellow Dwarf), the Victorian Pope Joan but most like the American game Tripoley (a proprietary name, occasionally called by the generic Michigan rummy, but not to be confused with 500 rum) which debuted eight years earlier in Chicago in 1932.^[4][5]

Rummoli board[edit]

A Rummoli board, used during play, has the shape of an octagon. It is generally simply printed on a large sheet of paper.^{[citation needed]}

In the centre of the board is a pot called Rummoli, surrounded by eight pots:

• The poker pot
• Ten of spades
• Jack of diamonds
• Queen of clubs
• King of hearts
• Ace and King of diamonds
• Sequence 7-8-9 of any suit

Each of these pots on the board is used to store chips. The ordering of the pots around the board is not important.

Play[edit]

Ace is high. For brevity, in the following description the 'lowest card' means the lowest card in a player's hand or, if two or more cards are equally low, either or any of them.

A game is played in one or more rounds. The game ends at the end of a round, at the discretion of the players. For example, it may be agreed to finish at a certain time, or when all but one player have exhausted their chips.

Rounds[edit]

For each round, there are four stages: the Deal, the Poker phase, the Rummoli phase, and the End of round, which are played in sequence.

Deal[edit]

Before the cards are dealt, each player pays one chip to each pot on the Rummoli board.The dealer then deals around the table to every player, and an extra hand (in some terminology known as a ghost hand) called the widow.

• All cards are dealt, so some players may have one more card than others.
• Once this is completed all players look at their own hands.
• The widow hand can (at the dealer's wish) be swapped with the dealer's hand (must not be exchanged if his hand contains a pay card).
• If the dealer does not exchange hands, the widow hand is auctioned off to the highest bidder, who pays their bid to the dealer, and that player exchanges hands with the widow. Any player except the dealer may bid at any time (must not be exchanged if his hand contains a pay card)

Once the bid is accepted the player is committed to the exchange regardless if the widow is a poorer hand. The widow hand takes no further part in the play.

Poker phase[edit]

• The player to the left of the dealer starts off the betting, having the option to check.
• Betting continues in regular poker fashion.
• The remaining player with the best poker hand wins the poker pot and begins the Rummoli phase. He or she then 'plays' the lowest card in the hand. To play a card, the player states the card he or she is playing and puts it down in front of them. For example, if the lowest card in my hand is the 3 of hearts, I put the card down in front of me, say, 'three of hearts.' If I have the four of hearts, I would play that as well. If I have two 3s in my hand, I may choose either 3.

Rummoli phase[edit]

While this phase is being played if any player lays down a card corresponding to a pot such as Ace of Spades, the player picks up that pot. If a player places down a card that corresponds to a pot without realizing so, then the chips stay in the pot.

The player with the next card in the sequence of the suit must lay that card, and this continues with players laying cards until nobody has the card that follows in sequence (remember, some cards are missing from the spare hand that is not being played).

• If no one holds that next card (that is, it has already been laid or is in the widow hand) the player who last laid a card then lays the lowest card in a suit of the opposite colour (that is, hearts or diamonds if the last card was spades or clubs, and the other way about).
• Having laid an ace the next card in sequence is the lowest card in the opposite colour. The player who played the ace continues.
• A player not having a card of the required colour, the play then moves clockwise. If the next player also cannot play, this step repeats as necessary.<ref>If an impasse is reached (all players only have red cards), everyone counts their cards, and throws one chip/coin in the center pot for each card in their hand. The winner of the next hand collects both pots.

A card once laid takes no further part in the play.

End of round[edit]

The first player to have an empty hand wins the Rummoli pot.

• All other players must then pay one chip for each remaining card they hold.
• All pots that are not won remain on the board and accumulate in subsequent rounds.
  • The pots for 7-8-9 and Ace and King of Diamonds often accumulate over several rounds, since these combinations are less likely to be held by one player alone, and even if they are, another player may win the round before there is any chance to play them.

The deal shifts after each round, one player clockwise.

End of play[edit]

After the agreed end of the round play, all chips on the board are placed into one pot and a round of poker dealt and played for it. A variation is to play a round for each pot that still has chips in it, starting with the pot with the fewest chips.

The player with the most chips at the end of the game wins.

References[edit]

1. ^'Rummoli'. canadiandesignresource.ca. 20 June 2006. Retrieved 1 December 2009.
2. ^'Card Games: Stops Group'. Pagat.com. Retrieved 3 April 2020.
3. ^'Poch/Le Poque'. Pagat.com. Retrieved 3 April 2020.
4. ^'Tripoley Rummy Card Game'. AddA52.com. Retrieved 3 April 2020.
5. ^'Tripoli'. AddA52.com. Retrieved 3 April 2020.

POKER PROBABILITIES

• Texas Hold'em Poker
  Texas Hold'em Poker probabilities
• Omaha Poker
  Omaha Poker probabilities
• 5 Card Poker
  5 Card Poker probabilities

POKER CALCULATOR

• Poker calculator
  Poker odds calculator

POKER INFORMATION

• Poker hand rankings
  Ranking of poker hands

In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.

Frequency of 5-card poker hands

The following enumerates the (absolute) frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement. Wild cards are not considered. The probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand by the total number of 5-card hands (the sample space, five-card hands). The odds are defined as the ratio (1/p) - 1 : 1, where p is the probability. Note that the cumulative column contains the probability of being dealt that hand or any of the hands ranked higher than it. (The frequencies given are exact; the probabilities and odds are approximate.)

The nCr function on most scientific calculators can be used to calculate hand frequencies; entering ​nCr​ with ​52​ and ​5​, for example, yields as above.

The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1.

When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be. The 4 missed straight flushes become flushes and the 1,020 missed straights become no pair.

Poker Hand Matchup Odds

Note that since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. For example, the hand 3♣ 7♣ 8♣ Q♠ A♠ is identical to 3♦ 7♦ 8♦ Q♥ A♥ because replacing all of the clubs in the first hand with diamonds and all of the spades with hearts produces the second hand. So eliminating identical hands that ignore relative suit values, there are only 134,459 distinct hands.

The number of distinct poker hands is even smaller. For example, 3♣ 7♣ 8♣ Q♠ A♠ and 3♦ 7♣ 8♦ Q♥ A♥ are not identical hands when just ignoring suit assignments because one hand has three suits, while the other hand has only two—that difference could affect the relative value of each hand when there are more cards to come. However, even though the hands are not identical from that perspective, they still form equivalent poker hands because each hand is an A-Q-8-7-3 high card hand. There are 7,462 distinct poker hands.

Derivation of frequencies of 5-card poker hands

of the binomial coefficients and their interpretation as the number of ways of choosing elements from a given set. See also: sample space and event (probability theory).

• Straight flush — Each straight flush is uniquely determined by its highest ranking card; and these ranks go from 5 (A-2-3-4-5) up to A (10-J-Q-K-A) in each of the 4 suits. Thus, the total number of straight flushes is:
  • Royal straight flush — A royal straight flush is a subset of all straight flushes in which the ace is the highest card (ie 10-J-Q-K-A in any of the four suits). Thus, the total number of royal straight flushes is

    or simply . Note: this means that the total number of non-Royal straight flushes is 36.

• Four of a kind — Any one of the thirteen ranks can form the four of a kind by selecting all four of the suits in that rank. The final card can have any one of the twelve remaining ranks, and any suit. Thus, the total number of four-of-a-kinds is:

• Full house — The full house comprises a triple (three of a kind) and a pair. The triple can be any one of the thirteen ranks, and consists of three of the four suits. The pair can be any one of the remaining twelve ranks, and consists of two of the four suits. Thus, the total number of full houses is:

Poker Hand Matchup Calculator

• Flush — The flush contains any five of the thirteen ranks, all of which belong to one of the four suits, minus the 40 straight flushes. Thus, the total number of flushes is:

• Straight — The straight consists of any one of the ten possible sequences of five consecutive cards, from 5-4-3-2-A to A-K-Q-J-10. Each of these five cards can have any one of the four suits. Finally, as with the flush, the 40 straight flushes must be excluded, giving:

Poker Hand Matchups

• Three of a kind — Any of the thirteen ranks can form the three of a kind, which can contain any three of the four suits. The remaining two cards can have any two of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of three-of-a-kinds is:

• Two pair — The pairs can have any two of the thirteen ranks, and each pair can have two of the four suits. The final card can have any one of the eleven remaining ranks, and any suit. Thus, the total number of two-pairs is:

• Pair — The pair can have any one of the thirteen ranks, and any two of the four suits. The remaining three cards can have any three of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of pair hands is:

• No pair — A no-pair hand contains five of the thirteen ranks, discounting the ten possible straights, and each card can have any of the four suits, discounting the four possible flushes. Alternatively, a no-pair hand is any hand that does not fall into one of the above categories; that is, any way to choose five out of 52 cards, discounting all of the above hands. Thus, the total number of no-pair hands is:

• Any five card poker hand — The total number of five card hands that can be drawn from a deck of cards is found using a combination selecting five cards, in any order where n refers to the number of items that can be selected and r to the sample size; the '!' is the factorial operator:

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

Poker Hand Matchups

Home > 5 Card Poker probabilities