Poker Dice Probability Full House
- Poker Dice Probability Calculator using the Monte Carlo Method 1. Problem Description The game of Poker Dice is a bit like standard poker but played with dice instead of cards. In this game, five fair dice are rolled. We will recognize one of seven different hands, in order of increasing value: 1. None alike: Five distinct die values occur.
- Probability and gambling have been an idea since long before the invention of poker. The development of probability theory in the late 1400s was attributed to gambling; when playing a game with high stakes, players wanted to know what the chance of winning would be.
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- The poker dice experiment consists of rolling 5 fair dice. Random variable (V) denotes the value of the hand. All distinct; one pair; two pair; three of a kind; full house; four of a kind; five of a kind; The value (V) is displayed on each update in the data table.
- Simple Dice Games. In this section, we will analyze several simple games played with dice—poker dice, chuck-a-luck, and high-low. The casino game craps is more complicated and is studied in the next section. The Dice Players by Georges de La Tour (c. For more on the influence of probability in painting, see the ancillary material on.
- Each one has an exact probability of 120 / 7776. Under these rules, a Straight beats a Full House (unlike in card poker, but correctly reflecting its probability) but does not beat Four of a Kind (incorrectly reflecting its lower probability). A Flush beats Four of a Kind (as in card poker, and correctly reflecting its lower probability).
The game of poker is a card game played among two or more players for several rounds. There are several varieties of the game, but they all tend to have these aspects in common: The game begins with each player putting down money allocated for betting. During each round of play, players are dealt cards from a standard 52-card deck, and the goal of each player is to have the best 5-card hand at.
Poker dice are dice which, instead of having number pips, have representations of playing cards upon them. Poker dice have six sides, one each of an Ace, King, Queen, Jack, 10, and 9, and are used to form a poker hand.
Each variety of poker dice varies slightly in regard to suits, though the ace of spades is almost universally represented. 9♣ and 10♦ are frequently found, while face cards are traditionally represented not by suit but instead by color: red for kings, green for queens and blue for jacks. Manufacturers have not standardized the colors of the face sides. The game can also be played with ordinary dice.
As a game[edit]
Craps Dice Probability
The classic poker dice game is played with 5 dice and two or more players. Each player has a total of 3 rolls and the ability to hold dice in between rolls. After the three rolls, the best hand wins.
In most variations, a straight only counts as a Bust (high-card). A Straight is less probable than a Full House, so, if counted, it should rank above a Full House, though tradition usually ranks it below Full House, as in card poker. Neither a 'flush' nor a 'straight flush' is a possible hand, due to the lack of suits on the dice.
In some rules, only a straight to a King is called a Straight, while a straight to an Ace is called (somewhat incorrectly) a Flush. Each one has an exact probability of 120 / 7776. Under these rules, a Straight beats a Full House (unlike in card poker, but correctly reflecting its probability) but does not beat Four of a Kind (incorrectly reflecting its lower probability). A Flush beats Four of a Kind (as in card poker, and correctly reflecting its lower probability).
Probabilities[edit]
The poker dice hand rankings and the corresponding probabilities of rolling that hand are as follows[1][2](not sorted by probability but from highest to lowest ranking):
| Hand | Exact probability | Percentage | 1 in .. | Example |
|---|---|---|---|---|
| Five of a kind | 6 / 7776 | 0.08% | 1296 | J J J J J |
| Four of a kind | 150 / 7776 | 1.93% | 51.8 | 10 10 10 10 A |
| Full house | 300 / 7776 | 3.86% | 25.9 | K K K 9 9 |
| Straight | 240 / 7776 | 3.09% | 32.4 | A K Q J 10 |
| Three of a kind | 1200 / 7776 | 15.43% | 6.5 | 9 9 9 K J |
| Two pair | 1800 / 7776 | 23.15% | 4.3 | Q Q 9 9 A |
| One pair | 3600 / 7776 | 46.30% | 2.2 | 10 10 K Q 9 |
| Bust (high card; no pair, no straight) | 480 / 7776* | 6.17% | 16.2 | A K Q J 9 |
*Busts have much lower probability than in card poker, because there are only 6 values instead of 13, making pairs and straights much more likely than with cards. In poker dice there are in fact only four possible bust hands: [A K Q J 9], [A K Q 10 9], [A K J 10 9], and [A Q J 10 9]; both other no-pair hands (i.e., in which either the A or the 9 are missing) are straights. Consequently, in some variants of the rules, straights are counted as busts.[3]
Variants[edit]
Marlboro once marketed a set of octahedral poker dice that included suits; each die had slightly different numberings, ranging from 7 up to ace. A similar set is currently manufactured by Koplow Games.[4][5]
In 1974 Aurora produced a set of 12-sided poker dice called 'Jimmy the Greek Odds Maker Poker Dice'[6] and in 2000 Aurora/Rex Games produced a similar set under the name 'Royal Poker Dice'.[7] The sets featured five 12-sided dice allowing for all 52 playing cards to be represented. The remaining 8 faces featured stars and acted as wild cards allowing for every possible poker hand to be rolled.
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See also[edit]
Dice Probability Table
References[edit]
- ^Deep, Ronald (2006), Probability and statistics with integrated software routines, Elsevier Inc., ISBN0-12-369463-9Chapter 1 p 42
- ^Bărboianu, Cătălin (2006), Probability Guide to Gambling: The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets, INFAROM Publishing, p. 224, ISBN973-87520-3-5Extract of page 224
- ^Arneson, Erik (2012). 'The Complete Rules for the Dice Game Poker Dice'. About.com. New York Times Company. 'Board / Card Games' subsite. Archived from the original on 2014-04-12.CS1 maint: unfit url (link)
- ^Koplow Games
- ^8-sided poker dice on BoardGameGeek.com
- ^Jimmy the Greek Odds Maker Poker Dice on BoardGameGeek.com
- ^Royal Poker Dice on BoardGameGeek.com
External links[edit]
Probability In Poker
- Rules for Dice Poker at BrainKing.com (similar to Yahtzee)
- Arneson, Erik (2012). 'The Complete Rules for the Dice Game Poker Dice'. About.com. New York Times Company. 'Board / Card Games' subsite. Archived from the original on 2014-04-12.CS1 maint: unfit url (link) (no straights)
- Poker dice at Britannica.com