1. Poker Dice Probability Full House Rules
2. Poker Probability Formulas

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.

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Poker Dice Probability Full House Rules

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]

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):

^*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.

See also[edit]

References[edit]

1. ^Deep, Ronald (2006), Probability and statistics with integrated software routines, Elsevier Inc., ISBN0-12-369463-9Chapter 1 p 42
2. ^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
3. ^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)
4. ^Koplow Games
5. ^8-sided poker dice on BoardGameGeek.com
6. ^Jimmy the Greek Odds Maker Poker Dice on BoardGameGeek.com
7. ^Royal Poker Dice on BoardGameGeek.com

External links[edit]

• 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

The odds of flopping a full house with a pocket pair is 0.98% or 1 in 102

Definition of Full House (also known as a Boat or Full Boat) –

Three cards of one rank and two cards of another. (I.e. three of a kind and a pair made at the same time).

Example – AdAhAsKcKh

Aces Full of Kings the strongest Full House hand in poker and is also referred to as “Aces Full”.

Odds of Making a Full House on the Flop

Full Houses are rare in poker. Hitting on the flop is hence not a common occurrence.

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Odds of flopping a Full House with any starting hand = 0.14%

Odds of flopping a Full House with any unpaired hand = 0.09%

Odds of flopping a Full House with a pocket pair = 0.98%

To put that into context;

A pocket pair will hit a Full House roughly once every 100 flops. An unpaired hand will hit a Full House once every 1,000 flops. Ignoring the exact starting hand, we should expect to flop (on average) one Full House for every 714 flops we see.

Assuming about 25% of our holdings see a flop, we should expect to flop a Full House once every 2,857 hands.

Of course, the above calculation is just an average, sometimes we’ll flop more often, other times less frequently.

The odds of making a Full House or better should not change drastically, because there simply aren’t that many better hands than a Full House.

Odds of flopping a Full House or better with any starting hand = 0.17

Odds of flopping a Full House or better with AKo = 0.1%

Odds of flopping a Full House or better with T9s = 0.12%

Odds of flopping a Full House or better with 88 = 1.22%

We can see that a pocket pair is by far our best shot at being able to make a Full House or better, hitting roughly 10 times as often as unpaired hands.

Odds of Making a Full House on the Later Streets

There are generally two main types of Full House draw postflop -

1) We have a Two Pair and are drawing for one of our Pairs to make trips.
2) We have Three of a Kind and are hoping that we make a Pair.

Scenario 1 is the easiest since we know exactly which cards we are waiting to Pair.

Example 1

Flop: KT7
Our Hand: KT

We already have two pair and can either catch a King or a Ten to make a Full House. There are two Tens and two Kings left in the deck, giving us a total of four possible outs.

Odds of hitting on the turn = 4/47 = 0.0851 or roughly 8.5%

Odds of hitting on the river = 4/46 = 0.087 or roughly 8.7%

Odds of hitting on the turn or river (we’ll calculate Odds of not hitting then deduct from 100).

Odds of not hitting on the turn = 43/47

Odds of not hitting on the river = 42/46

Odds of not hitting on the turn or river = 43/47 * 42/46 = 0.8353 or roughly 83.5%

Odds of hitting is, therefore (100 – 83.5) roughly 16.5%

Scenario 2 is a little bit tougher since we can also make a Full House if the board pairs.

Example 2

Flop KT7
Our Hand: TT

We already have Three of a Kind here and simply need any other card to pair. Either the King or Seven could pair for a total of 6 outs. It’s also worth considering that we can catch the case Ten (one out) to make Quads.

Assuming the turn bricks, it still puts another card out there that can pair by the river. In other words, unlike the previous example, we are guaranteed to pick up additional outs on the turn if we don’t hit.

Odds of hitting on the turn (including Quads) = 7/47 = 0.1489 or roughly 15%

Odds of hitting on the river (including Quads) = 10/46 = 0.2174 or roughly 21.7%

We are noticeably more likely to hit our Full House going from turn to river.

Odds of hitting on the turn or river (we’ll calculate Odds of not hitting then deduct from 100).

Odds of not hitting on the turn (including Quads) = 40/47

Odds of not hitting on the river (including Quads) = 36/46

Odds of not hitting on the turn or river = 40/47 * 36/46 = 0.6660 or roughly 66.6%

Odds of hitting by the river are hence (100-66.6) roughly 33.4%

Poker Probability Formulas

Implied Odds Analysis of a Full House

Like most other strong hands, the value of the implied odds depends much on the relative strength of the holding. There are strong Full Houses and weak Full Houses.

Keep in mind the following -

Overfull/Underfull – The terms “overfull” and “underfull” are used to describe nut and non-nut Full Houses, respectively. For example, on an 8-8-7 board, 87 is the overfull while 77 is the underfull.

In most cases, it’s just a cooler if these hands run into each other, but technically the two-card overfull carries better-implied odds than the two-card underfull.

One-Card/Two-Card – The issue of overfull/underfull becomes even more pronounced when we are dealing with one-card Full Houses (i.e. using only one of our hole cards to create the hand).

On a TT77x any Tx is the overfull while any 7x is the underfull. Seeing as it’s simply much more common that any player would have a Full House on a double-paired texture, the one-card underfull needs to be treated with caution.

The one-card underfull is actually more likely to generate reverse implied odds than implied odds due to the high possibility it is dominated if Villain wants to get the stacks in.

Basic Strategy Advice

Full Houses are ultra-strong hands in Hold’em and should nearly always be stacked off for 100bb stacks. The only exception is really the one-card underfull. This is still a relatively strong hand, but we’ll likely try and avoid getting all of the stacks in when facing aggression.