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Poker hands in five-card draw: Flush, Straight, Three of a kind, Two pair, One pair, High card

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Flush

A diamond king-high flush: K 10 8 4 3

The flush consists of five identical suit cards (not all within a sequential rank, otherwise it is a straight flush). The strongest color is the one that contains the highest ranking card. The color is a fairly strong game, giving a probability of significant gain (served or in a second round): 86% (32 cards) to 90% (52 cards), this is a hand a little weaker than the “one against ten” .

Its probability of occurrence is of the order of percent, and decreases with the number of card (unlike other figures) from 0.58% for 32 cards to 1.01% to 52 cards. Flush is served once in five, and is due to the improvement of a draw in the other cases.

Straight

A eight-high straight: 8 7 6 5 4

The straight consists of five cards of consecutive ranks (and not all the same color, if it is a straight flush). In the case of two straights, it is the high of the straights that allows the tie. If the straight 5 4 3 2 A is accepted (“white” straight), it is the lowest straight.

If all draws to straight were tempted, the straight would be twice as frequent: 9.2% to 32 cards, 1.6% to 52 cards, obtained one in five served, half the time by simply drawing, and by bilateral drawing in 30% of cases. However, simply draw reaches the straight once in ten, which on average is enough to stay in the game.

If simple drawings are not tempted in the second round, the straight becomes a little less frequent than the full house, 4.1% to 32 cards, and 0.8% for 52 cards. The straight is then served half the time.

“White” straight or “wheel”

A five-high “white” straight: 5 4 3 2 A

Although the Ace is the highest card, it can sometimes be used to begin or end a straight.

• Initially, with Ace/Two/Three/Four/ Five to form the lower straight called “white straight” or “wheel”.
• In the end, with Ten/Jack/Queen/King/Ace to form the largest known straight “Ace-high”.

To note that :

• Not all players accept this rule and some do recognize only the high value of the ace that its superior to the King. Before playing, it is appropriate to ask whether the white straights are accepted at the table.
• This convention is natural only with 52 cards. If the game is played with a truncated deck of cards (32 cards, for example), then the Ace is by convention inferior to the smallest (it is “Ace” or “six” in a deck of 32 cards).
• A straight flush can be “white” according to the same conventions.

The straight is the last “served” strong hand, which can not be improved. Its expected value (served or not) is 80% (32 cards) to 84% (52 cards), one against five. Although forming a strong hand, a straight remains vulnerable, which may prompt the holder to revive the auction to eliminate competition in intermediate games that can be improved.

Three of a kind

Three of a kind: K K K Q 5

Three of a kind is formed by three cards of the same rank, the other two being of any rank (otherwise, it is a four of a kind or a full house). The best three of a kind is the highest rank.

Three of a kind is a figure relatively common, 6.6% for 52 cards (one in twenty) and 14% for 32 cards (one in seven): three of a kind will (in theory) be to this table once every three turns . It is used in 30% of cases, and is due to the improvement of a pair the remaining time.

The served three of a kind gives an expected gain of 70% (32 cards) to 74% (52 cards), this probability drops only one percent if three of a kind is defaced (making it an excellent option).

The served three of a kind can be improved by asking two cards or simply one (three of a kind defaced). It improves in 10% (52 cards) to 20% (32 cards) of the case to form a full house or four of a kind.

In the second round, the expected gain for three of a kind is somewhat lower: 64% (32 cards) to 71% (52 cards), reflecting the rise of other hands that could improve.

Two pair

Two pair, kins and eights: K K Q 8 8

Two pair is formed by two pairs (of different ranks, otherwise it is a four of a kind) and an other arbitrary card (of different rank of the previous two, otherwise it is a full house). The strongest two pair is the one with the highest rank, and in case of equality of the first pairs it is the second pair of the highest rank that wins. Otherwise, the fifth card, called the kicker makes the difference.

The two pair is obtained with a frequency of 9.7% (52 cards) to 18.1% (32 cards). It is a figure quite common, half more than the three of a kind. It is served in almost 50% of cases, and is due to the improvement of a simple pair otherwise.

A served two pair gives appreciable expected gain of 45% (32 cards) to 48% (52 cards), largely conditioned by its improvement or not to full house in the second round. A served two pair can be improved by requesting a card. The hand does not improve in 10% (52 cards) to 15% (32 cards) cases, to get a full house. In the second round, a simple two pair expectancy of gain is smaller, 37% (32 cards) to 44% (52 cards).

One pair

One pair, eights: 8 8 K Q 5

One pair is formed by two cards of the same rank, the other three being arbitrary. The highest pair is one of the highest rank, and if equal, the strongest hand is the one with the highest single card.

A one pair is obtained with a frequency ranging from 36% (for 52 cards) to 54% (for 32 cards). It is usually served, but in the second round it comes from an attempt to improve a draw in 20-40% of cases.

A one pair is only a relatively small chance of winning: of the order of one against four or five on average, which justifies not enter the game with a sufficiently strong pair. Served one pair can be improved by removing three cards, or by defacing (to make it look a served three of a kind). Without improvements, a one pair is very small hand in the second round, which has an expected gain of about 9%.

High card

High card, King: K Q 8 6 5

High card is when there is no figure. This is a unremarkable hand, whose value is simply the one of the highest card.

A “high card” has virtually no value. Typically this type of hand is encountered when someone attempted an unsuccessful draw, and continued to bluff till to “call” and denounced.

Two hands of “high card” shall be separated according to the best card of each hand. If players have the same high card, then we look at the second highest card in their hands (always knowing that a poker hand consists of 5 cards). For example, if player A has KQJ85 and player B has KQJ87, player B wins. Otherwise, if the hands are identical, the gains are shared. A “high card” at the opening gives only a minimal gain expectancy: 7% (52 cards) to 15% (32 cards).

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