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Poker hands in five-card draw poker – Straight flush, Four of a kind and Full house

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Draw Poker

In the classic game (without joker or added cards) the hands, or possible combinations, of the lowest to highest, are:

  • No combination or draw,
  • Current games that can be improved: Pair < Two pair < Three of a kind,
  • Strong games: Straight < Flush < Full house (Full)
  • Four of a kind < Straight Flush (“five stars” game, practically unbeatable).

Straight flush

Royal Flush: A K Q J 10

Straight flush consists of five cards whose ranks follow and whose colors are identical. This is the highest possible hand in poker. This is both a straight and a flush, virtually unbeatable. It can be beaten only by a stronger straight flush. If two straight flushes are competing, the stronger is the one whose rank is the highest. A straight flush entry gives a virtual certainty to win the game: 99.98% for eight players/52 cards, 99.94% for four players/32 cards.

Straight flush to eight: 8 7 6 5 4

The straight flush is an extremely rare hand, the order of “ten thousand”: 0.036% to 32 cards, 0.006% to 52 cards. It is served in one in five cases (21 to 22%), and results from a draw at the straight flush in other cases.

When a straight flush is served, it can not be improved.

Just as a normal flush, a straight flush can be “white” if the agreement is accepted to the table.

Straight flush called “royal” (royal flush), or sometimes “imperial” is a straight flush to the Ace: there is no hand that can beat her.

Four of a kind

Four of a kind: K K K K 3

Four of a kind (or poker) is formed by four cards of one rank accompanied by any other card. This is a major combination, virtually unbeatable. The strongest foir of a kind is the highest rank.

Four of a kind appears with a frequency below 1%: 0.96% to 32 cards, 0.23% to 52 cards. It is obtained directly in 10% of cases, and it comes by improving a pair (50% of cases) or three of a kind (40%).

However, these improvements draw assume that the pairs and the three of a kind are not made up, that is to say that the player actually takes three cards if he has a pair and two if he has three of a kind. If the player chooses instead to systematically support the pair (asking two cards) or his three of a kind (a card), the probability of having four of a kind halves to 0.46% to 32 cards and to 0.11% 52 cards, it is used once in four,  coming from three of a kind in 40% of cases, or a pair in 15% of cases.

When four of a kind is served, it can not of course be improved, but it is generally useful to apply for a card to make it looks like a weak hand or a draw.

The four of a kind served is a practically winning hand, a hundred against one: 98.97% (32 cards) and 99.50% (52 cards) hope to gain. The expected gain in the second round is virtually identical.

Since it can not be two four of a kind of the same rank, the fifth card is of no use unless except the four of a kind is on the table.

Full house (Full)

Full of kings to threes: K K K 3 3

Full house consists of three of a kind and a pair. The strongest full house is the one with the highest three of a kind (it can not be two full house of the same rank).

It appears with a frequency of some percents, from 4.5% for 32 cards to 1.1% for 52 cards. It is directly obtained by drawing once in seven (13%), and it result from the improvement of a double pair (40% of cases), a simple pair (in 35% of cases) or a three of a kind (11%) not disguised. Its frequency does not vary substantially when the pair and three of a kind are disguised. The many ways to get a full from other combinations are ultimately more frequently present in the second round as the straight, although the straight is easier to obtain by direct draw.

The expected gain of a full house (seved or in the second round) is very important: 90% (32 cards) to 96% (52 cards), it is in the “one against ten ” zone to “one against twenty “. So it’s a very strong, but not completely unbeatable game which the holder must remain cautious.

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