A deck of cards contains 52 cards in each of four suits.

Because no two cards in the deck are identical, the 120 different orders in which five cards can be arranged can be factored out of all the calculations of the ways in which a given type of hand can be initially dealt without problems.

There are various forms of the game of Poker, some of which affect the rankings of the hands in various ways. In the original form of Draw Poker, hands of five cards are ranked in the following order:

- Royal Flush
- Example: 10 J Q K A The 10, Jack, Queen, King, and Ace of any one suit. All suits rank equally. Can be formed in 4 ways.
- Straight Flush
- Example: 5 6 7 8 9Five cards in sequence of any one suit. A 2 3 4 5 ranks lowest, 9 10 J Q K ranks highest. Can be formed in 36 ways.
- Four of a Kind
- Example: J J J J 3 Four cards of the same rank, with one extra card. Rank depends on the rank of the cards in the combination. 2 2 2 2 3 ranks lowest, A A A A K ranks highest. Can be formed in 624 ways (13*12*4).
- Full House
- Example: 8 8 8 K K Three cards of one rank, and two cards of another rank. Rank depends on the rank which occurs three times. 2 2 2 3 3 ranks lowest, A A A K K ranks highest. Can be formed in 3,744 ways (13*12*4*6).
- Flush
- Example: 2 5 7 8 J Five cards all of the same suit, not forming a straight flush. Rank depends on the highest card, and then on the next highest, and so on. Can be formed in 5,108 ways ((((13 choose 5) minus 10) times 4, that is, (((13*12*11*10*9)/(5*4*3*2*1))-10)*4)
- Straight
- Example: 7 8 9 10 J Five cards in sequence, without being in the same suit. A 2 3 4 5 ranks lowest, 10 J Q K A, also counted as a straight, ranks highest. Can be formed in 10,230 ways (10*((4*4*4*4*4)-1)
- Three of a Kind
- Example: 4 4 4 7 Q Three cards of the same rank, plus two others that do not form a pair. Rank depends on that of the three cards in the combination. 2 2 2 3 4 ranks lowest, A A A Q K ranks highest. Can be formed in 54,912 ways (13*4*(12*4*11*4)/2)
- Two Pair
- Example: 10 10 8 8 5 Two cards of one rank, two cards of another rank, and one other of a third rank. Rank depends on the highest-ranking pair first, then the next highest-ranking pair, then the odd card. 2 2 3 3 4 ranks lowest, A A K K Q ranks highest. Can be formed in 123,552 ways ((((13*6)*(12*6))/2)*11*4)
- Pair
- Example: Q Q 4 7 9 Two cards of one rank, the other cards being of different ranks. Rank depends on the cards in the pair first, then the remaining cards, with the highest ranking one being the most significant. 2 2 3 4 5 ranks lowest, A A J Q K ranks highest. Can be formed in 1,098,240 ways ((13*6)*(12*4*11*4*10*4)/6)
- High Card
- Example: J 9 7 4 3 All combinations of cards which contain no pairs, are not all of the same suit or all in sequence. Rank depends first on the highest ranking card, and then on the next highest ranking card, and so on. 7 5 4 3 2 ranks lowest, A K Q J 9 ranks highest. Comprises all the remaining 1,302,540 possible hands.

The following is a rather brief summary of the rules of Poker, and may contain omissions and inaccuracies.

In Draw Poker, first each player places an amount, called the ante, usually from 1/4 to 1/5 of the normal unit of betting, into the pot. Then, each player is dealt five cards. The opportunity to bet passes around the table: once one player enters a bet, all the other players can then match the bet (call), quit the game (fold), or match the bet and add to it (raise). Betting continues until, after a player has either made the initial bet, or raised, all the other players have had the opportunity to either make an equal contribution to the pot or quit the game.

Then, each player may elect to replace any, all, or none of the five cards in his hand with cards freshly dealt.

After this, there is another round of betting, and then the hands of players still in the game are exposed with the player still in the game with the highest-ranking hand winning the amount in the pot.

Note that, as there are 52 cards in the deck, to afford each player the opportunity of replacing his complete hand, should that be desired, no more than five people can play a normal game of Draw Poker.

Note that in the ranking of hands above, the Ace ranks high in pairs, but ranks either high or low in a straight depending on how it is used. One variation of Poker is to stipulate that the Ace is always high or always low. Another is to allow an "elbow straight", such as Q K A 2 3. A common variation of Poker is "Jacks or better", which means that a player must have at least a pair of Jacks in his hand to make the opening bet. Also, the Joker may be left in the deck as a "wild" card, one that can stand for any other card, or one can play "deuces wild", where the four 2s can be used as if they are Jokers.

As well, there is stud poker, where some cards are dealt to the players face up, and left exposed during play, and there are variations (such as the recently popular Texas Hold 'Em variant) where one or more cards are exposed face up in the center of the table, and are considered part of every player's hand. In these variants, a player may have more than five cards available out of which to form the best-ranking five-card hand possible at the end of the game.

As noted in the title of this page, a poker table has room for eight people, but Draw Poker, by the standard rules, only allows up to five people to play.

One simple cure for that would be to use two identical decks of cards. This allows, like variations with a wild card, the hand of five of a kind to be formed, which outranks a royal flush.

It might be considered that three kings of different suits ought to outrank two kings of one suit, and a third king of another, the latter being inaesthetic as an "impossible" hand with a single deck.

If one does make use of that principle to allow finer gradations between hands, it occurs to me that one could get really fancy by using a deck of the following kind for Poker:

Five regular decks of cards, plus an additional 13 cards belonging to a fifth suit. This makes 273 cards; as that is an odd number, a Joker would probably also be included. (Note that having one Joker out of 274 cards would tend to promote luck rather than skill, though.)

This makes it possible to have a five-of-a-kind where all five cards also belong to the same suit, since the deck has five regular decks in it, and it also makes it possible, due to the fifth suit, to have a five-of-a-kind with five different suits.

Let us consider five of a kind with some suits, but not others, occuring more than once as a "mixed" five of a kind, one with each suit occuring once as a "true" five of a kind, and a hand with five cards of the same rank and suit as a five of a kind flush. In the case of four of a kind, if the four cards of the same rank are also of the same suit, but the fifth card is of a different suit, that would be a "pure" four of a kind, while if the fifth card is also of the same suit, that would be a four of a kind flush.

A mixed hand would rank just below an otherwise identical true hand, and a hand with a Joker in it ranks just below an otherwise identical mixed hand. So three tens formed through the use of a Joker would still outrank three nines, all three of which were different suits.

Pure hands, and flush hands, though, would usually have a significantly higher rank, depending on the number of cards in the combination. As well, terming the fifth suit the suit of stars, since there is only one of each card in that suit, while there are five of each card in each of the four other suits, flushes and straight flushes in that suit would be harder to form, and therefore could also be significantly higher in rank.

In the case of two pair and a full house, the hand would be pure only if both parts were pure, and true only if both parts were true; otherwise, the hand would be mixed.

In this form of Poker I suppose that one way the hands might be ranked is the following:

- Star Royal Flush
- Star Straight Flush
- Pure Five of a Kind
- Star Elbow Straight Flush
- Five of a Kind
- Royal Flush
- Straight Flush
- Elbow Straight Flush
- Four of a Kind Flush
- Full House Flush
- Star Flush
- Pure Four of a Kind
- Four of a Kind
- Pure Full House
- Full House
- Two Pair Flush
- Pair Flush
- Flush
- Straight
- Pure Three of a Kind
- Three of a Kind
- Pure Two Pair
- Two Pair
- Pure Pair
- Pair
- High Card

Just to make things interesting, I would have the straights ranked from 2 3 4 5 6 up to 9 10 J Q K, then A 2 3 4 5, and finally 10 J Q K A. The elbow straights, would rank from lowest to highest in this order: K A 2 3 4, Q K A 2 3, J Q K A 2, and would all rank below regular straights.

Of course, a game this complicated is probably better suited to a science-fiction novel, giving this complicated form of Poker as part of the background, than for actual play.