Everything You Need To Know About Poker Odds

There are many variations on the game of Poker. In the most basic game, “Straight Poker“, each player is dealt five cards. The player with the “best” hand wins. To determine a winner, the hands are ranked from highest to lowest, with the hands that are less common being highest. The hands that are recognized in straight poker (in no particular order) are:

Note that C = Clubs, D = Diamonds, H = Hearts and S = Spades. Example: QS = Queen of Spades.

A Straight Flush
Any five sequential cards of the same suit; note that A 2 3 4 5 is considered sequential as is 10 J Q K A

A Straight
Any five sequential cards, ignoring suit

Four of a Kind
Four of the same rank, for example 7C 7D 7H 7S 3D

Three of a Kind
Three cards of the same rank and two unrelated cards, for example 9C 9H 9D QS AC

One Pair
Two cards of the same rank and three other cards which do not combine with any of the others to make a different hand, for example 3C 3H AC QH 10D

Two Pairs
Two cards of one rank, two cards of another rank and a third of a different rank

Full House
Three cards of one rank and two of another

A Flush
Five non-sequential cards of the same suit, for example AD 5D 6D JD KD

No Pair
Five cards which do not meet any of the combinations above, for example AH 6S QD JC 5C

Question 1:
How many different five card hands are possible in one deal?

Question 2:
How many different ways can we select a hand which is a Royal Flush? (Hint: How many choices are there for the suit? Once that has been chosen, how man choices are there for the lowest card? After that, how many choices do we have for the remaining four cards? Does the multiplication or addition priciple appy here?)

Question 3:
What is the probability of drawing a straight flush in one draw of a five-card poker hand? (Hint: Remember that the probability of an event occuring is the ratio of the number of ways the event can occur to the number possible outcomes. In this case, that’s the number of ways of drawing a straight flush divided by the number of ways of drawing five cards.)

Task:
By calculating the number of ways a player can draw each of the hands, rank the following hands according to their relative frequency: Straight Flush, Straight, Four of a Kind, Three of a Kind, One Pair, Two Pairs, Full House and Flush.