Understanding the poker odds

When playing poker one of the most important things is to understand the odds of being dealt a particular hand and the chances of improving it. There are 2,598,960 different possible hands in standard poker where 52 cards are used to make five card hands. The chart below will show you the odds of being dealt a particular hand in poker

As you go down the chart you will see how hard it gets of being dealt higher ranking cards in your first hand. It starts with the odds 1/1 to 649,739/1. Getting royal flush is nothing short of a miracle. This will give you some idea about which hands to play with and which hands to fold. As you can see pairs are very common and in most case a high ranking pair is enough to win the game.

So, players are mostly competing lower ranking hands. This is basically true in holdem games where no further cards are exchanged. Where as in draw poker games the odds of getting higher ranking hands increase dramatically, when players are allowed to exchange cards for new ones from the pack.

Let’s take for example your hand is K, K, K, 6, 3. Now what are the chances of improving this hand? Now you know you have an opportunity to make either a full house or four of a kind. A pair can be made in 72 ways. Now by discarding two cards you reduce the number of ways a pair can be made to five. Therefore 72 – 5 = 67 ways in which you can make a full house.

You currently hold five cards, leaving 47 other possible cards. Since some cards already have been dealt to other players, you don’t now what they hold. So, by taking all possibilities with 47 cards there are 1081 ways in which two cards can be dealt. So, the chances or odds of making a full house is (1081-67) / 67 that is 15/1.

To improve the hand to four of a kind you need the last king. By exchanging one card, you are giving yourself odds of 46/1. By exchanging two cards, your odds of having the king are 46/2 or 23/1. Finally you need to know what are your odds of winning depending upon the cards you hold and also the type of game you play. As you can see the odds change dramatically, depending upon the type of game you play.