Here's a formula for counting the total number of possible starting Omaha hands. This chart shows how a mathematician would calculate the number of starting hands for any four-card combination where order does not matter. You'll find more than 204 times as many starting hands as you would in hold 'em, which has only 1,326.

In this series I will calculate the number of starting hands and unique starting hands for each of the following: four-of-a-kind, three-of-a-kind, two pair, one pair and no pair. The total number of unique starting hands does not take into account similarly suited hands.

The chart below shows (not shown) how we calculate all possible four-of-a-kind starting hand combinations. You may receive any one of the 52 cards in the deck as your first card. After you receive your first card, there are only three cards of the same rank that you may receive as your second card.

In poker terms if your first card is a king, there are only three other kings left which may become your second card. If you are dealt that second king, then there will be only two left for your third card. When you are dealt three cards of the same rank, only one card remains to give your quads.

If we now multiply the number of ways we may receive each card we get 312 possible combinations. Since we are dealing with only four cards and order does not matter, we divide the 312 by factorial 4! to eliminate the various ways we may layout the four kings. Remember, in laying out the four kings, the king of spades may occupy the first, second, third or fourth position without changing the value of the hand. Therefore there are only 13 ways in which we may form quads. Since we are using one card from each suit there are also only 13 unique possible starting hand combinations. This will become clearer when we look at three-of-a-kind next.

Now that you know how to perform the calculation for quads, you should be able to figure three-of-a-kind right. Well maybe not so fast.

To calculate the total number of ways you may generate a hand consisting of three-of-a-kind we must first split our calculation into two parts. First, we need to know how many sets we may be dealt in a manner similar to that for quads. Then we need to figure how many cards are remaining to complete our hand.

Please remember that it makes absolutely no difference how our set is dealt to us. A set can be formed with our first three cards, our last three cards, or any combination thereof. This applies to both the total possible number of starting hands and unique starting hands. The number of unique three-of-a-kind starting hands is different than the total number of possible three-of-a-kind starting hands.

On the chart below (not shown) we can see that we may be dealt any of the 52 cards for our first card. Like the chart for quads we then only have three and two cards left for our second and third cards. Multiplying these numbers together yields 312 possible combinations. Since we are only selecting three cards we must divide this number by factorial 3! This gives us 52 combinations.

We are not finished yet. Each of these 52 three-card combinations may combine with any of the 48, (52 - 4) remaining cards that are not the same rank as our set. Therefore we now have an m * n situation. Our set may be formed in 52 ways and the remaining card may be dealt is 48 ways. Therefore we have 52 * 48, or 2,496 possible starting hands containing three-of-a-kind.

This is not the number of unique hands, but rather the number of possible hands. The difference is that Ac-Ah-As-Kh is the exactly the same hand as Ac-Ah-As-Kc when counting unique hands. When counting the 2,496 possible starting hands they would each be counted as a separate possible combination.

Your assignment for next time is to figure out the number of unique combinations, and here's a hint. There are only two types of three-of-a-kind hands, suited as in 3S and non-suited as in 3NS. I will give you the answer next time along with how the answer is calculated.

So what have we learned? Quads may only be dealt in one way so there are only 13 possible starting quad hands. There are 2,496 possible starting hands containing three-of-a-kind. The unique number is something less, and we'll examine that next time.

Sam Mudaro, BA, MBA, is a practicing tax accountant and financial executive with 35 years of analytical business expertise. He uses simulation software to analyze and develop strategies for Omaha/8 and other forms of poker. Reach Sam at: realguru2003@yahoo.com.