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I will continue analyzing the play of hands after the flop today by looking at two forms of 3 of a kind. There are three ways to make 3 of a kind in Omaha on the flop. First: the flop may contain 3 of the same rank. I will not consider this probability as it offers all players the same advantage. If you are holding two cards of the same rank and flop a third you will have 3 of a kind. This is commonly referred to as a set. When a pair flops and you hold a single card of the same rank this is referred to as flopping trips. Today I will attempt to answer the question: Are you better off flopping a Set or Trips?

I set this analysis up by running each hand 5 million times. In each case the player was assigned the hand as indicated in the Hand column. The flop was forced to contain the card or cards listed under flop. The win percent column shows how often the hand won and the net is the average amount won. The columns labeled Trips through Fours shows how often our tight player won with each of those hands.

First let me present and explain the data for a Set:

The first thing to point out is that when you flop a set, regardless of the rank you have a profitable hand. No surprise that A-A is the most profitable. This pair when combined with two random cards in your hand and the four other board cards may make both a high and low. The second most winning and profitable hand is the K-K, followed by 2-2 and Q-Q.

With 3 Aces our player only won 40% of the time with his set. He completed a winning full house 28.6% of the time and quads 6.4% of the time.

The column labeled “Rank” represents the ranking of the hands in terms of net won. The A-A is ranked number 1, the most profitable. K-K is ranked second. Where is number 3? Let’s take a look at the second chart where a pair is flopped and you have trips. Rankings 3 through 11 appear on this chart. Let’s begin by pointing out that A-A again wins most often with a win percent of 42%. However it is not followed by K-K and is not the most profitable. The most profitable is 2-2 followed by 3-3 with A-A coming in a close third. All hands except for the 1st, 2nd and 12th ranked appear on this chart. While the two most profitable hands are on the first chart when you look at the money won the second chart is more profitable overall. When you flop trips almost every hand will average a net win of $7.00 or more. When you flop a set, all but 3 hands are under $7.00. There are 6 hands under $3.00.

On the chart for Set’s the distribution of winning Set’s peak at the extremes and drops toward the central ranks i.e. 7, 8 and 9. These are the worst cards for the player. The swing when you flop Trips is far less dramatic. The 7, 8 and 9 are still the worse but the winning percentage stays close to 5%.

Intuition can be deceiving. I would have guessed you had a better chance of winning when you flopped a Set as opposed to flopping Trips. After all if you are holding two of the same rank no one else can make trips. Having a pair on the flop cannot make you feel too comfortable with your trips as one must worry about a full house. The numbers show differently. You also have a 20% better chance of converting to a full house when you flop Trips as opposed to as Set. So what have we learned? Set and trips are very playable especially if it’s Aces. Overall it is better to flop Trips. You will complete more full houses when you flop trips opposed to a set. This is attributable to the fact that in most cases you will have 3 different cards to pair as opposed to 2.

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