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Sam Mudaro: Omaha Guru

In Omaha you need two of the same suit in your hand to make a flush. If you have three or four of the same suit you cannot use the additional cards to make a flush. You must use two and only two cards from your hand. Does it hurt your chances of making a flush if you have more than two of a suit? Is it worse to have four of the same suit?

The answer should be obvious. If you hold more than two of the same suit in your hand, your chances of making a flush are diminished. One or two of the cards you want on the board are dead in your hand. With two hearts in your hand there are 11 hearts left in the deck that may complete your flush. When you hold three or four hearts there are only 10 or 9 left in the deck to complete your flush. The real question is: How much are your chances of completing a flush diminished?

For this simulation I chose five hands, namely A-6-7-9, K-2-7-9, Q-2-7-9 and A-K-7- 9 and ran them a million times with the first two cards suited. I then ran them again with the first three cards suited and followed that up with all the cards suited. The results are summarized in the wide chart below.

Looking at the first and last hand, which both contain an Ace high flush draw, the Net win per hand decreases about 10% on average for each additional card of the same suit held. That is not the case for the 3 middle hands, not containing an Ace. This is partly attributableto the fact that a draw to the nut flush is superior to a draw to the second, third or fourth nut flush. You can generally tell by the betting if you are up against the nut draw, especially if there is not a low draw.

The column labeled Flush is the number of times the flush was completed and it held up. Totaling these columns and then taking the average of those totals produced the following results 3,565, 2,261 and 1,198 respectively. From these averages we can calculate that having three cards of the same suit reduces our chance of completing a flush by approximately 37%. By holding that fourth suited card our chances are reduced an additional 47%. Put another way by holding 4 suited cards, opposed to two, you reduce your chance of making a flush by over 66%.

The chart below shows the pure mathematical probability of flopping a 4 flush, completing it on the turn and river when holding 2, 3 or 4 of the same suit in your hand. I am sure some of you are asking why does the probability of completing a flush increase with one card to come vs. two? Stay tuned. Next time I will explain how to calculate the numbers in the chart, answer that question and compare the above to Hold-Em.

So what have we learned? Holding 3 or 4 of the same suit definitely reduces our chance of completing a flush. It reduces both our net and the probability of completing the flush. Should we muck every hand when we have 4 suited cards? Definitely not! Which ones are playable and which ones are not will be the topic of a future article.

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