Suited Omaha Starts

Hakim was taking a break from his Omaha/8 game on a cloudy Monday afternoon in midwinter. He looked glum so I went over to lend him some cheer. After some pleasantries, he asked me about suited starts in Omaha. It seemed to him that his suited starting hands weren't standing up. When there were three or more trumps on the table, there was often a pair on the table, making someone else a Full House; when there wasn't a pair, then his Flush would lose to a higher one.

He said he had played [As]-[2h]-[9h]-[Tc], figuring the two hearts added value to his marginal, bare Ace-Deuce. He was pleased with the Flop, [Kh]-[3h]-[8s], which gave him a draw to the nut Low and a Flush draw. The Aa on the Turn made his Flush and counterfeited his Low. The River was the [5c]. At the showdown, Hakim's Flush lost to a higher one. "Those darn hearts cost me $36," he groused.

I asked Hakim about how often he would have a suited start in Omaha. About half the time, he thought. I told him he wasn't even close, it's about 90%.

The chance that your four cards will be rainbow is 52*39*26*13/4!/C(52,4) = .105. The probability that your hand WON'T be rainbow is (1 - .105), or .895. More than 89% of the time you'll have a single- or double-suited hand, I told him. The chart shows the distribution.

Hakim thought that even the smallest Flush would win often enough to show a profit. When the tableau is unpaired, I told him, in ten-handed Hold'Em the smallest Flush wins 76% of the time, but not in Omaha. Because four cards are dealt in Omaha, I told him, it's quite likely that someone else also has two trumps. Only if no one else had two trumps would the smallest Flush prevail. In a ten-handed Omaha game, there are eight other trumps that could have been dealt among your nine opponents, so your only hope is that they're all singletons: that chance is .1221, about 1 in 8.

In spite of that bad news, Hakim became even more excited about having suited starts: with a suited Honor and fortuitous tableau, he would have much better than 12.2% chance for High; plus, he might occasionally win an "emergency High" with low-ranking trumps, I warned Hakim not to go wild. With a single-suited starting hand, it's only one chance in 104 that he'd flop a Flush, and even then he'd have to worry about the tableau pairing on the Turn or River. He'd flop a Flush draw about 1 time in 9, I told him, and not only must another trump appear, but also the board mustn't pair. His chances for three or more trumps on an unpaired tableau are about 4.5%. A double-suited hand would double his Flush chances, still less than 10% after all the cards were out.

I told him he should think of suited starting hands just as having some extra values. He thanked me for the information and hustled back to his Omaha/8 game with a smile on his face and a spring in his step.

"De nada."