The story of how David Baazov, the 34-year-old CEO of Amaya Inc. (TSX:AYA), managed to turn the company from a tiny TSX venture stock to the world’s largest online gambler in just five short years is truly extraordinary.

After making a few small acquisitions, Baazov set his eyes on the biggest prize in the sector, PokerStars and Full Tilt Poker, owned by a company called the Rational Group. After finally getting permission to approach bankers with a potential deal, Baazov did the nearly impossible. He found a way to get Blackstone to lend Amaya more than $1 billion as well as buy the company’s shares at more than $18 each—even though they traded below $10 at the time.

The rest, as they say, is history. Other bankers agreed to lend the company the rest of the US$4.9 billion needed to complete the deal, and Amaya has emerged as the largest company in the space. But as exciting as that deal was, it might just be the beginning of Amaya’s dominance. There are three reasons why the future still looks pretty bright.

Moving beyond poker

One of the reasons why Baazov was so attracted to Rational Group is because PokerStars essentially owns the sector. Estimates claim that it has a market share approaching 70%. Between it and Full Tilt, Amaya controls nearly three-quarters of the market. Approximately 90 million accounts exist between the two platforms.

This means there are a lot of potential customers and the company could expand into other areas, namely other casino games and sports gambling. In a recent trial run in Spain earlier this year, the company managed to get a double-digit market share just by offering casino games as an option for existing customers.

Both casino games and sports betting will be rolled out to all customers by the end of the year. If the company could get a double-digit market share just by offering an optional download, imagine what it can accomplish with a big marketing push. It’s a huge potential market.

U.S. potential

As avid poker players know, online gaming is essentially illegal in the United States. Three states—Delaware, New Jersey, and Nevada—allow online gambling, but only for state residents.

In today’s world of tight budgets and seemingly endless deficits, I don’t think there’s a level of government in the United States that couldn’t use a little more money. Online gambling is an easy way for this to be accomplished.

The market is definitely there in the United States. More than a million people regularly played online poker alone before it got shut down, and the potential market for casino games and sports betting is even bigger.

If you’re an optimist like I am, then it’s easy to see a situation where the United States eventually legalizes online gaming at a federal level. Technology makes it easy for tax revenue to be collected, and the consumer demand is clearly there. That would be a huge boost to Amaya’s business.

Cheap growth

According to the analysts who follow the company, the growth story still has plenty of legs.

The consensus expectations for 2015 are that the company does $1.6 billion in revenue, and earns $1.74 per share. Expectations get even rosier for 2016, with $1.8 billion in revenue expected and net income of $2.46 per share. To put that into perspective, the company earned just $0.52 per share from $688 million in revenue in 2014.

For a stock trading at about $30 per share, that puts the company at just 17 times forward earnings, which is right about average for the TSX Composite. But considering the potential growth in expanding into other games, further visibility when the company lists on the NASDAQ later this year, and the potential of the U.S. market in the future, it’s easy to make the argument that Amaya is a pretty cheap stock.

For those reasons, I think the company deserves the chance to be in your portfolio.

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Fool contributor Nelson Smith has no position in any stocks mentioned.