Royals and sports betting

7 April 2013

By John Grochowski

QUESTION: On your recommendation, I’ve been practicing video poker on my computer, and looking at some of the stats for the different games. The software I use says royal flushes come up once every 40,391 hands on 9/6 Jacks or Better, but a little less often at once per 40,170 on 8/5 Jacks or Better. If you look at 10/7 Double Bonus Poker -- pretty rare, but a game I love when I can find it -- it’s once per 48,035.

I can understand the Double Bonus difference. There needs to be fewer royals to make up for the bigger pays on four of a kind. But why the difference between 9/6 Jacks and 8/5 Jacks? We get less payback on the flushes and full houses, AND we get royals less often, too. That hardly seems fair.

ANSWER: The difference isn’t about making up for other payoffs. It’s the result of player strategies.

In 9/6 Jacks or Better, flushes pay 6-for-1, and we’re a little more aggressive about pursuing flushes and straight flushes than in 8/5 Jacks or Better. A side effect is that we make plays that result in a few more long-shot royal flushes in the 9/6 game.

If you’re dealt ace of spades, king of clubs, queen of diamonds, jack of diamonds and 5 of hearts, then in 9/6 Jacks or Better you discard ace-king-5, hold the two high diamonds. Lower pays, especially high pairs, are more likely, but you leave an outside shot at a royal. Per five coins wagered, the average return is 3.00 coins when you hold queen-jack, and 2.98 for the next best play, holding ace-king-queen-jack.

In 8/5 Jacks or Better, the best plays are reversed. The lower flush return diminishes the value of holding two suited cards. The average return of holding all four high cards is still 2.98 coins per five wagered, but the return for holding queen-jack drops to 2.95.

Strategy adjustments such as that mean we give ourselves more chances to draw royals in 9/6 Jacks or Better than in the 8/5 game.

In 10/7 Double Bonus Poker, payoffs on flushes are kicked up another notch to 7-for-1. That enhances the value of flush and straight flush draws so much that we hold extra suited cards that eliminate some royal draws.

One example comes when we’re dealt four parts of a flush, including three parts of a royal. If the deal brings 6, jack, queen, king of diamonds and 5 of clubs in 10/7 Double Bonus Poker, the average return for holding all four diamonds is 7.66 coins, and that beats the 7.59 for holding jack-queen-king and leaving open the royal shot. In 9/6 Jacks or Better, the average return is 7.41 on jack-queen-king, and only 6.70 if you hold all four diamonds.

You make more plays in Double Bonus that preclude chances of a royal, so royals happen less often. It’s your strategy that changes the frequency of royals, not any need for the game to make up for pay table differences.


QUESTION: Please explain to me about the courts overturning the legalization of sports betting in New Jersey. Isn’t it up to the states? How can Nevada be allowed to legalize it, without New Jersey having the same right?

ANSWER: The issue is whether a 1992 federal law represents unconstitutional, unequal treatment of states is the key issue. A U.S. District court upheld the law that banned sports betting in states that did not have it prior to enactment. New Jersey Gov. Chris Christie says the state will appeal, leaving it to higher courts to decide the constitutional issue.

The federal ban was sponsored in the Senate by Sen. Bill Bradley, the former Princeton and New York Knicks basketball star. It allowed states that had sports betting to continue, so Nevada, Oregon, Montana and Delaware were exempted. New Jersey at the time was the only jurisdiction other than Nevada to have full-service, land-based commercial casinos, and was given a grace period of one year. The state could have legalized sports betting at the time and joined the four exempt states, but proposals never made it through the legislature.

Fast forward a couple of decades, and the competitive situation is much different. The original ban was enacted early in the national expansion of gambling. The Indian Gaming Act of 1988 opened the door to building casinos on tribal lands, and commercial riverboat casinos followed, with Iowa being first to pass an enabling act in 1989. The pressures Atlantic City faces today from Connecticut, Pennsylvania, Delaware and other states did not exist when the sports betting ban was passed.

That’s a long way around to answer your question. Nevada can have sports betting because it was already legal there before the federal ban was passed. New Jersey can’t have it because it didn’t legalize it within the grace period. And whether that federal law is constitutional is for the appellate court to decide.