The annual NCAA men’s basketball tournament is underway, which means millions of Americans have filled out brackets and put down money on games and in March Madnesspools. What’s different this year is that in many places, sports wagers are not only popular but actually legal. Illinois isn’t one of those places, but if things go right, it will be before long.

In his budget address, Gov. J.B. Pritzker implored legislators not to waste time or take their eyes off the prize. Past gambling expansion efforts, he lamented, had gotten “bogged down in regional disputes and a Christmas tree approach.” Such mistakes are to be avoided with this new market. “Every day we argue about who’s in and who’s out,” he stressed, “is money that goes to other states and to the black market.”

The governor wasn’t wrong. There’s much yet to be said about the totality of his budget proposals. But we’re glad state Rep. Mike Zalewski, D-Riverside, has advanced the talk about sports betting by introducing four proposals on how it might work here. The House Revenue Committee will be evaluating those distinct options to determine which might work best for Illinois.

Illinoisans may differ among themselves about the wisdom, morality or economic effects of legalizing sports betting, but they can’t deny two obvious facts: It’s going to be allowed in some states, and people are going to take advantage of new opportunities to gamble legally. The size of the existing underground business, which amounts to tens of billions of dollars, suggests there is considerable potential for a legal, regulated market.

It would be foolish, though, to expect a flood of revenue. Pritzker proposes issuing 20 licenses, divided among physical establishments and online operations, that would go for $10 million apiece. That would bring in some $200 milion right away, but the annual take from taxes on these wagers would be smaller. A 20 percent rate, it’s estimated, would capture between $77 million and $136 million — a tiny share of the nearly $39 billion budget the new governor proposed.

Pritzker is in a taxing mood, but greed can be as risky for lawmakers as it is for poker players. States that legalize sports wagers, says analyst Richard Auxier of the Washington-based Tax Policy Center, “must set a tax rate high enough to maximize revenue but not so high that it discourages casinos or bettors.” As with any tax policy, Illinois has to consider what other states levy, because the tax rate will affect payouts to winners, and gamblers will gravitate to places where they stand to win the most money.

But that’s not the hardest part of the deal. Thanks to the Illinois Gaming Board, the state has done an excellent job of regulating casinos to keep them free of organized crime and political graft. This is no time to relax the vigilance that on at least four occasions intercepted what could have become scandals. If that ever happens, gamblers will flee Illinois for states that give them certifiably honest ways to bet.

It’s crucial, then, that new licenses be awarded in a way that prevents corruption and promotes public confidence. In 2002, Gregory Jones, who was chairman of the Gaming Board, stressed the importance of “openness, fairness, competitiveness and transparency” in the process of awarding a casino license.” The same standards apply to online betting operations.

One way to keep the legislation honest: Invite Gaming Board attorneys to review any bill(s) before the voting in Springfield. The agency has three decades of experience in demanding, and enforcing, integrity in Illinois gambling.

Given that legal sports betting is now taking shape across the country, the people of Illinois have something to win from joining the game. But the state needs to establish sound standards and follow through with diligent regulation to make sure they don’t get taken.