In this presidential year like no other, conventional wisdom has joined common sense in the rubbish can of politics. One of the hoariest bits of conventional wisdom in New Mexico has always been that our presidential primaries don’t matter because by the time they roll around in June, the nominations are a forgone conclusion.

Well, this year think again. There is in reality an excellent chance that New Mexico Republican voters will have a decisive voice on June 7 in the Republican presidential nomination contest.

By June 7, New York businessman Donald Trump will almost certainly have maintained a substantial lead in primary votes cast, states won and delegates selected. But it is equally likely that he will not own a majority of delegates to the national convention. The votes cast on June 7, the last day of presidential primaries, will probably determine if Trump goes to the convention with enough committed delegates for a first-ballot victory, or if instead he has only a plurality and several candidates will have slug it out over multiple ballots to achieve a majority. Since the founding of the Republican Party in 1858, no presidential candidate has been chosen as its nominee without attaining a majority of the delegates.

Five states vote on June 7. The 303 delegates selected on that date include 24 from New Mexico. By far the biggest June 7 jackpot—in fact the biggest national jackpot—will be California with 172 delegates. But because the Golden State selects most of its delegates in 53 separate congressional district races, its total will be split up among Trump, Texas Sen. Ted Cruz and Ohio Gov. John Kasich. Our measly 24 votes could well be decisive.

So here’s the way the arithmetic breaks down. The magic number is 1,237—50 percent plus one of the delegates to the national convention. Trump currently has 739, meaning he needs to win an additional 439 before the July convention to achieve a first-ballot victory.

Remaining to be elected are 934 delegates, of which 601 will be chosen before June 7. To achieve a majority before June 7, Trump would need to win 78 percent of the delegates chosen during April and May. But Trump has never won anything like that percentage in any election. In fact, he has yet to win a majority of the votes anywhere.

If Trump fails the nearly impossible task of winning 78 percent of the delegates chosen in the dozen primaries in April and May, he will face voters in New Mexico, California, New Jersey, South Dakota and Montana at a decisive point in his campaign, needing to win a significant portion of their 303 delegates to secure the nomination.

One calculation by a political scientist at the University of Virginia is that Trump will get a total of 1,239 delegates—two more than a bare majority. His New Mexico total includes 10 votes for Trump, 10 for Cruz and four for Kasich. A shift of only three New Mexico delegates—a single congressional district, for example—from Trump to Cruz or Kasich would, in this calculation, deny Trump a first-ballot victory and in all likelihood deny him the nomination.

How will New Mexico vote?

The math is a bit daunting. Three delegates will selected from each of the three congressional districts. Another 10 delegates will be selected at-large based on the statewide totals. In addition three delegates go to party leaders and a bonus of two are added to the candidate with the most delegates.

The preference of New Mexico Republicans is entirely unclear. Gov. Susana Martinez made the misstep of endorsing and campaigning for Florida Sen. Marco Rubio just days before he withdrew form the race in humiliation. An outdated public opinion poll showed Cruz leading slightly (within the poll’s margin of error with 25 percent, followed by Trump with 24 percent and Rubio with 19 percent. The keys to the New Mexico outcome will probably be two factors: the decisions of Rubio supporters and what the remaining 32 percent (either undecided or favoring other candidates) will do.

So hold onto your hats New Mexicans, we’re in for a wild rodeo ride over the coming weeks.