Instead, his chances may come down to the whims of 54 unpledged Pennsylvania delegates.

No other state leaves so many of its delegates unbound — allowed to vote for whomever they please at the convention. That’s because it conducts its loophole primary in two parts. First is the “beauty contest,” which is a presidential primary preference vote. The winner of the beauty contest gets all of Pennsylvania’s 17 at-large and bonus delegates.

But the remaining 54 — the three delegates awarded to each congressional district — are unbound and elected in the delegate selection primary. In this part, voters directly elect delegates to the national convention. What makes Pennsylvania’s G.O.P. delegate selection primary so distinctive is that the ballot includes no guidance on whom a delegate will support at the national convention (the prospective Democratic delegates commit to a candidate). A voter will just see a list of names — some of whom might be recognizable, but others might as well be Joe Schmo.

(It’s called a loophole primary because it could circumvent the delegate allocation rules. Voters could, in theory, elect a slate of delegates who unanimously support one candidate, even in cases where a winner-take-all contest was prohibited.)