This question assumes that Constantine was a calculating politician who converted to Christianity for personal advantage and not out of pure holiness.
Your assumption is (half) wrong (and half right). As to the former (half wrong) part, most people living before the European Enlightenment were theists, and leaders, be they political or military, were usually no exception to the rule. As for the latter, see below.
What strategic value did Christianity hold for Constantine that made him convert to Christianity?
His continued rule as Roman Emperor, by trying to please or appease the specific deity he personally deemed responsible for his military victory over his political adversary. (Whether this is to be construed as an expression of deep religious fervor, or of pragmatic self-interest, is another question altogether, pertaining more to the realm of psychology, rather than history proper).
Coming from a polytheistic background, after having previously been raised in the paganism of his father, his acceptance of said deity was, at least at that moment in time, not necessarily a conversion to monotheism, especially since he personally was not properly introduced to (nor particularly acquainted with) it before, his mother Helen's Christianity notwithstanding.
Basically, shortly before fighting the decisive battle against his rival claimant to the throne, Maxentius, he (obviously) requested assistance from the gods (as almost any man of his times would have done under similar circumstances). He then noticed a certain starry formation, which, according to the superstitions of the time, he took as a divine response to his request (but he was a soldier, not an astronomer, by profession, and -even if- back then, in prescientific times, there was no meaningful difference between astronomy and astrology). Then, a certain Christian soldier, of which there were many in the Roman Imperial army, sensing the opportunity at hand, proposed a certain Christian interpretation of the perceived event, which he, desperate for some glimmer of hope (no pun intended) during the upcoming bloody ordeal, gladly accepted.
The main reason he was only baptized on his deathbed consists primarily of the fact that there was a certain pious belief going around in his time, based on a particular interpretation of a specific passage from Paul's Epistle to the Hebrews, that sins committed after baptism might be unforgivable. (Many fourth century Church Fathers, whose devotion and piety to their faith no one seriously questions, have also been baptized late in life, despite having been born to Christian parents, so there is no real reason to believe that Constantine's similar delay is based on any other reasons).
Admittedly there was a certain decline in the practice of infant Baptism during the fourth century. At that time even adults postponed their Christian initiation out of apprehension about future sins and fear of public penance, and many parents put off the Baptism of their children for the same reasons. But it must also be noted that Fathers and Doctors such as Basil, Gregory of Nyssa, Ambrose, John Chrysostom, Jerome and Augustine, [...] were themselves baptized as adults on account of this state of affairs [...].