Lol, you're certainly asking a complicated question. I can tell you what some historians think, though I am not really knowledgable on this subject.

The traditional story of Constantine's conversion is as follows, though versions differ: Constantine goes to battle with the pagan Maxentius to become emperor of the Western Roman Empire, receives a sign from God and going into battle with that sign, he wins the war.

According to Lactantius, Constantine sees a sign in his dreams and a message that this sign will make him win the battle. After this happens, he instructs his soldiers to paint the sign on their shields and they win the battle with Maxentius.

According to Eusebius, he asked God for help after careful consideration who to ask for aid in the war. After that, he sees in the sky a cross and text that with this cross he will conquer. After this he converts and wins the war against Maxentius. Funnily enough, this is a story Constantine personally told Eusebius.

However, can this really be true? The story of Eusebius is certainly bullshit, but the general gist may be true, that Constantine thought he received a sign. But then again, there's the question if he was already a Christian before that, but one who hadn't come out of the closet, so to speak, since his mother was already a Christian. Either way, both versions say he converted for religious reasons but these stories are highly circumspect, so what now?

Constantine's conversion is a subject on which historians have been divided for a long time. Some say it was for political gain, such as Jacob Burckhardt, while others say it was out of sincere political belief, such as Barnes and Naerebout. So it's a complicated question, though most historians nowadays think it was sincere belief.

However, Constantine wasn't necessarily all that explicit about his Christianity. While it was no secret that he was Christian, few coins in his reign bear Christian symbols according to Naerebout, which has often been used as an argument he conversed for political convenient reasons. On the other hand, he empowered the Christian church greatly during his reign.

A third view, by Drake, simply says that the question is somewhat irrelevant. State and church were not seperated, so seperating religious motives and political motives is pretty tricky to the point that it's not really worthwhile, and it's better to simply look at what Constantine did in the framework of imperial practice.

So, nobody really knows for sure why Constantine really converted.