Rather than just pointing out degrees, let's talk about what you can hold a conviction in. These terms also connote degrees.
- You can think a conjecture is true.
- You can believe in a theory, holding it to be true.
One of them requires some foundation even if only subjective from the perspective of the speaker. While the other includes possibilities that may be clearly absurd.
I think these lottery numbers will be lucky.
Raises no questions to me.
I believe these lottery numbers will be lucky.
Makes me wonder what you know about the method of number selection at the lottery.
That's not to say every belief is reasonable. Most are certainly not reasonable, but they're still not random.
I'm a Christian: I believe the world was created in 6 days.
You're clearly nuts. But, I understand why you believe that. It's in your cannon.
As for reckon it has two meanings.
- Meaning to calculate. This is the archaic definition from which the current usage derives, largely lost in the United States.
- A southern regionalism for belief. Often used sarcastically or pejoratively by outsiders to mock southerners.
I'd stay stay away from reckon entirely. Unless you're planning a comedy skit.