So it turns out that for cubic Bezier curves, t values of 0, 1/3, 2/3 and 1 have special meanings. A general cubic polynomial is of the form
y = a0 + a1 * x + a2 * x^2 + a3 * x^3
where ai’s are real constants.
If the variable x is limited to the interval x0 <= x <= x0 + χ (that's the Greek letter Chi), where χ > 0, then it’s equivalent to a special case of cubic Bezier curves. Namely, when the t values are 0, 1/3, 2/3 and 1.