Throughout Hindu scripture, the order of the Yugas is given as Satya, Treta, Dwapara, Kali. (See my answer here for more information on Hindu timescales.). Yet in his ISKCON commentary on the Srimad Bhagavatam, Bhaktivedanta Prabhupada says this:
There is a chronological order of the four millenniums, namely Satya, Dvāpara, Tretā and Kali. But sometimes there is overlapping. During the regime of Vaivasvata Manu, there was an overlapping of the twenty-eighth round of the four millenniums, and the third millennium appeared prior to the second. In that particular millennium, Lord Śrī Kṛṣṇa also descends, and because of this there was some particular alteration.
So Prabhupada seems to be suggesting that in most Mahayugas, the order of the Yugas is Satya, Dwapara, Treta, Kali, but in the 28th Mahayuga of the Vaivasvata Manvantara (the present Mahayuga), the order is Satya, Treta, Dwapara, Kali. And this seems to be a common belief in Gaudiya Vaishnavism (the sect that Prabhupada and ISKCON belong to). For instance, in this web page Swami Gaurangapada says that the order of Yugas is reversed in the present Mahayuga so that Krishna and Chaitanya Mahaprabhu (whom Gaudiya Vaishnavas consider an incarnation of Vishnu) could be born close together:
There is a confidential reason for why the cycle of yugas was changed in this Chatur Yuga with Treta Yuga coming before Dvapara Yuga.
So even though normally Dvapara comes after Satya Yuga and before Treta, He reversed the order of the Yugas and Dvapara now came after Treta and before Kali Yuga. This is because Lord Krishna wanted to distribute His Vrindavana love to all conditioned souls in the form of Lord Gauranga [Chaitanya Mahaprabhu] without a big time difference between these two advents of His so that the Vrindavana pastimes are still fresh in the hearts and minds of the people so that when He distributes them as Lord Gauranga, people will accept this love very easily.
So my question is, what is the reason that Gaudiya Vaishnavas believe that the Dwapara Yuga usually comes before the Treta Yuga, and that our Mahayuga was some unusual exception? Is it mentioned in the Chaitanya Charitamrita or some other Gaudiya Vaishnava work?
Could the reason for this belief be the fact that the root of the word Dwapara is "two" and the root of the word Treta is "three"? My understanding is that the names of the Yugas derive from the names of dice rolls. In the traditional Vedic game of dice, the best roll you could get was a 4, known as Krita, the second-best was a 3 or Treta, the third-best was a 2 or Dwapara, and the worst possible roll was a 1 or Kali. But perhaps Gaudiya Vaishnavas don't accept this etymology.