We are all familiar with the parable of the Publican and the Pharisee. Using the journalistic technique of the “5Ws and 1H” we will examine this parable more closely.
Who were the Pharisees and the Publicans?
The Pharisees were a Jewish religious sect who believed in the efficacy of tradition and the need to for everyone to conduct themselves as if he were a Temple priest. The latter requirement included the use of ritual washing and prayer as if one were in the Temple. While the concept is good, Jesus criticized the Pharisees for imposing man-made tradition on the Jewish populace instead of Sacred Tradition as defined by Christianity. handed down from God himself. 
Publicans were collaborators with the Roman rule. Romans valued two things from their provinces: peace and taxpaying. Publicans were most notorious for collecting taxes for the Roman. As if this weren’t bad enough, the Publicans would also take a share for themselves.  Publicans were roundly criticized by the population as a whole and became caricatures for sinners. Zacchaeus was an example of a Publican.
What was wrong with the prayer of the Pharisee?
The perfect prayer has the ACTS components–adoration, contrition, thanksgiving, and supplication. The Pharisees prayer was notable for not having any contrition, deficient thanksgiving, and a lack of supplication. The Pharisee did not ask for strength or ability to end a sinful life. Indeed, he did not even recognize he had a sinful life.
The prayer of the Publican was sincere and carried all the elements required for a good prayer: Oh God, be merciful to me, a sinner. The Publican admitted he was a sinner (contrition); he asked God for mercy and forgiveness (supplication); he implicitly performed adoration by acknowledging the power of God to forgive sins (adoration); and implicitly thanked God for His mercy and grace (thanksgiving). The Prayer of the Publican is part of the prayer before Holy Communion in the Byzantine churches and the Jesus Prayer, both notable features of Byzantine worship.
The canon of matins for the Sunday of the Publican and the Pharisee points out the Pharisee was wretched in his self-sufficiency. In the history of the Catholic Church, this became known as the heresy of Pelagianism, or the belief salvation was attainable without the help of God. This heresy was combated by St. Augustine, one of the great Fathers of the Church and the author of The City of God. One must also recognize the Jewish religion is thought to be a religion of action rather than faith. While the Pharisee’s actions were good in themselves, the Pharisee failed in his prayer under Christian thinking because he did not give proper regard to God.
Where can I find the Parable of the Publican and the Pharisee?
Most of the wonderful parables we know, such as the Prodigal Son and the Publican and the Pharisee are found in the Gospel of St. Luke. This parable is found in Luke 18:9-14. It immediately follows the Parable of the Unjust Judge6, also a parable about praying. In the Parable of the Unjust Judge, the widow continues to approach the judge persistently until the he relents and grants her justice. In the Parable of the Publican and the Pharisee, the Publican is also persistent as he asks the Lord for mercy. This is one reason why The Divine Liturgies of St. Basil and John Chrysostom use the prayer “Lord have mercy!” more and more insistently throughout the Divine Liturgy.
When did the Pharisee fast?
The Pharisees fasted two days a week: Monday and Thursday. Eastern monastics fast on Wednesday and Friday. It is possible the fast days were changed to distinguish the Christians from the Pharisees. Wednesday and Friday were chosen as fast days because Judas betrayed Jesus on a Wednesday and Jesus was crucified on Friday.
How did the Pharisee and Publican pray?
We are used to praying silently. This was not the practice of the ancients. Prayers were read out loud. In II Kings 1:12-16, Hannah the mother of Samuel was praying silently. The priest Eli assumed she was drunk because she did not pray out loud.
This adds a whole new dimension to the parable. The Pharisee was probably praying out loud, so it is entirely possible the Publican heard the Pharisee deride him . Even though they stood at a distance from each other, voices do carry. This is yet another way the prayer of the Pharisee could have been deficient. Comparing ourselves to others in prayer, let alone doing it verbally with the other person in the room is not a recommended method of prayer.
Why is the Parable of the Publican and the Pharisee a trap?
Jesus constructed this parable very subtly. Certainly, there is nothing wrong with someone who fasts twice a week and tithes to the church. If we knew of someone like that we would say he was a model church member. Yet, the Pharisee takes pride in his practice, demonstrating the Biblical saying pride goes before the fall.
Today, we read this parable and we say of course we
are the Publican. We are humble and not
prideful. Yet, isn’t this action itself
one of pride? The Sunday of the Publican
and the Pharisee is the first of the pre-Lenten Sundays on the Byzantine church
calendar. There is no fasting during the week of the Publican and the Pharisee to
remind everyone of their sinfulness and pride.
This week is a preparatory week for fasting. With each succeeding week up to the beginning
of Lent, the fasting and absolution becomes more stringent.
 This description is limited to the more germane aspects of the question. The history and practices of the Pharisees are complex and worthwhile topics. Modern Judaism contains many Pharisaic aspects including the use of the synagogue. Some scholars have posited Jesus himself was much closer to Pharisaic teaching than generally supposed. This should not be surprising given the Sadducees, a Jewish group strongly associated with the Temple had been decimated when the Romans destroyed the Temple.
 http://www.newadvent.org/cathen/12553d.htm Accessed July 8, 2019.
 Lenten Triodion. Order of the Sisters of St. Basil. Canon for the Sunday of the Publican and the Pharisee.
 Byzantine Christians and the Polish National Catholic Church laity also fast on Wednesdays and Friday during Lent.
 Luke 18:11