1. Prayer = petition; petition requires possibility that it can affect decision. Why should our petition be able to affect G-d's decision? (a) Either we deserve it, in which case we will get it without asking, or we don't deserve it, in which case we will not get it even if we do ask. OR (b) G-d's decision depends upon more factors than just merit - why should our petition be one of those factors?
2. Prayer is legally coordinated with sacrifices. If prayer = petition, they represent opposite directions of "flow" - prayer = from G-d to us; sacrifices = from us to G-d?!
3. Purposes of petition
a. for oneself, but with acknowledgment that G-d runs the world - genuine (if minimal) religious consciousness
b. for service of G-d - expresses loyalty to G-d, offering oneself to G-d [R. Akiva: when X is judged, offer a sample of X so that X can receive a blessing; prayer on Rosh Hashonna!] - now "flow" of prayer and sacrifices the same
4. Prayer expresses and reinforces the dedication of the petitioner to G-d, and prepares him psychologically to use the item well when received. Therefore it is a factor in G-d's decision.
5. R. Hirsch: "to pray" = "to judge oneself" - necessary to evaluate what I really need to serve G-d.
6. How can we trust our judgment? Petition is a means to get what we ask for - a means to change the world. Our condition requires that we make judgments of what we need to serve G-d and use physical means to get it (since we lack prophecy); using the means of prayer is included.
7. Highest level of petition: G-d wants us to be healthy, safe, without pain, etc.: we ask because He wants us to have! Levels of petition are degrees of attachment to G-d.