I will start my trans-Siberia trip on Nov.18 in Moscow.
Do the Russian Railways offer discounts in November?
I am not a student. I just expect special discount since Nov. should be low season.
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I don't think that there will be some special actions in November for Russian Railways. May be some additional trains for the Unity Day, but this isn't the case for you.
But I have a good news for you - there always some discounts depending on the train, and some special pricing for international trains. Bad news is that the main interesting actions are in Russian.
For International trains you can explore this page on Enlish version of their site, but this information only about international trains, so I wouldn't get the details here.
For inner trains there are two main option to save the money (all links will be in Russian, please try to use the Google Translate for it):
First one is strategy to encourage the passengers to but tickets earlier - for inner trains you can buy ticket up to 45 days from deliver date, up to 60 days for international trains, and for some trains you can rally save money with early purchase.
The process still in progress, as for many trains carrier has a monopoly, and can't quickly introduce such discount according to the laws. You may be interested in route Moscow - Ufa - Moscow, other destinations are far too away from Trans-Siberian railroad.
The main thing you should note about this option is that the Couchette (platzkart, плацкарт) class tickets aren't available, so you have to buy expensive tickets, but with a discount :) Note that upper seats in Corridor coach (kupe, купе) class are cheaper than lower ones. Sleeping car are also available for some trains.
Second one is a repeatable discount, so each Tuesday you can buy cheap platzkart tickets even with discount. Right now, today you can buy ticket for October, 7 to 27 for a set of trains. Some of them are quite unusual, but Moscow - Ufa still available. Bad news is that the trains can be a random choice, and the seats are platzkart-sided, which isn't very comfortable, and personally I suggest you not to try this one out without good company:
So, if you're feeling lucky, choose train you like, and Good Luck with your travel!
Yes, Russian Railways uses prices, that depend on season.
You can see it (but only in Russian) for 2015, previous years were the same. Usually from mid-September to a week before New Year's Holidays tickets are 10% cheaper.
Also, Russian Railways has a good tradition to set 50% discount for everyone on Victory Day. But in other holidays tickets has higher cost, than usually.