Hi, 

this is a community about Eurail Pass, this is a pass where you can use almost all trains in one country in Europe or in over 33 countries. 

But to your question about normal Point-to-Point Ticket: prices are not fixed. Like for planes, there are saver fares, where you have to take this train you book or flexible tickets that cost more, but you can take one of the many trains of this day. Sooner the day of travel, more you will pay for the train tickets. Tickets can be purchased till the departure time. 

With an Eurail Pass, the train will be included and you can travel much flexible. In Germany you can reserve a seat, but it is not compulsory, but recommended on busy trains. 

Are you travelling with a Eurail pass? If so then all trains in Germany have optional reservations at fixed prices that only change with inflation, and are only a few euros per seat if you book ahead. You can always reserve at the station if the train is filling up. Other than that there is no extra to pay and you would simply catch the next train if you miss one and change the train details in your trip and add to your pass. 
 

If you are buying advance tickets without a pass, then look carefully at the terms and conditions, Saver tickets are usually very limited in refunds and exchanges so if you miss the train you may have to pay the expensive on the day price for a different train, These prices and availability is dynamic so the nearer the time, or the busier the trains are going to be means they may go up in price or even disappear to leave the full scheduled fare.

The bad point is that these fast trains-named ICE-are often late or even very late in Germany. Also Stuttgart main station is under complete renovation and rebuilding making it as for now sometimes a nightmare to pass through when you board/alight at busy times.

Tickets will never ever get cheaper, but you can simply compare for next week or over 4-5 weeks-and see what the difference is. bahn.com is the site

Here is a credible report on D-bahn punctuality showing 3 in 4 ICE trains arrive within 6 minutes of scheduled arrival time. Considering the distance some of these trains (e.g. Hamburg to Munich) cover a 6 minute delay is nothing to be surprised at.

Overall almost 19 out of 20 D-bahn trains arrive on time.

https://www.railtech.com/policy/2022/01/07/major-punctuality-drop-long-distance-trains-deutsche-bahn/?gdpr=accept
I appreciate that 3 in 4 is poor, but many of those classed as late will still only be in the 7 - 20 mins category, so please keep reality in these posts, and facts are far more valuable for many of us.

The report says D-bahn is working hard to get all trains running punctually and by mid next year I would not be surprised if there isn’t a dramatic improvement in the next report.

To answer your question @Sh Tan

Both connections have hourly (direct) trains between each other.

Information about schedules and (ordinary) ticket prices are found here: https://www.bahn.com/en.