What you are saying is absolutly true. Every roll is an independent event, so the chance to roll a 10000 is always the same. The statistical average can be calculated easy:
You multiply every reward with it's probability and sum them up. You have to note for this that the 0 and the 10000 have only half the probability as all other numbers. (That was discussed multiple times before and is true!) By doing this you basically assume that in 20000 rolls you will roll one time the 0 and the 10000 and two times all other numbers. Of course you can roll 20000 without rolling the 10000 once, but you can also roll the 10000 one, two three ... times in the 20000 rolls. By calculating the average you calculate these fluctuations out. If you roll infinite times you will hit exactly the average and if you roll like 2000000 times, you will get close to it.
The problem with this statement is that your expected value depends on the number of events you count to get it. Change that number and your expected value will change as well. In other words, you have as many different expected values (or average as you call them) as the number of events you count in your series.
By the way it is not clear to me why 0 and 10k should have only half of the probability in respect of all the other numbers.