Quote from: Senzacervello on April 27, 2018, 07:00:49 PM

Quote from: Triple_S on April 27, 2018, 06:23:35 PM

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.

The thing with the half probability is easy: They generate a number from 0 to 4,294,967,296 and then divide it by 429,496.7296 resulting in a number from 0 to 10,000 which is then rounded giving the rolled number. All numbers from 0 to 0.4999999... will be rounded down to 0 resulting in a rolled 0. All numbers from 9,999.5 to 10,000 will be rounded up and result in a rolled 10,000. If I now look for example at the 5,000, it is being rolled either if a number from 4,999.5 to 5,000 is rounded up or if a number from 5,000 to 5,000.499999... is rounded down. In other words a 0 can only be resched by rounding down and a 10,000 only by rounding up while every other number can be reached either by rounding up or down. Therefore the 0 and the 10,000 are only half as probable as all other numbers.

To the average: There is only ONE AVERAGE. Of course if you roll, there is always a probability not hitting average, but the more often you roll the more close your average claim amount gets to the global average. To demonstrate the calculation of the global average lets assume all numbers were equally probabale because that easies the calculations. Because of this I assume all numbers would be rolled exactly once to make all numbers appear exactly with the same probability as proposed. Then I sum up all rewards I would get by rolling each number once and divide by 10,001, because I summed up the rewards of 10,001 numbers.

If this is still unclear, please read some literature about stochastics, because I don't think I can explain this very well in this thread, but I am 100% sure that my calculations are correct.