All these measures won't stop bot users just because of one reason:
Bot users can calculate with the AVERAGE claim amount, because for example if a bot user has 1000 accounts that claim 24/7, he will roll a 10000 almost every day - It's pure statistics. Therefore the amount bot users will calculate with is the AVERAGE claim amount, not the MINIMUM. The AVERAGE claim amount is currently around 172 satoshi. Before you halfed the MINIMUM reward it was like 10 satoshi higher, so not significaltly different. All this does only apply to users with lots of accounts, cause they will hit the high rewards in reasonable time. Regular users will need multiple years because of the low chances.
I wouldn't be so sure. If each roll is an independent event (and very likely this is the case), the chance to get a 10.000 is always the same regardless of the number of rolls you make. And it is equal to the chance to get every other number.
In my opinion is also wrong your assumed average: you can easily roll 10.000 getting always the min amount. Then, if you want to support your theory and you want to come to the average you say by including in the sample rolls paid more than the min (but having the same chance to happen of all the others) you are simply choosing an arbitrary interval and produced a biased result.
All of this if each event (=roll) is set as an independent one. If you evidence that is not so, please let me know
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.
If you are a legit player, you roll maybe 15 times a day. With this speed you need almost 370 years to get to 2000000 rolls, but if you are a bot user with 1000 bots that claim 24/7, you get 2000000 rolls in less than 90 days! Therefore legit players can't really calculate with the AVERAGE claim amount because they would need just way too long to get to an amount of claims where the fluctuations are negliable. A bot user can claculate with the AVERAGE claim amount because he will reach a very large amount of claims in a few months.
Because of this a legit user is motly affected by the minimum claim amount and the lower reward stages. A bot user can calculate with a income close to statistical AVERAGE because of negliable statistical fluctuations and is therfore mostly affected by the higher reward stages and not the minimum reward.
Since only the minimum reward was changed, bot users are only a bit affected by it. It's all pure statistics.