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It's got nothing to do with paying or not paying. It's just bad luck.
https://steamcommunity.com/sharedfiles/filedetails/?id=3474991199
The problem is perception. People have a few bad, maybe critical to the game, rolls. And they remember those and deem them unfair. But it's still random, and essential to the game of Risk. I've absolutely suffered to bad dice before, but I don't jump to the conclusion that it must just be rigged against me.
To add. If your rolls were NOT even. Then that'd show it WASN'T random. But they are, so it is.
Yes, we've all suffered greatly at times from bad dice rolls. It IS part of the game.
There is a difference between "possibility" and "probability", which is something most people don't understand. Each number has the possibility, or equal chance, of getting picked versus any other number. However, each number doesn't have the same probability, because certain numbers do in fact get picked more. That's the randomness of it all.
The number of tries is very important. And I feel when you quote lottery stats this is the point not being factored in. What you're pointing out is anomalies. Anomalies tend to disappear with more tries. To say "25 has been pulled 8 times this year, 14 has been pulled only 2 times", is not the same as "25 will always be pulled 4 times as often as 14.".
Random number generators are tested by this exact nature. A good RNG will eventually even out (like Risk 16% across the board, this is a sign the RNG is GOOD). A bad RNG; will often avoid the lowest/highest numbers, or have a tendency towards a certain value (imagine a shallow bell curve, etc).
Also worth noting. The randomness of sets of values is a lot different than individual numbers. If you were to measure the results of 2d6, you'd have a bell curve centred over 7. But that even this is a results of the individual rolls being even.
EDIT: Just wanted to come back and share this with you: https://anydice.com/
There was a better tester somewhere that shows the rolls over time, letting you see the anomalies but I can't recall where that was.
I've havn't seen any difference in the dice rolls or the bots behavior in FFA.
Ps...I've never lost a 7-2...and the 5 on 2 doesn't always work for me either.