As Catch already noted, the Bernoulli distribution works well for long battles, so I am submitting my specific proposal for consideration and constructive criticism. It is quite strict regarding hardcore random number generation, but I believe there is no other way. 1. In a round, there should be no more than 1 trigger with morale (luck) +1 and no more than 2 triggers with morale (luck) +2, +3. 2. For any 12, 8, 4 consecutive rounds, there should be no more than one trigger with morale (luck) +1, +2, +3, respectively. 3. Morale and luck can occur simultaneously only once in a battle when both indicators are +3; on units attacking twice and with indicators of +2. The case of negative morale can be considered separately, but for battles in several rounds, it can be considered zero.

What about checking? Does each player send a step-by-step description of the moves in each battle?

Of course not. If someone wants to cheat with the new restriction, nothing prevented them from doing so before, only with other restrictions (and simply breaking intermediate battles), because not everything is caught even now. But if a cheater takes a high place, they will be asked to provide a walkthrough and a description. So, those who want to cheat will have to aim for mediocre places.