- A reference guide and manual in Russian for Heroes 3.

I have a question:
Let's say I have a save from the end of the seventh day, and I want Monday to be a special day – for example, a monster week.
How can I achieve this in practice?

There's no way. There's no guarantee that you'll get all the possible outcomes by trying different combinations. I believe the system uses some kind of random numbers that it collects as the game progresses. For example, if you replay a battle that took place on Thursday, completely different monster week combinations will be generated for the night from Sunday to Monday... But, nevertheless, this is just speculation based on experience. It's unlikely that anyone can say for sure.

Or: I restart the save from the end of the seventh day a large number of times. This doesn't work. Can I be sure that this won't work for anyone else on the same starting tournament save?

No. Each player will have their own results for the reasons mentioned above.

I can't resist commenting on the roulette:
The casino doesn't win on zero.
The casino wins because of the player's euphoric memory.

These are two independent reasons. The casino wins because the player usually leaves after losing, not after winning. But it's not reasonable to think that the roulette was created with the player's psychology in mind. Pure mathematics is at work here – there are 37 (or 38, if there are two "zeros") fields on the table, and the maximum payout is 36 to 1. If you take a large number (for example, a million) of bets of $1 on random fields, then for every $37 of bets, $36 will be paid out to the players.

The casino's guaranteed income is 1/37 of the turnover. And the "zero" is said to be the casino's income – purely figuratively. Because "zero" does not participate in any of the standard combinations – straight, four of a kind, black, red, dozen, etc. That is, with any bet on a combination, "zero" will be the casino's income. All other bets will be divided among the players – on average, based on the theory of probability with a large number of bets.

We're not talking about defects in the drum – there's just a shift in the probability of certain combinations occurring, which, of course, with a skillful approach, allows you to increase the chances of winning, but does not guarantee them...

Martingale systems don't work for only one reason – the upper limit of the bet on the table. The maximum I've seen is a ratio of maximum to minimum bets of 1:500, but usually it's much less – 1:100.

That's it. There are no other reasons. This has been proven long ago. Not by me... ;)

Added after 17 minutes

I have a question.
What is the probability of neutral units behaving the same way in battles?
I'm asking to know if it's possible to achieve 100% repeatability of their behavior.

In relatively simple cases – yes – for example, Archers will always try to attack or block a stack of archers with their first move (depending on the balance of power). And they will never attack slow units... That is, their behavior is predictable here.

But in most cases, battles are much more complex, and the occurrence of random events such as morale and luck can significantly change the battle tactics. Even if the player blocks these random events, it will not be possible to achieve the same amount of damage being dealt by the troops. This is a completely random value within a certain range. And here, tactics can be adjusted depending on the change in the balance of power during the battle.