Algorithms, usefull or not?

I typically start with calculations and algorithms and refine those by playtesting. There's definitely a mix involved.

Definitely a mix. Although I tend to be lazy and sloppy with maths and prefer mostly to just run simple computer-simulations instead (and when I do use maths, it's a good thing there are such things as R to do calculations so I don't have to remember the exact formulas).

One thing I sometimes try to do deliberately (and probably should do more) is to actively think about using my programming skills to improve my game design. Trying to go in directions that would be very difficult or impossible for non-programmers to do or that would not occur to them. I think everyone is at an advantage if working in a direction supported by other things they know. So if maths is your thing, you could probably make games work that the less math-skilled designers could never do or would never think of doing.

I am working on only 1 board game (wargame). And it is taking years because I simply don't have much time in my private time. However, my work allows openings for math. And I play test whenever a friend wants to.
The amount of math that I did is abnormal, I am sure of that.
But during your math making, make sure you keep track of the play testing as well. Don't bother them with math. Let them play and you watch them play.

So a good mix where you start with math is my suggestion. But always play test along the road.

Down here I have summarized my math/play test history. And the results. A TLDR post, I understand if you skip it. Anyway, it looks like how the long history of minecraft has come to live. Every little addition got calculated and play tested.

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The very beginning:
I started with 1 game rule formula.
Calculated, and personally play tested.
Recorded the results.
Transformed these results in a playtest-formula and expanded to all possibilities.

Added a second game rule formula.
And repeated the process.
With each addition I also monitored the combination effects of each game rule.

Overall, I changed 50% of the game rules after finding results I didn't want.
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During all this calculating. It is very important that other players take a look as well at your game.
They have to:
- Like the game (the rules).
- Understand the game (each rule).
- And being able to make strategies themselves (kinda bending the rules if they find a way :) ).

When you monitor this, you will notice that each player has his/her own playing style and decisions:
- Safe or Risky. (I still hate/love my cousin for doing that rush in the third game, but it was the best help ever)
- Smart or Dumb. (Being smart should not show the results right away, being dumb should not show the results right away either. Or the game ends to soon)
- Slow or Fast. (A combination of the previous options, but they could go both ways too).
- Honourable/Nice/Negotiable or Mean(in a fair way). (Allowing mean things can add a lot of fun, especially if the results are humorous for all players.)

You can put those results in table's as well. All I know is that since I "finally" did that. I had to change 1 of the first game rules. Witch meant a 50% change and again exporting all data into results and into data again. A chain reaction, sort of speak.
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Play-tester input:
Players can ask questions on which you never had thought.

- After training, you get certainty that you unit can kill others with 100% chance. Is there a way to have a chance on throwing 0 for every weapon?
So I have started finding another suitable damage dice table plus XP gain on this damage dice table. The original table also might be useful if the XP gain is altered. This in combination with that I still have not adjusted yet to the health reduction of 6 to 3. Each XP now increased with 2 levels instead of 1.

- After training a lot, your unit does overkill! Why even train it?
So now I can add more FAQs to my FAQs as guidance.
+Take along another unit in the same region, protect it during the battle and give the XP to that unit once you have made a kill.
+You can divide XP as well, making one unit a stronger meat unit while another one gains damage XP instead. This is especially helpful if one unit has the right armor and the other one has the right damage.
+You can have units keeping watch in the same region. Only to have their Range increased afterwards and have them join the fight the next round. However, this can be very expensive but rewarding if done right.

I also had the question of one of the players. Will there be upgrades? Or is using XP the only way?
So I started on making upgrade formula's. The costs need to be balanced (I want them to be, just like you) but there also needs to be diversity. This is pure math. But also pure giving in to the players.