Maths (probability) for unit types fighting each other

[Lord Dan]

Thanks - the other thread will be useful for newer players who don't already know all that stuff but I did read it and its worth sharing what you wrote.

In this thread I'm trying to focus down on determining the math that can give you specific outcomes from fights. Yes they're not important for large scale tactics, relatively. But to figure out how to get answers through math here, is for the function of unit balancing in a new game. If it can't really be done, we'll use playtesting.

I still think I need to create distribution graphs of each unit(s) fighting each other, to compare how often they will lose or win, and how many survivors on each side.
Yes, this is useful for small fights, not so much big fights. But in games there are both - also large fights are technically made up of lots of small fights, I think.

[Lord Dan]

Ok, here is what I've been talking about in terms of binomial graphs.
I've only put in the data for every 5 swings instead of every 1 swing.

axe vs sword time to be killed.png

This tells you what % chance at any time death occurs.
The Sword will most likely kill axe at 10 swings. You can see what chance this has to occur at different times.
The Axe will most likely kill sword at 25 swings.
The use of this information - to see how long until a unit can kill his enemy, and/or how close the enemy is to death. And compare them to each other.

At the bottom of have shaded areas - are these or another selection of areas what will tell us their overall strength?

axe vs sword chance to be killed.png

This tells you what % chance a unit has to have killed his opponent at given time. Or have survived!
This charts chance of death vs survival at any point in time.
The use of this information - to see how long a unit can survive (by not being dead).

I have shaded it again - could the area of these shapes be compared - the bigger the area covered - the more powerful the unit is in comparison?

Another practical use - when we know how long a unit can last, we know how long it could hold out to be flanked and killed if its stronger.
or know how long it can hold out to have a friend flank his opponent!
So we can tell how useful it is, and whether it needs to be buffed etc, to suit this purpose.

Here's an example,
If a sword fighter is being attacked by 2 axe fighters, it takes about 24 swings, or 8 swings in this case for him to have 50% chance to be dead.
IF you can get someone behind those axe fighters to kill them within 8 swings - about 10-15 seconds, then you have a good chance of saving him and killing the enemy.
If you can't get help within that amount of time, do something else (or at least don't try this manouver).

So here is where I draw the heavy use of maths into being useful for game tactics and game design

[Krom]

This thread covers KaM fights. I don't see how it ends up in Knights Province Development section. I have asked admins to move it.

[Lord Dan]

Ok well we can leave this as it is for now - I can revise or delete most of what I wrote in the first page if its irrelevant/wrong.

I think I've found at least 3 good systems for comparing strength, determing outcomes, and data on survival time for unit combat, even if its only duels (1v1)

Next I could invert the second chart above - it would give you chance for the unit to be alive after X seconds

Hopefully this thread can be left as a reference for future use

[equalizer]

I like this kind of research and also the dialogue, funny how a old game as KaM can be such complicated to understand!