How to Improvise in early design?

Math is really your friend in this.

There are some discrete things you need to define - like how often do I want an archer to beat a knight, or a knight to be infantry, or infantry to beat archers.

Balancing a game, for me, is a matter of zero-sums to start with desired outcomes.

I believe that "just improvise" is bad advice. If you don't have method behind your numbers, then what will be the method of fixing problems? It will likewise be direction-less - because you won't understand how all of the numbers integrate fully.

I usually begin with formulas, and variables before I add numbers.

Knights hit for 2x damage, and have x-1 hit points, and have x range
Archers hit for x-1 damage, and have x hit points, and have 2x range
Infantry hits for x damage, and have 2x hit points, and have x-1 range

Abstractly - I'm deciding that range, damage, and hit points are of equal power in my game. I might be wrong, but I always start that way - so when you look at the units, each has a 2x stat, a 1x stat, and an x-1 stat. They all seem balanced.

X could be a discrete number for a hard strategy game, or else it could be a die roll for a less strategic game. But defined in this way, you can see what the expected result is - Archers kill Knights, Knights kill Infantry, Infantry kill Archers.

If X was 3, then the values would look like this:
Unit_________Damage________Health__________Range
Knight_______6______________2______________3
Archers______2______________3______________6
Infantry______3______________6______________2

If you wanted to do dice, it might end up like this (where x = 1d6):
Unit_________Damage________Health__________Range
Knight_______2-12___________0-5______________1-6
Archers______0-5____________1-6______________6
Infantry______1-6____________2-12_____________0-5

Or you could do a combination. Like making Health and Range static, but Damage variable.

Then you play the game (I usually like to keep number small like this). If something seems weak, DOUBLE it - if something seems too powerful, HALVE it. This seems extreme, but it is a much faster way of narrowing down the right value (oh double was too powerful, that means I need to find a value between the original and the doubled value). If you can't get the granularity you need - then double ALL values in the game, this will give you half steps.

But what that means is you need to start with an idea of what you want the outcomes to be. You introduce dice (or a dice like mechanic - ie. a deck of values, a spinner etc) if you want a variable outcome (Knights should beat infantry 40% of the time), and you use static values if you want a discrete outcome (Knights ALWAYS beat infantry). And then lay out the stats on a piece of paper expressed as a simplified formula, and then adjust values in your formula to balance the game.

At least, this works for me - your mileage may vary.

I second (third?) the maths approach for dice-based games.

With regards to calculating probabilities, as onihero says it quickly becomes very hard to do theoretically (i.e. using Pure Maths). Luckily, a spreadsheet can help you here (i.e. using Applied Maths).

For example, I was experimenting with a game system that involved opposed rolls to inflict casualties over 3 rounds of combat. Each unit has a size and skill level. Theoretical probabilities are very difficult to calculate in this scenario. Instead, I used a spreadsheet to conduct a combat between my two units using the built-in random number generator to roll the dice. By putting the initial size and skill ratings of each unit as editable fields, I can play with the outcome. Once I'm relatively happy with it, I cut-n-paste the combat 100 times and tally the number of wins. Hit F9 to "reroll" and watch the outcome. This gives me a good approximation for the probability of side A beating side B.

This spreadsheet approach is also good for determining "lethality" in a wargame. In my example above, I found that there were too many draws -- that is, after 3 rounds of combat between evenly matched sides neither side had eliminated the other. For my game, I wanted draws to be rare, not common. So I tweaked the combat resolution to increase the casualty rate.

Similarly, you can play with different scenarios. If a Skill 4 unit is facing off against a Skill 1 unit of equal size, of course the Skill 4 unit wins. But what if the Skill 1 unit is bigger? What is the probability of a Skill 1 unit with 400 men beating a Skill 4 unit with 100 men? My spreadsheet can answer this question within seconds. This then guides my decisions about the relative cost of recruiting troops.

Yes, I like spreadsheets.

Special abilities are hard to work into a spreadsheet like this, because it gets very complicated very quickly. But I focus on balancing the game for "normal units" first, then gradually add special abilities once I know that the core of the game works.

Regards,
kos

Very useful answers !
Thanks to Yamahako and Kos, your replies are very inspiring....

...I generally just throw numbers that seem "right" when I start and adjust as the playtesting goes. Sometimes, we'll stop playtesting right then and there and just start over again with new numbers if we can see that some numbers are weighted so badly that the game is broken from the start.

The spreadsheet idea is brilliant! I never thought to use Excel that way (for those of you that don't have/want Excel...just grab OpenOffice...it's free and it's compatible with Excel...you'll also get a word processor, presentation software, some drawing software, etc.)

My latest game is a Sci-Fi based space game. One aspect is mining asteroids. Some asteroids have better yields than others, but you don't know what your yield is going to be until you start mining. So...I used a Fibernachi sequence to determine the possible mining yields. To get a Fibernachi sequence, you simply start a number line and add the next number to the one right in front of it to get the next number: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. The asteroids can yield anywhere from 1 mineral to 4 minerals per turn. I have a bunch of mining tokens in a bag. When you start mining, you grab a token from the bag.

There are 3 tokens that yield 4 minerals
There are 5 tokens that yield 3 minerals
There are 8 tokens that yield 2 minerals
And there are 13 tokens that yield 1 mineral

You'll notice that I didn't start the sequence at one or two....that's because I wanted just a few more chances to get the big 4...there's nothing that says you can't start the sequence anywhere you want.

I still need to playtest this, but it gave me a good place to start. I might find that the 4's are just too much...fine...I'll eliminate them and make it so the most an asteroid can yield is 3 minerals. All my adjustments can come from a lot of playtesting, which is what everyone should do anyway...playtest, playtest, playtest! :) The game also allows you to blow up an mining operation, or you can battle over it and take it away...I have to playtest this, too.

Anyway...I thought it was a good place to start and adjust from there. I hope it's helpful.

-CB-

Ahh, ok I get it.

I did a poor job of explaining in my example is why I start with math.

You don't know what numbers will work, you have to determine how the parts of your game work in relation to each other. For this reason its easiest to work in a formula.

If you're trying to create different elements, you come up with things like "I want this mechanic to cost twice as much as this mechanic because it does 1.5 times as much - and I want actions in the game to be precious."

So you've decided 3 things, each of those effects will cost 1 action (static value), they each have a cost, and they each have an effect. That creates 2 game elements

Element # 1
Actions: 1
Cost: X
Effect: Y

Element # 2
Actions: 1
Cost 2X
Effect: 1.5Y

Now, it is true that how I'm choosing the cost relative to the effect seems arbitrary - but it does come from a specific design goal - That of making Actions have greater value. Since it costs twice as much to do an additional 50% of an effect, It's more cost effective for me to do element 1, twice - but I save an action by doing element 2 - meaning (roughly) an action is worth (Y/2).

This means I can express all of the elements in this game in terms of "Y" based on a semi-arbitrary valuation of game parts.

Element # 1
Actions: Y/2
Cost: Y
Effect: Y

Element # 2
Actions: Y/2
Cost: 2Y
Effect: 1.5Y

You'll notice, that if you add up the "Y"s, each Element is worth 2.5Y, which I could then use to balance all of the other cards in the game to that standard.

This type of balancing is just a beginning to the balance of the game, its a way to start with a goal in mind. But you're not sure if what you've designed is going to work properly. You will need to define what Y means in costs and effects as well. If you want the smallest amount of currency in the game to cost 100$, and the effect to be deal 20 damage. Then you know that

Y = 1/2 action
Y = 100$
Y = 20 Damage.

You can then fill out all of your elements with a discrete value. If you later determine that you are over, or under, valuing a stat - you can adjust its "Y value" - This is the actual balancing of the game values to its mechanics.

You've already "balanced" the game to itself previously by relating all the mechanics back on each other - in sometimes arbitrary ways - so the really balancing comes in tweaking those values.

For example - If I've found in playtesting that 100$ is too much in this game to deal 20 damage, because the economy doesn't generate enough income - I can go a change the value - so I halve it. Now I have

Y = 1/2 action
Y = 50$
Y = 20 damage.

And all my numbers will change - but they will all change in relation to each other - because I know how I WANT the game to work.

If you have some great mechanics, but don't know what you want the outcome of those mechanics to be yet - then you might not really ready for a full on prototyping - I think you still want to do some thought experiments on the game. Thinking about how you want the narrative of the game to go will help a lot in this. Do you want a lone solider to have a chance to defeat 20 (variable combat mechanic)? Do you want people to mostly be playing with boats, but planes to exist (disproportionate costing)? All of these things can be expressed mathematically without having a single created digit.

Sometimes you know what you want a player to do (roll a die to combat against other players) and need to make sure you understand the consequences of that on the game (there will be a chance for either side to win) before you can express that in numbers - and that might be where people run into some problems.

Some other people might run into issues where they want combat to, 5% of the time, the loser totally wins - but not know how to express that in game terms. This board, I think, is perfect for helping out with that kind of assistance as well. But you still need to know, at least to a small effect, what you WANT to happen before you begin - then make a prototype with your best effort of that outcome being present - and then make all the tweaks that will certainly be necessary as your playtesters break your game.