math and boardgames

The outcome of playtesting - is what "breaks" or "makes" a game. For example in my WIP, originally we would trade 2x card to buy cards. Well it just took too long. And so I modified it to 1x. So you trade 5 points for cards = 5 points.

Another idea that I scrapped because "in practice" it sucked was "charging weapons". In one of our scenarios, you battle an alien vessel. Well originally the aliens would charge their weapons. It turned out "not enough charging" made it virtually impossible to attack your homeworld (Planet). And so we had to alter the mechanic such that it's an alternate way to lose the game ("Critical mass"). Now we roll 1d6 to determine the firepower and damage that alien starship does...

So I would conclude IDEAS that are NOT playtested are worth 0%. You need to see if they work in the context of the game. The ideas may sound great but unless you actually TRY them... I wouldn't set them in stone...

For what it's worth (I've not published anything yet - this is just a hobby for me) I often do initial calculations/test runs using a python script or occasionally a spreadsheet (for instance, in a card or tile game involving drawing, I use these tools to calculate odds of certain desirable/undesirable occurrences/combinations) then I check my results with as much playtesting as possible.(Because I cant write code to predict human fun-levels). Of course I only do this when something is non-obvious/non-deterministic and obviously important enough to balancing the game.

Jarec, that doesn't always work.
A couple of months ago, I added something "new" to one of my games. And the average showed something totally different than what the real outcome would be.

Probabilities is something where you can use averages. But you need to keep your eye on all other possible numbers. And their true effects.

Math in games contain simple calculations, probabilities AND cause and effect situations.
If an effect situation is not wanted, you need to adjust the cause.

Both.

I come from a video game background, so it's slightly skewed, but I've met many designers who are pure math. They believe that numbers and statistics are supreme and they design based on it.

But they tend make those games games where you grind for 20 hours to get an item your friend got in 1 try. (Yay for "Replay Value") or casino games/mobile equivalents. This IS a valid way to look at things, and it is profitable when the house always wins.

But honestly, in the gaming realm, you also need to consider psychology. Two statistically equal events can feel VASTLY different from one another, and 99 of 100 players don't know much math and will assume their initial feelings are true.

Mathematics can give you a starting point, but you need proper playtesting to feel out the human element. Skew some numbers based on player response, remove elements that people feel are vastly different (Overpowered/Weak) than the math suggests, etc.

I've also chatted with many of the big name board game designers about design methods and math rarely came up. Playtesting ALWAYS did.

This isn't to say math isn't useful or that they don't use it... but that simply to stress the importance of live human testing.

Off the top of my head, I can't think of any specific examples either. But I know I've thrown out cards and full mechanics due to strong player response.

Certain effects can have added psychological impact like "Skip a turn", "Cancel opponents move", or even "Win the game if..."

Even if the odds of that instant win were one in a billion, the player who loses to it will often feel cheated. A player may have only lost 1 or 2 turns or actions... but this can often be exaggerated by emotions. It doesn't take much for a player to feel cheated.

For actual examples of Math Vs. Perception, two Sid Meier examples.

When developing one of the Civilizations he was using pure math. He had testers coming because it was "Broken", they had a %50 chance to win, but they lost 3 times in a row!

It was even worse in larger number battles... yeah 1 vs 2 should be %50, but now it's 10 on 20!

Eventually, he skewed the math to make it more intuitive. It'll cheat regularly to be a little closer to the "Perceived" Odds.

- - -

The same goes for the new X-Com. Alot of people complain about cheating dice rolls on higher difficulties, but that's not quite right.

Turns out, they added a bonus to your rolls on the easy difficulties so you can't miss 99% shots, and 50% is likely to hit regularly.

It's only when they start playing fair that things seem off.

- - -

And some gambling games (Including mobile F2P games) do the exact opposite. They skew the numbers to ensure they hit the minimum legal payout rates.

Keep in mind, board games ARE different because you are rolling the dice by hand. People are quick to blame AI for cheating, but slower to jump to the loaded dice conclusion.

Just keep in mind that player perception matters as much as reality. This can both be a valuable tool and an awful curse.

You make absolutely sense. But I didn't understand the last part.

I agree on copying nature. It worked for me a lot, even if it feels counter intuitive to some.

I also agree that a snowball effect needs to be stopped. They might slow down the game exponential. That is if they increase the number of steps in your game. Or they create infinity.

Exponential effects are indeed dangerous. Unless you have a linear effect cancelling them into becoming a linear effect themselves.

But what do you mean with a feedback mechanic? The cancelling that I just spoke of? Or something different?

Mathematics can be important and using something like python to script details is very useful at times.

But any part of your game that can be balanced using maths alone without playtesting has been solved and is not something very deep or interesting to play. So if your excel-sheets or python-scripts or whatever can tell you what the outcomes will be, with certainty, then you need to add something to the game to make the outcome more interesting and difficult to solve.

Of course small subsystems are OK if they can be solved. You do not need every little detail to be as deep as chess or go. But if for instance tactical battles are an important part of your game and you want player decisions related to battles to matter it is a really bad sign if you can balance the battles using spreadsheets without playtesting.

If a system (entire game or part of a game) has any decision in it, you will have to make sure that your calculations can account for the best possible ones, or they will not say anything at all about game balance, because a human player will sooner or later find the strategies you did not cover.

If the decisions are so trivial that you can easily script something (even in a spreadsheet!) that covers all possible decisions by both players, some player is going to solve that as well. It just can't be very meaningful decisions because if the correct/best answer is known there isn't really a decision at all, you just know what to do and do that.

Scripts are great for optimizing tiny subsystems for mechanics that run automatically, like a single battle in a larger strategic game, or when there are only a few player choices that you can enumerate. But if you can automatically for instance balance your unit types without serious playtesting then that means how players use those units, what decisions they make, are no longer important.

If I can calculate with maths that unit type A is exactly as powerful as unit type B, that means nothing either player does to tactically use those units matter unless you have managed to account for all possible tactical moves they can make ("wait, what if unit A moves into a forest hex, then takes special action X, retreats two hexes, takes special action Y, THEN it can easily beat a unit of type B at range 7... no wait what if that other unit is in an area with a unit of type C and then makes its special move Z to ..."). If your game is not full of interesting tactical decisions to make, why bother playing? So your script is better able to simulate all the possible combinations of actions that the units can take (and in combinations with other units) before it can say anything about game balance.

The most important use of maths is probably to ensure that the game can not be solved, which is the opposite of being able to simulate it for auto-balance.

Yes, calculations as input to playtesting is a great idea. As you say for simple things like calculating probabilities of drawing cards etc that do not rely on player choices they can provide very useful data. For slightly more complex interactions they can be used to give a good idea what values to use, but I would not put too much effort into making the scripts "perfect" because playtesting is too likely to reveal that the initial values were way off anyway.

I only use it to get games balanced. The "solvable" part. Sure the game has an unsolvable part. But where would you put the following?

Unit A and B are balanced. Now to see what kind of rock paper scissors can be made with both A and B in an army. By using spreadsheets you know that there is not one super team. But 2A2B beats 3A1B, which beats 1A3B, which beats in turn 2A2B.

Would you say that I solved it myself? Would you say that I made sure there is a RPS present at a bit more complexer level? What if other players solve this, would it matter?

I think it is important to check balances by math. Of course this means that you check the best playstyles as if players try hard.

Im agree. It was only an example. RPS is just purely random game... but it was an extreme example about incomplete information game.

Not all incomplete information game are purely random, in the 1/3 is a pure luck game, or very close (maybe you can use, after all, some complex analysis and psychology as in poker). When probability move from the mode to the extreme it is when the game make sense.

The point for any strategy game is making some plans and try to play it. But to make plans you need a really simple way to do it, other way you are playing a non-strategy game. As I said: chess and go are perfect examples, only masters and very experienced players can play a real strategy game, other people it is just trying random things because to see ahead you need a lot of experience and practice.

Poker and many other games are just the opposite: they are more closer to a pure strategy games... you only play strategic actions, not mechanic-algebraic-computer ones. The same for all kind of incomplete or imperfect information games as Stratego, Bridge, Truco, GOPS, maybe Hive and so on.

I never use only RPS. I only showed that as example. Just an example is not a game.

There are plenty of stuff to add to games.
Perhaps we should see RPS as an helping ingredient to a game. Not the game itself.

Just purely RPS is madness. We need a story around it. Other factors that are the game.

It might sound strange, but a lot of FPS these days also use RPS. Not as the core of the game, but as an extra. Somehow people love these games. Why? Perhaps they have now better ways in planning ahead. Buying the right weapons. Having enough ammo. etc. You have an economy/planning part. Which is strategy.

Playing a game with RPS, that is not just a random pull of luck. I agree there. But there are plenty of other mechanics to help with this. If it is board or video.

- Scouting, what is the other player building.
- Trying to trick the other player into building something by showing something that you build yourself. Here you use the RPS mechanic against your opponent in an entirely different way.
- If there is a possible battle, fight or run/retreat to better grounds? Perhaps you have created an ambush. You need to look a bit weaker for lurking in your enemy into the trap.
- If a direct fight occurs, which target should be destroyed first. Does the player have a helping tool for that ready? (ex. Event Card)

RPS might steer players into a certain direction. But it is up to the designer to make sure they keep plenty of choices in other area's.

And you can always make a game with several different rocks, papers and scissors. Or a scissor that is also paper.

How strong is the difference between the RPS? That is also important. Especially when you have randomness added.
A>B could be 10>1 or 5>4 or 5434>5433
If B is the weaker one, a player still might use B against A. And if B wins, B can have it's true use further ahead. Like blowing up a building or removing an important card.

However, 10>1 is very extreme. This is a hard counter.
5>4 can be a hard counter, or a soft one. Soft counters are the best to make a game, yet keeping some sort of RPS.
5434>5433 is probably just a result of trying to balance a game where A=B. But we all know that perfect balancing is almost impossible.

Unless you get infinite counters. Like a rock that beats scissors that beats paper,.. no exceptions.
And it is for that reason that people don't like a game purely based on RPS. Because then it is indeed just a random pull of luck.

first, i understand mathematic to be more related to a model, and then you have the probability

for example:
a game for 2 players, with a deck of 2 colours numbered from 1 to 15, each player chooses his colour

the mechanic is simple
the players draw 3 cards each
actions:
1 - deploy a card on the table
2 - draw a card or cards, according to the sum of values of deployed cards the player has, the total sum of both its the max cards possible that can be in hand
3 - put cards in a reserve deck
4 - attack, this can be done if you have deployed the same number of card that your opponent has, if u win the attack u take that card (from your opponent)
5 - add a card to attack or defence from your hand or the reserve

victory condition: to leave opponent without cards

so if u put less valuable cards you will have less card in your hand, but if u put more valuable cards you have less valuable cards to fight.

the mechanic works, but its incredible boring, even more boring than in the papers. Its long, few decisions, its almost a sum 0 and all the bad things you can say. But until you dont test you cant have the very real criteria.