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How to design and balance a Rock-Paper-Scissor like mechanism

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X3M
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@lariennaIf you like. I

@larienna

If you like. I could focus entirely on one of your games in progress. That you wish to use this mechanic on.

I could work on an excel sheet that calculates the balance.
Make it more functional as well. So that changing numbers would be easier.

I am thinking of a pre-matrix in which you enter the number of dice used against a target. Then another pre-matrix in which you enter the number of dice used in a counter attack. (2 pre-matrixes since this is simpler to work with)

Heck, I can even throw in an extra column for a basic set of dice.

Edit:
The only issue is that I cannot calculate a winchance. But I could have the excel sheet look it up from a separate tab.

X3M
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A sheet that calculates the winchance

While anydice is like a program. I made a sheet where you can fill in the dice. And the result is calculated immediately as well.

These are only the winchances.
I made these matrix up to 14 dice.
Based on your 1/3rd succes rate per die.
I also included a calculation if a tie means a win.

The only problem is. I cannot implement this into the matrix balancer. Unless I am going to make an insane huge field in a secondary tab. Computing the winchance for every combo. Stay tuned. I might actually attempt this later on. :)

Edit: Scrap that. A look up table would be better.

X3M
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Simple weights

True balance depends on how much you use a certain ammount of dice.

But I have a list of simple weight factors.
Perhaps you can use this one as "damage" value's.
Solely based on a continues system of winning.
Ties are not included.

So, each unit you design, will deal this "damage" value.
And if the unit uses a different ammount of dice. A different "damage" value can be applied. Regardless of the ammount of dice the opponent uses.

3: 1
4: 1.6
5: 2.35
6: 3.26
7: 4.38
8: 5.73
9: 7.38
10: 9.39
11: 11.85
12: 14.86
13: 18.54
14: 23.07

How to use this?

Let's say, you have an unit that can use 6 dice.
There are 24 possible opponents.
To 6 of them, you can use 9 dice.
To 6 of them, you can use 10 dice.
So, to 12 of them, you can use only 6 dice.
The total weight will be; 12x 3.26 + 6x 7.38 + 6x 9.39 = 140.

If you have an unit that can use only 3 dice.
But has the same bonusses.
To 6, it uses 6 dice.
To 6, it uses 7 dice.
And of course, 12 of them, only 3 dice.
The total weight will be; 12x 1 + 6x 3.26 + 6x 4.38 = 58.

If you have some sort of cost. Then you might want to divide the numbers by 20.
You get 3 and 7 for these 2 examples.
It isn't perfect. But it is 100 times faster to calculate.

Perhaps I should see a top tier version of this. 9 dice, again with the same bonusses.
The total weight will be; 12x 7.38 + 6x 14.86 + 6x 18.54 = 289.
14.4, lets say 14.

So, 3, 6 or 9 dice, with those bonusses. Result in the weights of 3, 7 and 14.

Let me know, if this is better.

larienna
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One mechanic I am considering

One mechanic I am considering is 1 card vs 1 card, where each card could be associated to 2 different unit. It's a bit more complicated to calculate the contribution of a unit, but I think its still possible.

For example, each card could be something like:

If unit A and B is not present: Do effect W
if unit A is present: Do effect X
if unit B is present: Do effect Y
If unit A and B is present: Do effect Z

Or something similar. The inspiration is Starcraft the board game, In that game, you had stats if unit A was present or missing. I though I could put 2 unit combos on the card to promote natural synergies within the game.

Else it must be group battles and its much more complicated to evaluate the contribution of a unit. So I guess the main restriction criteria for this study is the one vs one dueling. Systems like Axis and allies makes it AI unfriendly because you need to manage targeting of damage.


The objective is to have different unit configuration, with strength and weakness. In order for this to work, you need a certain amount of complexity. Rolling the dice is not the slowest portion of the combat system. Matching units is the slowest part, especially if cards are chosen by players (instead of random with my variant)

I am not sure if there are better "duelist selection" mechanism that could be faster. The War card game could be a solution, flip the top card, roll and resolve. But that would work great only if you have many copy of the same card. It also makes it more AI friendly, he just draws the top card.

Which makes me realize that many multi unit system could be converted this way. For example, in my Dracula conquers Europe game, I wanted different types of unit, but was complicated to handle on the board. Now I could use a deck of card for the unit for your entire army, and simply use colored cube for the quantity of units.


As for why my variant, there are various reason. The action system was weird, some action were shared like in Puerto Rico, others was specific to the player. I decided to make them all player specific because many actions would make no sense to be shared. I also improved how trading works as a 2nd way to collect resources than gather.

The combat rules where improved to avoid the RPS mind game, allow retreat to reduce army annihilation which are hard to rebuild. The victory system has also been improved, victory cubes are assigned by the game, The only flaw is the wonder point reward, I could not figure out how to calculate this because its very sensible to the number of players. So a quick fix, is you win if you make the wonder. Else I made new buildings to power up certain actions ignored by the buildings.

So its really a melting pot of improvements selected mostly from community suggestions.

X3M
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Analysis paralysis

What if a player has to select x cards from its hand.
Shuffle them. And place them face up on the table.
The opponent does the same.
Then have the combat resolution follow the order of cards.

The cards that can have synergy together are often picked together.
There would be hardly any analysis paralysis this way.

And when a card that gives synergy ends up in the front and is defeated first. You simply know that this synergy is not in play.

X3M
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The balancer

Back to that AOM balancer.
I am done for 99%.

The whole vanilla is done.
It isn't much user friendly yet.
But I will work on it.

I have one special ability implemented.
The rest is still vanilla.

What can be changed are the number of dice, 3 possible attributes, then 2 attack-attributes, and 2 number of dice for those attacks.
The table will transpose what you fill in. Calculates the number of dice needed. Calculates the number of dice that fight back. Then looks up in a table of win chances, based on that a tie is discarded and rolled again.

These win chances are put in the table. And I made it so that if the faction is the same, they are not included.
(not sure if this works with changing sides for some, regarding balance)

I calculate the weights and counter weights with each itteration. Also what the true weight will be of an unit. And there is a red value showing how small the rebalance was.

The last rebalance has the smallest red number. close to 0.
This means that there won't be much changes to the balance anymore.

I also included the total weight for each faction.
Just remember that if you PAY this weight in one way or another, the game is balanced.

So far it seems that Greek is the strongest and Egyptian is the weakest. In vanilla firepower.

Only the mythical hero is included so far, with its special ability.

Still have to do some others. With medusa requiring a new lookup table. With ties being added for results.
Some others also need this table as well.

***

Quote:
Would you like me to include an imbalance factor based on a weight that you think is right?

And should I implement special cases? Or keep it vanilla?
Thus removing that one special?


***

I think that some units are better of, if I implement a weight factor prior on the winchances. Then I can do this in one go. The balance is slightly different. But more handable.

For example, if an unit doesn't die, but retreats. The loose factor gets closer to 0, while the win factor gets closer to 1. By 50%. So, 0.8 winning chance and 0.2 losing chance? It will now be 0.9 and 0.1. Not sure yet, but something like this.

***

I can tell that this rebalancer is needed, because the expected weights of some units double or half after the whole mix.
Even though I still need to implement all special cases.

larienna
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I will need to see your

I will need to see your numbers, it's hard to understand what is actually going on.

X3M
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Weight - AverageWinrate - AverageLosserate

0,71 12,75 9,04 Jarl
0,66 10,59 7,00 Throw Axeman
0,64 9,93 6,33 Huskarl
0,78 11,12 8,67 Dwarf
0,79 11,09 8,76 Valyrie
1,26 11,19 14,13 Classical Hero
0,99 11,49 11,33 Troll
0,64 8,78 5,59 Fenris Wolf
1,55 10,15 15,72 Hersir
1,11 11,56 12,88 Nidhogg
1,16 11,06 12,79 Frost Giant
2,34 7,77 18,19 Einherjar
0,67 10,19 6,86 Hoplite
0,69 12,47 8,61 Hippokon
0,65 10,59 6,93 Toxotes
0,73 10,83 7,90 Centaur
0,87 11,11 9,63 Minotaur
1,27 11,17 14,18 Classical Hero
0,82 11,36 9,28 Manticore
0,87 11,19 9,77 Medusa
1,57 10,12 15,91 Heroic Hero
0,97 11,40 11,03 Hydra
0,97 11,22 10,84 Cyclops
2,85 7,01 19,95 Mythical Hero
0,59 9,06 5,35 Chariot Archer
0,75 13,14 9,85 Spearman
0,66 9,88 6,57 Elephant
0,78 11,12 8,73 Anubite
0,84 11,08 9,31 Scorpion-Man
1,08 11,84 12,84 Priest
0,83 11,20 9,33 Wadjet
0,82 11,26 9,28 Mummy
1,39 10,92 15,17 Pharaoh
0,88 11,62 10,25 Sphinx
0,92 11,81 10,85 Phoenix
2,26 8,13 18,32 Son of Osiris

Warning!!
Only the Mythical hero in this one has a special ability, might as well remove it though.
I have NOT implemented any other one yet.

larienna
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Somebody on BGG made

Somebody on BGG made this:

https://onedrive.live.com/?redeem=aHR0cHM6Ly8xZHJ2Lm1zL3UvYy9iMWU3ZWUwOT...

It only calculate probabilities to win using brute force.

Effectively, egyptians looks weaker especially chariot archer.

larienna
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X3M, I am trying to

X3M, I am trying to understand your values:

Weight: Is an indicator you have designed?
Average win rate: Is the average number of battle they could win?
Average loss rate: Is the average number of battle they would loose?

The maximum number of battles I guess is 24.

How come the "Einherjar" has a loss rate the double of the win rate, while having a weight above 2 which is very strong. It should be as it is one of the strongest unit in the game.

In the other stats I posted above, it has approximately 69% chance to wins, that does not reflect in your numbers.

The chariot archer only have a lose rate of 5, so I guess there is a lot of ties (retreat).

X3M
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The title is wrong, oops. It

The title is wrong, oops.

It is not
Weight - AverageWinrate - AverageLosserate
But it has to be
Weight - AverageLosserate - AverageWinrate

Anyway this forum isn't very usefull to post things imho.

***

Explaning the numbers:

First know that this is a list that comes from "my approach". Hence, I bruteforced the numbers too.
But the win and loss rates are based on ties being rerolls.
So if the win-tie-loss is 0.4-0.5-0.1 Then I changed this into win-loss 0.8-0.2.

A big portion of the calculations is to see how much winrate an unit has. Then based on that, the winratio's of other units weight more or less depending on the targets weight of the winrate.
I rinsed and repeated this table.
What you get if you follow a number is that if the weight starts at for example 14. If most of the targets are heavy winners, this weight will increase to maybe 15 or even 16. After all, defeating a strong target should way more.

(The only special ability applied so far is the Mythical Hero.
The next one will probably be Medusa. She is going to be much much stronger for sure.)

At the end, we get a list of winrates. That has been balanced in weight.
But that same list of weighted winrates is then used as a weight to get a list of weighted lossrates.

If an unit has an overal of 12 weighted winrates and 6 weighted lossrates. Then you get 12/6=2.
2 will be the true weight number of that unit. It wins twice as much as it loses.

The Mythical Hero does seem to be the most expensive one here. At 2.85 it looks strong. Before the rebalance, it had a weight of even 5.3.
And if we look at the lowest weight, being 0.59 (comes from 0.295) for the chariot archer. One could recalculate the chariot archer to 1. And we get 4.83 for the Mythical Hero.

If I had a boardgame with these pieces and I would have a cost of 5 for the chariot archer, then the mythical hero gets 24.

***

Either way, what I didn't include is something with towers and walls. What is that all about?

Also, I will send the file I made in excel. As soon as I cleaned it up. But I have several options for the paths:
- Would you like me to apply all the special abilities as much as possible? Which will be too difficult for me.
- Or remove that one special ability for the mythical hero.
- Perhaps only having the ties of influence. Adding the tie ratio to the win or loss ratio and offer this as extra option in the table.

Lot's of options here. I don't know what you want to have for Ratscraft. Also, 3 factions, 12 units. Is that the ammount you need for Ratscraft?

X3M
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Combat density

I forgot. But if the combat density of an unit goes up. So has the cost.

This means that an unit that is twice as strong. Has a combat density that is twice as high.

To counter this. The only option is a higher cost. I apply this in my boardgames as well.

The triangle factor of 4 is 10.
The squared factor of 4 is 16.

Seeing as how this game only allows 1 on 1 battles per roll. I think we need to look at the squared factor. And thus take the square root of this number.

If an unit weights 4 times that of the smallest unit. Then the cost should be 8 times that of the smallest unit.

larienna
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Towers defend territory, wall

Towers defend territory, wall defend buildings in the city.

The attacker chose if he attacks the land or the city, it gives him different rewards.

The corresponding building should give +2 dices when defending one of those 2 areas.

X3M
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larienna wrote:Towers defend

larienna wrote:
Towers defend territory, wall defend buildings in the city.

The attacker chose if he attacks the land or the city, it gives him different rewards.

The corresponding building should give +2 dices when defending one of those 2 areas.


+2 dice when the attacked area can defend. That... is a big factor. Especially at the lower tiers.
And certain units will get the upper hand with more ease now.
The chariot archer for example will now have 8 higher chances and 2 equal chances if it defends.

Those units that negate this +2 effect are good attackers too.
Only the Cyclops and Elephant have this effect.

Since defences gives a bonus to all units. This isn't a yes/no situation anymore. And a clear example of the synergy that you are seeking.

The units have their own costs. But when defending. The effect of the walls makes them stronger. Here the average difference of the wall can be turned into an additional cost. That has to be placed on the wall.

If the average weight of the attackers go from 5 to 6. Then the wall certainly has to cost 1.

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