My take on balancing the openEtG economy.
Okay, so yesterday I saw a player rage quit when they found out that upgrading required six of a given card…
I do have to agree, it would be nice to have the option of either 1) using 6 cards -> 1 upgraded card or 2) Crap tons of gold + 1 card -> 1 upgraded card.
There should be incentive to use the 6 card method, so the upgrade cost should be set appropriately…
Maybe set it to be 12 times the effective value of an unupgraded shard? (That comes out to about 400G)
Also, since there is no bazaar to sell cards at, we should probably put in a way to downgrade cards... easy thing would be to give back gold in exchange (200G maybe?... ie 2 upgrades shredded -> 1 new upgrade of your choice)
This all got me to thinking about the economy in openEtG and how to balance it better.
While fiddling with my entropy deck I was reminded that Zanz was a chemical engineer at one point (because chemists have to deal with the concept of entropy a lot)... which made something click!
Entropy could be the key to balancing the economy... Or at least give us an idea of what the distribution of card rarities should be for AIs.
Spoiler for background:
Entropy is the way a system will naturally try to distribute its energy out over a given number of states with various amounts of energy.
The probability a given 'quantum' of energy is placed in a state is given by a Boltzmann distribution
E.g. P(state) = exp( - Estate / Eavailable) / Q
where Q is basically the sum of the exp() values for all states
Well… we can think of our currency as energy!
Each card counts as 1 "state".
We know the values of each card based on booster pack prices and rarity counts
-> The "energy" of a state is the value of that card's rarity
-> For upgraded cards, we just multiply by 6 since it takes 6 unupped to make 1 upped
We can think of each AI level as an independent "system" where the available "energy" is the gold reward value for that AI.
… so… For the simplest approach, we can just use the 4 types of winnable rarities.
From some linear algebra, you would get:
common -> 1.667G, uncommon -> 6.667G, rare -> 28.33G, shard -> 33.33G
I have included the spreadsheet I made for this approach and committed it to my openEtG branch on GitHub, so anyone who wants can grab a copy or have a look:
https://github.com/OdinVanguard/openEtG.git… To do a really thorough job, I should actually include degeneracy… basically this would be a count of the total number of cards in each rarity.
This is a bit more complex, so I'll add it in later. For now, this is just a proof of concept.
Have a look at the sheet. The reward probabilities actually do seem to make good sense at a glance, even with this slightly easier approach.
In sticking with vanilla EtG I'll give the results where no shards are obtained from AIs (comma sperated format)
unupgraded probabilities
#AI_Type,P(common),P(uncommon),P(rare)
commoner,72.86%,26.79%,0.35%
mage,49.90%,28.44%,3.26%
champion,35.10%,27.33%,9.25%
upgraded probabilities
#AI_Type,P(common),P(uncommon),P(rare)
mage,20.38%,1.01%,0.00%
champion,23.14%,5.16%,.01%
demigod,67.09%,31.68%,1.23%
interestingly enough it seems that each AI level will have its own unique rarity optimum.
I.e. commoners are best for… commons
mages are good for uncommon
champions are good for rares
demigods are good for upped
Using this would be pretty simple… When AI decks get constructed, we have the deck generator pick a rarity first, then pick which card of that rarity to put in.
Rewards are automatically generated from the AI's deck so this should work out perfectly.