The art of hunting is keep learning and improving your strategy. There are four steps.
Set your goal. Coins? Deck Power? Collect a specific card? A hybrid goal?
Test your parameters. Main card, supporting cards, challenge cards.
Analyze the results. Which set of parameters best meet your goal?
Take action. Need more tests? Adjust your parameters?
How to calculate Average Chance To Win (ACTW) [top]
Traits
Traits are statistically independent. That means: probability
that trait A and trait B are activated simultaneously
= (probability that trait A is activated) x (probability that trait B is activated).
Some traits will only be activated against opponents of certain power types (see 'Against' column).
Only the original power types (not changed by traits) will be considered.
Trait types can be attack (power added to you), defense (power deducted from your opponent),
or a power type (change your power type to this type).
Trait of supporting cards count.
Luck
Can be considered as a special trait. When a luck is activated, your power doubles.
Luck of supporting cards does not count.
Power Types
The five power types are: (1;6) fire, (2;7) metal, (3) wood, (4) earth, and (5) water.
Power type (x) is superior to Power types (x+1) and (x+2) for all x=1,2,3,4,5.
After taking into account activated traits (including luck), a superior power type receives a 15% power bonus;
an inferior one receives a 15% power reduction.
Now you have calculated a final power from one side.
Power types of supporting cards are not relevant.
Chance to Win
If your final power is zero or negative, you automatically lose.
If your final power is positive and your opponent's final power is zero or negative, you automatically win.
If both sides' final powers are positive, then chance to win = your final power / (your final power + opponent's final power).
Average Chance to Win (ACTW)
Each trait has two possibilities (activiated or not activated). So does luck.
If there are N traits from both sides (including supporting cards),
then there are 2^(N+2) possible encounters (luck of the two main characters are considered as a trait).
For each possible encounter, calculate probability and chance to win.
Treat traits (including luck) as statistically independent events.
For instance, probability that traits A and B are activated while traits C are not activated =
Probability that trait A is activated x
Probability that trait B is activated x
(1 - Probability that trait C is activated).
Find an expected value of chance to win =
summation of (probability of an encounter x chance to win according to that encounter).
I call it 'Average Chance to Win'.
An optimization approach would consider selection of main and supporting cards together.
Let me call a set of a main card and chosen supporting cards as a 'setup'.
Specify a goal. Maximizing coins? Maximizing deck power? Catching a specific card?
If your goal is to catch a specific card, the MythMonger
Batter Analyzer is best for you. For now, we don't help you choose yet.
Please try different setups and see how they work.
DO THIS: Choose a setup with the highest average chance to win.
If you do not have a specific card to catch, then you need to consider probabilities of
confronting each card in the area.
This tool (not owned by Pooflinger) may be able to help you about probabilities of
confronting each card in an area.
A score for each opponent is average chance to win that card x value of that card.
A value of a card encountered should correspond to your goal (coins, deck power, or
a function of coins and deck power).
DO THIS: Choose a score that corresponds to your goal.
Then select a setup that maximizes your setup's overall score.
If your goal is to maximize profit (coins), your score should be based on price
(your setup's overall score = price per hunt).
If your goal is to maximize power, your score should be based on power
(your setup's overall score = power per hunt).
However, this solution is a bit oversimplied. If you are sophisticated,
adjust your setup's overall score with cards that you will sell.
DO THIS: When you need to sell cards, sell cards that have lowest power-to-price ratios
so that you will lose least power given an amount of money raised.
You may need to keep certain cards for quests or collections (especially those
that are very difficult to encounter and/or to collect).
Choose in terms of an increase in average chance to win.
Suppose your original power = x, your opponent power = y.
You have one trait (power = a, chance = p). Your opponent has no trait.
Both you and your opponent have no luck.
If you trait is an attack type and is activated, then your chance to win increases by
(x+a)/(x+a+y) - x/(x+y)
= ay/(x+a+y)(x+y).
So, on average your chance to win increases by p*a*y/((x+a+y)(x+y)).
Similarly, if you trait is a defense type, then your average chance to win
increases by p*a*x/((x+y)(x+y-a)).
Note that defense type is, on average, better than the attack type of the same power and chance
if the combined power of yourself and your trait is higher than the power of your opponent.
p*a*x/((x+y)(x+y-a)) > p*a*y/((x+a+y)(x+y)) if x+a > y.
This means that if your power is 10 and your opponent's power is 16,
then you'd better go with an attack type trait if the trait's power is less than 6.
And you'd better go with a defense type trait if the trait's power is more than 6.