Introduction
I'm comming to this post to tell something i realised yesterday. I thinked "Maybe we pay too much for ultraballs". So i go to bulbapedia to see the capture mechanics in this game.
The third generation (Fire Red and Emerald) have a simple system of catch, based on three formulas. The calculus will be omited because I think nobody will like it (and i cant add gif's and png's at this forum).
Introduced these concepts (if you wanted to read) we will try simplificate this f*ck. To do you need have in mind this results are rounded.
The major simplification when i had is an adiction of one in the numbers like 2^k-1.
Now we will assume initials values for the variables, before do that we will consider an hard capture pokemon (the lower catch rate in this game is 3).
First case: At the first case we will use to think in a poke sleeping with one point left on HP. Well, in this case the value of "a" will be, rounding, 6 times the ball value, and "b" will be 2^14 times the fouth root of a.
Second case: For this case the poke have full HP and no status. Well, in this case the value of "a" will be same then the ball value, and "b" will be 2^14 times the fouth root of "ball".
The Probability of each shake
To find the probability we will find the how much possibles values of s our b beats. For this we have to divide b for maximum of s, 2^16. Probability will be the fouth root of a divided for 4
Test of Pokeballs
I will test the efectiveness of 4 kinds of pokeballs, the normal, great, ultra and repeat. They have 1x, 1.5x, 2x and 3x of efectiveness, respectively. The founded Value is for the first shake of the ball.
First Test: The probability for first shake will be:
Pokeball: p=39,13%
Greatball: p=43,3%
Ultraball: p=46,53%
Repeatball: p=51,49%
Second Test: The probability for first shake will be:
Pokeball: p=25%
Greatball: p=27,67%
Ultraball: p=29,73%
Repeatball: p=32,9%
Probability for capture: For capture we will need four shakes, the formula will be "a" divided for 4^4
First Test: The probability for capture will be:
Pokeball: p=2,34%
Greatball: p=3,51%
Ultraball: p=4,69%
Repeatball: p=7%
Second Test: The probability for capture will be:
Pokeball: p=0,39%
Greatball: p=0,59%
Ultraball: p=0,78%
Repeatball: p=1,17%
How many pokeballs we have to use for 90% of capture chance?
First Test:
Pokeball: 97 balls
Greatball: 65 balls
Ultraball: 48 balls
Repeatball: 32 balls
Second Test:
Pokeball: 588 balls
Greatball: 391 balls
Ultraball: 294 balls
Repeatball: 195 balls
Final test: Capture Rate if You use same money for Pokeball and Other ball
Pokeball costs 200 pokeyens, Greatball 600, ultraball 1200 e repeatball 1500.
Greatball: In cash one greatball costs for three pokeballs.
First Case:
Greatball have 3,51% of capture rate.
Three Pokeballs have 6,85%
Second Case:
Greatball have 0,59% of capture rate
Three Pokeballs have 1,16%
Ultraball: In cash one ultraball costs for six pokeballs.
First Case:
Ultraball have 4,69% of capture rate.
Six Pokeballs have 13,24%
Second Case:
Ultraball have 0,78% of capture rate
Six Pokeballs have 2,31%
Repeatball: In cash one repeatball costs for seven and a half pokeballs.
First Case:
Repeatball have 7% of capture rate.
Seven and a half Pokeballs have 16.27%
Second Case:
Repeatball have 1,17% of capture rate
Seven and a half Pokeballs have 2,88%
Conclusion: Even on the hardest case, Buy Pokeballs