viewtopic.php?f=36&t=13837#p29443
It is to answer which strategy on leveling up skill is better, 1 material card but smallest chance per strengthen or 6 material card highest chance?
I have write a script to simulate the situation and a sample results is attached at message end.
The (theoretical) answer is , they are the same.
Statistically, about 6.67 cards (note: 6.67 * 15% = 100%) need to level up one skill level, no matter using 1 or 6 cards per strengthen.
The 6 cards 90% chance strategy may be only psychologically fell better, until you miss the level up at 90% chance ;p
The calculation is purely theoretical, under the assumption the randomness follow the numerical value presented from the game.
It may not be the case in reality.
My personal believe is that the developer may 'cheating' in favor of the players ;p
In this case, 15% is better than 90%.
bye~
- Code: Select all
from random import *
def draw(n):
return random() < n * 0.15
def reach(m,n):
c = 0
t = 0
while c < m:
t = t + 1
if draw(n):
c = c + 1
return t
def sample(m,n,r = 10000):
c = 0
for i in range(r):
c = c + reach(m,n)
return c/r
# start ------
seed()
for j in [1,2,3,4,5,10,16]:
print("=== reach lvl ",j)
for i in range(1,7):
s = sample(j,i)
print("Each use {:1d}, total strengthen {:3d}, total used {:3d}, per level used {:5.2f}".format(i,int(s), int(s *i), s * i/j ))
# sample result
"""
=== reach lvl 1
Each use 1, total strengthen 6, total used 6, per level used 6.62
Each use 2, total strengthen 3, total used 6, per level used 6.72
Each use 3, total strengthen 2, total used 6, per level used 6.73
Each use 4, total strengthen 1, total used 6, per level used 6.68
Each use 5, total strengthen 1, total used 6, per level used 6.65
Each use 6, total strengthen 1, total used 6, per level used 6.67
=== reach lvl 2
Each use 1, total strengthen 13, total used 13, per level used 6.70
Each use 2, total strengthen 6, total used 13, per level used 6.69
Each use 3, total strengthen 4, total used 13, per level used 6.67
Each use 4, total strengthen 3, total used 13, per level used 6.74
Each use 5, total strengthen 2, total used 13, per level used 6.69
Each use 6, total strengthen 2, total used 13, per level used 6.67
=== reach lvl 3
Each use 1, total strengthen 20, total used 20, per level used 6.69
Each use 2, total strengthen 9, total used 19, per level used 6.66
Each use 3, total strengthen 6, total used 20, per level used 6.70
Each use 4, total strengthen 4, total used 19, per level used 6.67
Each use 5, total strengthen 3, total used 19, per level used 6.66
Each use 6, total strengthen 3, total used 20, per level used 6.68
=== reach lvl 4
Each use 1, total strengthen 26, total used 26, per level used 6.66
Each use 2, total strengthen 13, total used 26, per level used 6.71
Each use 3, total strengthen 8, total used 26, per level used 6.69
Each use 4, total strengthen 6, total used 26, per level used 6.64
Each use 5, total strengthen 5, total used 26, per level used 6.68
Each use 6, total strengthen 4, total used 26, per level used 6.66
=== reach lvl 5
Each use 1, total strengthen 33, total used 33, per level used 6.65
Each use 2, total strengthen 16, total used 33, per level used 6.62
Each use 3, total strengthen 11, total used 33, per level used 6.69
Each use 4, total strengthen 8, total used 33, per level used 6.63
Each use 5, total strengthen 6, total used 33, per level used 6.67
Each use 6, total strengthen 5, total used 33, per level used 6.66
=== reach lvl 10
Each use 1, total strengthen 66, total used 66, per level used 6.66
Each use 2, total strengthen 33, total used 66, per level used 6.67
Each use 3, total strengthen 22, total used 66, per level used 6.65
Each use 4, total strengthen 16, total used 66, per level used 6.66
Each use 5, total strengthen 13, total used 66, per level used 6.67
Each use 6, total strengthen 11, total used 66, per level used 6.66
=== reach lvl 16
Each use 1, total strengthen 106, total used 106, per level used 6.66
Each use 2, total strengthen 53, total used 106, per level used 6.67
Each use 3, total strengthen 35, total used 107, per level used 6.70
Each use 4, total strengthen 26, total used 106, per level used 6.66
Each use 5, total strengthen 21, total used 106, per level used 6.67
Each use 6, total strengthen 17, total used 106, per level used 6.67
"""