66 lines
2.2 KiB
Python
66 lines
2.2 KiB
Python
import numpy as np
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import numpy.linalg as la
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import matplotlib.pyplot as plt
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# Super slow attack speed. (Idealized to 1 hit/2s, 2/3 chance of proc
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mana_consumption = 6
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mana_steal = 14 # /3s
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mana_regen = 6 # /5s
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#mana_steal = 5 # /3s
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#mana_regen = 5 # /5s
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natural_regen = 1
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ms_period = 2
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ms_chance = ms_period / 3
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no_ms_chance = 1 - ms_chance
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MAX_MANA = 20
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TIME_CYCLE = 10
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transition_matrix = np.zeros((MAX_MANA * TIME_CYCLE, MAX_MANA * TIME_CYCLE))
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for j in range(TIME_CYCLE):
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for i in range(MAX_MANA):
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natural_state = max(0, i - mana_consumption + natural_regen)
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if j % 5 == 0: # mr activation
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natural_state = min(19, natural_state + mana_regen)
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next_ind = ((j+1) % TIME_CYCLE) * MAX_MANA
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if j % ms_period == 0: # ms activation
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ms_state = min(19, natural_state + mana_steal)
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transition_matrix[next_ind + natural_state, i+j*MAX_MANA] = no_ms_chance
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transition_matrix[next_ind + ms_state, i+j*MAX_MANA] += ms_chance
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else:
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transition_matrix[next_ind + natural_state, i+j*MAX_MANA] = 1
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eigval, eigvec = la.eig(transition_matrix)
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print(eigval)
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eps = 0.00001
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ind = np.argwhere(abs(eigval - 1) < eps)
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steady_state = np.sum(abs(eigvec[:, ind]).reshape((TIME_CYCLE, MAX_MANA)), axis=0)
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steady_state /= np.sum(steady_state)
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cumulative = np.cumsum(steady_state)
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print("mana\tcumulative probability")
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for i in range(MAX_MANA):
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print(f"{i+1}\t{cumulative[i]}")
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mana_limit = 6+mana_consumption
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x_ticks = list(range(len(steady_state)))
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plt.figure()
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plt.scatter(x_ticks, steady_state, label="mana values")
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plt.xlim(0, 19)
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plt.ylim(0, 0.3)
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plt.axvline(x=mana_limit, color="red")
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plt.xlabel("Mana Value")
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plt.xticks(x_ticks)
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plt.ylabel("Probability at t=infty")
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plt.legend()
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ax2 = plt.gca().twinx()
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ax2.plot(x_ticks, cumulative, label="cumulative probability", color="pink")
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plt.text(mana_limit - 0.2, cumulative[mana_limit] + 0.03, f"time with sprint loss: {cumulative[mana_limit]*100:.2f}%", horizontalalignment='right')
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plt.scatter((mana_limit,), (cumulative[mana_limit],), color="red")
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ax2.set_ylim(0, 1)
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ax2.set_ylabel("Cumulative probability at t=infty")
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plt.title(f"Super Slow Speed: Build={mana_regen}mr,{mana_steal}ms,{mana_consumption}mana/sec")
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plt.legend()
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plt.show()
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