あなたはこれを考えすぎているのではないかと思います。単純な確率を使用して、コンピューターのスコアが「追いつく」頻度と量を見積もることができます。さらに、コンピューターのスコアと人間のスコアの差を計算し、これをシグモイドのような関数に入力して、コンピューターのスコアが増加する度合いを知ることができます。
例示的なパイソン:
#!/usr/bin/python
import random, math
human_score = 0
computer_score = 0
trials = 100
computer_ahead_factor = 5 # maximum amount of points the computer can be ahead by
computer_catchup_prob = 0.33 # probability of computer catching up
computer_ahead_prob = 0.5 # probability of computer being ahead of human
computer_advantage_count = 0
for i in xrange(trials):
# Simulate player score increase.
human_score += random.randint(0,5) # add an arbitrary random amount
# Simulate computer lagging behind human, by calculating the probability of
# computer jumping ahead based on proximity to the human's score.
score_diff = human_score - computer_score
p = (math.atan(score_diff)/(math.pi/2.) + 1)/2.
if random.random() < computer_ahead_prob:
computer_score = human_score + random.randint(0,computer_ahead_factor)
elif random.random() < computer_catchup_prob:
computer_score += int(abs(score_diff)*p)
# Display scores.
print 'Human score:',human_score
print 'Computer score:',computer_score
computer_advantage_count += computer_score > human_score
print 'Effective computer advantage ratio: %.6f' % (computer_advantage_count/float(trials),)