葡萄牙U21 VS 荷兰U21 总进球数

python
from PIL import Image
import matplotlib.pyplot as plt

img = Image.open('/mnt/data/image.png')
plt.imshow(img)
plt.axis('off')

(-0.5, 522.5, 35.5, -0.5)

python
import math, numpy as np
lam=2.6
probs=[math.exp(-lam)*lam**k/math.factorial(k) for k in range(7)]
p_gt6=1-sum(probs)
probs.append(p_gt6)
probs

[0.07427357821433388,
 0.1931113033572681,
 0.25104469436444854,
 0.21757206844918872,
 0.14142184449197268,
 0.0735393591358258,
 0.031867055625524505,
 0.017170096361437848]

python
odds=[18,6.5,3.8,3.6,4.75,8.10,14.50,20]
ev=[p*o-1 for p,o in zip(probs,odds)]
list(zip(range(7),probs,odds,ev))

[(0, 0.07427357821433388, 18, 0.3369244078580098),
 (1, 0.1931113033572681, 6.5, 0.2552234718222426),
 (2, 0.25104469436444854, 3.8, -0.04603016141509564),
 (3, 0.21757206844918872, 3.6, -0.21674055358292055),
 (4, 0.14142184449197268, 4.75, -0.32824623866312974),
 (5, 0.0735393591358258, 8.1, -0.4043311909998111),
 (6, 0.031867055625524505, 14.5, -0.5379276934298947)]

python
ev_gt6=probs[-1]*odds[-1]-1
ev_gt6

-0.656598072771243

python
lam=2.8
probs2=[math.exp(-lam)*lam**k/math.factorial(k) for k in range(7)]
probs2.append(1-sum(probs2))
ev2=[p*o-1 for p,o in zip(probs2,odds+[20])]
ev2

[0.09458112725392342,
 0.1067431397789671,
 -0.09417330713475325,
 -0.19905850315072926,
 -0.26024153416004847,
 -0.29356959977894326,
 -0.409854439321504,
 -0.5117876095131026]

python
k=100
s0,s1,s2=[k/18, k/6.5, k/3.8]
tot=sum([s0,s1,s2])
profit=k - tot
prob_under=p := (probs2[0]+probs2[1]+probs2[2]) # for lam 2.8
ev=prob_under*profit - (1-prob_under)*tot
tot,profit,prob_under,ev

python
k=100
stake0=k/18
stake1=k/6.5
stake2=k/3.8
tot=stake0+stake1+stake2
profit=k - tot
prob_under=sum(probs2[:3])
ev=prob_under*profit - (1-prob_under)*tot
ev

-0.31059206718687804

python
lam=2.6
prob=[math.exp(-lam)*lam**k/math.factorial(k) for k in range(8)]
stake=1
exp=prob[0]*(18*1-2)+prob[1]*(6.5*1-2)+sum(prob[2:])*(-2)
exp

0.6028154025098811

python
odds=[18,6.5,3.8,3.6,4.75,8.1,14.5,20]
implied=[1/o for o in odds]
implied

[0.05555555555555555,
 0.15384615384615385,
 0.2631578947368421,
 0.2777777777777778,
 0.21052631578947367,
 0.1234567901234568,
 0.06896551724137931,
 0.05]

python
lam=2.6
probs=[math.exp(-lam)*lam**k/math.factorial(k) for k in range(7)]
probs.append(1-sum(probs))
ratio=[p/i for p,i in zip(probs,implied)]
ratio

[1.3369244078580098,
 1.2552234718222426,
 0.9539698385849045,
 0.7832594464170793,
 0.6717537613368703,
 0.5956688090001889,
 0.46207230657010534,
 0.34340192722875695]

python
lam=2.6
p=probs[0]
o=18
q=1-p
f0=(p* (o-1)-q)/(o-1)
p=probs[1]
o=6.5
q=1-p
f1=(p*(o-1)-q)/(o-1)
f0,f1

(0.019819082815177042, 0.046404267604044126)

python
from PIL import Image
import matplotlib.pyplot as plt

img = Image.open('/mnt/data/image.png')
plt.imshow(img)
plt.axis('off')

(-0.5, 522.5, 35.5, -0.5)

python
odds = {0: 18, 1: 6.5, 2: 3.8, 3: 3.6, 4: 4.75, 5: 8.1, 6: 14.5, 7: 20} # 7 stands for >6
# stakes strategy A: 2% and 4.6% of bankroll (BR). Let's assume BR=100.
BR=100
stake0 = 0.02*BR
stake1 = 0.046*BR
print(stake0, stake1, stake0+stake1)
for k in [0,1,2,3,4]:
    if k<=1:
        profit = odds[k]*(stake0 if k==0 else stake1) - (stake0+stake1)
    else:
        profit = -(stake0+stake1)
    print(k, profit)

python
target=100
stakes={}
stakes[0] = target/odds[0]
stakes[1] = target/odds[1]
stakes[2] = target/odds[2]
total_stake = sum(stakes.values())
profit = {}
for k in [0,1,2]:
    profit[k] = target - total_stake
total_stake, profit

(47.25596041385515,
 {0: 52.74403958614485, 1: 52.74403958614485, 2: 52.74403958614485})

python
import math
lam=2.6
prob={}
exp_value= -total_stake
for k in range(0,3):
    prob[k] = math.exp(-lam)*lam**k/math.factorial(k)
    exp_value += prob[k]* (target)
exp_value

4.586997179749904

python
stakes_ratio = [1/18, 1/6.5, 1/3.8]
total = sum(stakes_ratio)
ratio_perc = [s/total for s in stakes_ratio]
ratio_perc

[0.11756306520704426, 0.32555925749643033, 0.5568776772965255]

python
lam_p = 1.8
lam_n = 0.8

def poisson_prob(k, lam):
    return math.exp(-lam) * lam**k / math.factorial(k)

# compute probabilities up to e.g. 5 goals each
max_goal = 6
dist_p = [poisson_prob(k, lam_p) for k in range(max_goal+1)]
dist_n = [poisson_prob(k, lam_n) for k in range(max_goal+1)]

# compute result categories
p_win=0
draw=0
n_win=0
score_probs={}
for i, ppi in enumerate(dist_p):
    for j, ppj in enumerate(dist_n):
        prob=ppi*ppj
        score_probs[(i,j)]=prob
        if i>j:
            p_win+=prob
        elif i==j:
            draw+=prob
        else:
            n_win+=prob

p_win, draw, n_win

(0.608769582777148, 0.22647916448141567, 0.16216110958579572)

python
sorted(score_probs.items(), key=lambda x: x[1], reverse=True)[:10][:10]

[((1, 0), 0.13369244078580098),
 ((2, 0), 0.12032319670722089),
 ((1, 1), 0.10695395262864078),
 ((2, 1), 0.09625855736577671),
 ((0, 0), 0.07427357821433388),
 ((3, 0), 0.07219391802433253),
 ((0, 1), 0.0594188625714671),
 ((3, 1), 0.057755134419466024),
 ((1, 2), 0.04278158105145632),
 ((2, 2), 0.038503422946310685)]