六合彩每注期望值$3.3 28/12/2024,20.39

# 定義變數
total_bet_amount = 100856692 # 總投注額 (港幣)
golden_bet_amount = 43814452 # 金多寶 (港幣)
bet_per_unit = total_bet_amount / 10 # 每注投注金額 (港幣)

# 計算獎金基金
jackpot_fund_total = total_bet_amount * 0.54 # 獎金基金 (港幣)

# 定義獎金
fourth_prize = 9600 # 第四組獎金 (港幣)
fifth_prize = 640 # 第五組獎金 (港幣)
sixth_prize = 320 # 第六組獎金 (港幣)
seventh_prize = 40 # 第七組獎金 (港幣)

# 定義中獎機率
probabilities = {
"頭獎": 1 / 13983816,
"二獎": 1 / 2330636,
"三獎": 1 / 55491.33,
"第四組": 1 / 22196.53,
"第五組": 1 / 1082.76,
"第六組": 1 / 812.07,
"第七組": 1 / 60.9,
}

# 計算各組獎金的期望中獎人數
expected_winners = {
"頭獎": probabilities["頭獎"] * (total_bet_amount / 10),
"二獎": probabilities["二獎"] * (total_bet_amount / 10),
"三獎": probabilities["三獎"] * (total_bet_amount / 10),
"第四組": probabilities["第四組"] * (total_bet_amount / 10),
"第五組": probabilities["第五組"] * (total_bet_amount / 10),
"第六組": probabilities["第六組"] * (total_bet_amount / 10),
"第七組": probabilities["第七組"] * (total_bet_amount / 10),
}

# 計算第四、五、六及七組的總獎金
lower_prizes_total = (
(fourth_prize * expected_winners["第四組"]) +
(fifth_prize * expected_winners["第五組"]) +
(sixth_prize * expected_winners["第六組"]) +
(seventh_prize * expected_winners["第七組"])
)

# 計算金多寶扣數
sixty_percent_jackpot_fund = 0.6 * jackpot_fund_total
golden_bet_deduction = (
0.09 * (jackpot_fund_total - lower_prizes_total - 0.55 * sixty_percent_jackpot_fund) +
0.55 * sixty_percent_jackpot_fund
)

# 計算第一、二、三組獎金
first_prize = 0.45 * (jackpot_fund_total - lower_prizes_total - golden_bet_deduction) / max(expected_winners["頭獎"], 1)
second_prize = 0.15 * (jackpot_fund_total - lower_prizes_total - golden_bet_deduction) / max(expected_winners["二獎"], 1)
third_prize = 0.40 * (jackpot_fund_total - lower_prizes_total - golden_bet_deduction) / max(expected_winners["三獎"], 1)

# 計算每組獎金的期望值
expected_values = {
"頭獎": first_prize * expected_winners["頭獎"],
"二獎": second_prize * expected_winners["二獎"],
"三獎": third_prize * expected_winners["三獎"],
"第四組": fourth_prize * expected_winners["第四組"],
"第五組": fifth_prize * expected_winners["第五組"],
"第六組": sixth_prize * expected_winners["第六組"],
"第七組": seventh_prize * expected_winners["第七組"],
}

# 計算總期望值
total_expected_value = sum(expected_values.values())

# 計算每注的期望值
expected_value_per_unit = total_expected_value / (total_bet_amount / 10) # 每注的期望值

# 輸出結果
print(f"獎金基金: {jackpot_fund_total:.2f} 港幣")
print(f"金多寶扣數: {golden_bet_deduction:.2f} 港幣")
print(f"第一組獎金: {first_prize:.2f} 港幣")
print(f"第二組獎金: {second_prize:.2f} 港幣")
print(f"第三組獎金: {third_prize:.2f} 港幣")

# 輸出期望中獎人數
print("\n期望中獎人數:")
for prize_name, expected_value in expected_winners.items():
print(f"{prize_name}: {expected_value:.2f} 人")

# 輸出每注的期望值
print(f"\n每注的期望值: {expected_value_per_unit:.2f} 港幣")
獎金基金: 54462613.68 港幣
金多寶扣數: 19373757.52 港幣
第一組獎金: 6374982.26 港幣
第二組獎金: 491051.97 港幣
第三組獎金: 31177.90 港幣

期望中獎人數:
頭獎: 0.72 人
二獎: 4.33 人
三獎: 181.75 人
第四組: 454.38 人
第五組: 9314.78 人
第六組: 12419.70 人
第七組: 165610.33 人

每注的期望值: 3.30 港幣
Formula source:https://special.hkjc.com/root2/marksix/info/ch/mark6/important_notice.asp

獎金基金: 54462613.68 港幣
金多寶扣數: 19373757.52 港幣
第一組獎金: 6374982.26 港幣
第二組獎金: 491051.97 港幣
第三組獎金: 31177.90 港幣

期望中獎注數:
頭獎: 0.72 注
二獎: 4.33 注
三獎: 181.75 注
第四組: 454.38 注
第五組: 9314.78 注
第六組: 12419.70 注
第七組: 165610.33 注

每注的期望值: 3.30 港幣

你肯定係計數咁計？

前排先有期懷似做漏野有5個字一樣

幾好 真技術討論
不過你個計算
1. 計漏左補底 頭三獎有補底
2. max(expected_winners["頭獎"], 1) <-- 我未必同意 由其得8球+下期金多寶會勁少有買 2/3獎就分別未必好大
3. 你個答案係adjusted expected value (用事實去入para)
我會建議你將估計頭獎獎金同投注額同中獎人數做個regression/correlation
再出個事前expected value

啱
update左下
但過往中彩注數我只係識逐個逐個input所以驚sample size太細
# 定義變數
total_bet_amount = 100856692 # 總投注額 (港幣)
golden_bet_amount = 43814452 # 金多寶 (港幣)
bet_per_unit = total_bet_amount / 10 # 每注投注金額 (港幣)

# 計算獎金基金
jackpot_fund_total = total_bet_amount * 0.54 # 獎金基金 (港幣)

# 定義獎金
minimum_first_prize = 8000000 # 頭獎補底 (港幣)
fourth_prize = 9600 # 第四組獎金 (港幣)
fifth_prize = 640 # 第五組獎金 (港幣)
sixth_prize = 320 # 第六組獎金 (港幣)
seventh_prize = 40 # 第七組獎金 (港幣)

# 定義中獎機率
probabilities = {
"頭獎": 1 / 13983816,
"二獎": 1 / 2330636,
"三獎": 1 / 55491.33,
"第四組": 1 / 22196.53,
"第五組": 1 / 1082.76,
"第六組": 1 / 812.07,
"第七組": 1 / 60.9,
}

# 計算各組獎金的期望中獎人數
expected_winners = {
prize: probabilities[prize] * (total_bet_amount / 10)
for prize in probabilities
}

# 計算第四、五、六及七組的總獎金
lower_prizes_total = (
(fourth_prize * expected_winners["第四組"]) +
(fifth_prize * expected_winners["第五組"]) +
(sixth_prize * expected_winners["第六組"]) +
(seventh_prize * expected_winners["第七組"])
)

# 計算金多寶扣數
sixty_percent_jackpot_fund = 0.6 * jackpot_fund_total
golden_bet_deduction = (
0.09 * (jackpot_fund_total - lower_prizes_total - 0.55 * sixty_percent_jackpot_fund) +
0.55 * sixty_percent_jackpot_fund
)

# 計算第一、二、三組獎金
remaining_fund = jackpot_fund_total - lower_prizes_total - golden_bet_deduction

first_prize = max(minimum_first_prize, 0.45 * remaining_fund / expected_winners["頭獎"]) # 仍然考慮補底
second_prize = 0.15 * remaining_fund / expected_winners["二獎"]
third_prize = 0.40 * remaining_fund / expected_winners["三獎"]

# 計算每組獎金的期望值
expected_values = {
"頭獎": first_prize * expected_winners["頭獎"],
"二獎": second_prize * expected_winners["二獎"],
"三獎": third_prize * expected_winners["三獎"],
"第四組": fourth_prize * expected_winners["第四組"],
"第五組": fifth_prize * expected_winners["第五組"],
"第六組": sixth_prize * expected_winners["第六組"],
"第七組": seventh_prize * expected_winners["第七組"],
}

# 計算總期望值
total_expected_value = sum(expected_values.values())

# 計算每注的期望值
expected_value_per_unit = total_expected_value / (total_bet_amount / 10) # 每注的期望值

# 輸出結果
print(f"獎金基金: {jackpot_fund_total:.2f} 港幣")
print(f"金多寶扣數: {golden_bet_deduction:.2f} 港幣")
print(f"第一組獎金: {first_prize:.2f} 港幣")
print(f"第二組獎金: {second_prize:.2f} 港幣")
print(f"第三組獎金: {third_prize:.2f} 港幣")

# 輸出期望中獎注數
print("\n期望中獎注數:")
for prize_name, expected_value in expected_winners.items():
print(f"{prize_name}: {expected_value:.2f} 注")

# 輸出每注的期望值
print(f"\n每注的期望值: {expected_value_per_unit:.2f} 港幣")
獎金基金: 54462613.68 港幣
金多寶扣數: 19373757.52 港幣
第一組獎金: 8838935.44 港幣
第二組獎金: 491051.97 港幣
第三組獎金: 31177.90 港幣

期望中獎注數:
頭獎: 0.72 注
二獎: 4.33 注
三獎: 181.75 注
第四組: 454.38 注
第五組: 9314.78 注
第六組: 12419.70 注
第七組: 165610.33 注

每注的期望值: 3.48 港幣

從數學上用幾多錢買邊種投注方式係最大機會中頭獎？
N注單式？好多個字複式？
N注小數字既複式？定拖膽？

https://special.hkjc.com/root/marksix/info/ch/mark6/chance.asp
啱睇完份表
我聽日試下計

from math import comb
# 總可選號碼
n = 49
# 中獎號碼數量
k = 6
# 複式投注的注數
m
# 計算單式投注的中獎機會
def calculate_single_probability():
return 1 / comb(n, k)

# 計算不同拖膽方式的中獎機會
def calculate_drag_probabilities(drag_numbers):
return comb(n - drag_numbers, k - drag_numbers) / comb(n, k)

# 計算複式投注的中獎機會
def calculate_multiple_probability(num_bets):
return num_bets / comb(n, k)

# 複式投注的中獎機會
prob_multiple = calculate_multiple_probability(m)

我計到單式係最大機會

咁馬會係幾錢注？
如果10蚊注 每買1注等於10-3.48 65折咁又幾抵喎

10蚊注
每買10蚊期望回報3.48係35折

所以結果係$10注最大機會？

d 人鐘意買生日
會偏左去 1-31

係

比想像中好
難怪我買千幾二千蚊飛，通常真係中返幾舊水

屌