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NFL 中的過關投注

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本頁的分析是基於1994年至2012年賽季的4450場NFL比賽。我從1994年開始分析,因為那一年引入了兩分轉換規則。除了樣本量差異之外,我還必須假設讓分盤口卡的讓分是如何產生的。為了節省時間,我沒有分析所有12種已知的過關卡,而是分析了其中5種。為了理解額外積分如何影響中獎機率,我創建了我的「巫師讓分盤口方程式」

讀者應理解,本頁面中任何關於獲勝機率和預期回報的統計數據都存在一定的誤差。歸根結底,體育運動最終是由人而非統計數據進行的,因此,任何基於過往結果對未來結果的預測,請務必謹慎。

場外預告片

「場外讓分盤」(OTB)是指投注時投注盤外的讓分盤。無需填寫任何卡片。投注者只需告知投注者讓分盤的投注局數、每局的額外分數、希望投注的號碼以及投注金額。例如,投注者可能會說:“NFL 三隊 6 分讓分盤,投注 213、218 和 224,投注金額 100 美元。”

投注者可以選擇在每輪過關投注中獲得6、6.5或7個額外點數。當然,投注者獲得的點數越多,獲勝的幾率就越低。各個地方的獲勝賠率各不相同,因此請參考我的賠率表,以了解哪個地方的賠率最高。不過,對於那些懶惰的讀者來說,Jerry's Nugget 擁有場外過關投注中,在輪數和點數方面都最高的賠率。

以下是我對 6 分、6.5 分和 7 分預測的個人分析。

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6分即場過關盤

下表顯示了根據所選投注數量和體育博彩組別,6分場外讓分盤投注的賠率。本表中的賠率以「一比一」為基準。換句話說,如果投注獲勝,則將退還原始投注金。

6分即場過關投注-賠率表

體育博彩
2 3 4 5 6 7 8 9 10
博伊德10至13 8點到5點5比2 9點到2點7比1 9比1 10比1
凱撒5到6 7點到5點5比2 4比1 6比1
CG技術5到6 8點到5點14 至 5 9點到2點7比1
金塊8點到5點5比2 9點到2點7比1 9比1 10比1
傑瑞的金塊4到5 8點到5點5比2 9點到2點7比1 8比1 10比1
米高梅10至13 8點到5點5比2 4比1 6比1 10比1 15比1
南點5到6 8點到5點5比2 9點到2點7比1 9比1 12比1
車站5到6 8點到5點5比2 9點到2點7比1 8比1 10比1
平流層5到6 8點到5點5比2 9點到2點13比2 9比1 11比1
金銀島5到6 7點到5點5比2 4比1 6比1
西門10至13 8點到5點5比2 4比1 6比1
威廉希爾20至23 8點到5點13點到5點4比1 6比1 8比1 10比1 15比1 20比1
永利5到6 8點到5點14 至 5 9點到2點6比1

下表顯示了隨機投注者在最佳6點過關賠率下的中獎機率和預期回報。請注意,賭場優勢在10%到52%之間。

6 分 OTB 讓分盤 — 隨機選擇

支付機率獲勝預期值
2 20至23 0.469264 -0.122679
3 1.8 0.321460 -0.099913
4 3 0.220209 -0.119163
5 4.5 0.150850 -0.170327
6 7 0.103336 -0.173309
7 10 0.070788 -0.221328
8 15 0.048492 -0.224127
9 15 0.033218 -0.468504
10 20 0.022756 -0.522132
透過不隨機選擇球隊,而是跨越常見的勝率差距,有可能顯著提高球員的勝率。下表列出了NFL中最常見的十個勝率差距。

NFL 最大勝場差距

勝利的差距頻率
1 3 15.7%
2 7 9.3%
3 10 6.2%
4 6 5.4%
5 4 5.0%
6 14 4.8%
7 1 4.0%
8 17 3.6%
9 2 3.5%
10 5 3.2%

請注意,25% 的比賽以 3 分或 7 分的勝負分差結束。透過購買同時跨越這兩個數字的點數,玩家可以大幅提高獲勝機率。當點數為 6 分時,唯一同時跨越這兩個數字的讓分盤口是 -8.5、-8、-7.5、1.5、2 和 2.5。平均而言,NFL 中 20% 的比賽會有一方的點數為上述某個數值。這些點數的讓分盤口被稱為“黃讓分盤口”,因為斯坦福·黃 (Stanford Wong) 在其著作《 精明體育博彩》(Sharp Sports Betting ) 中展示瞭如何擊敗它們。

下表顯示了黃氏投注者在最佳 6 分預告賠率下的獲勝機率和預期回報。

6分OTB讓分盤-Wong Bettor

支付機率獲勝預期值
2 20至23 0.536192 0.002446
3 1.8 0.392628 0.099357
4 3 0.287502 0.150009
5 4.5 0.210524 0.157881
6 7 0.154156 0.233252
7 10 0.112881 0.241694
8 15 0.082657 0.322520
9 15 0.060526 -0.031583
10 20 0.044320 -0.069273

請注意,在pick-8選秀中,球員優勢高達32%。可惜的是,大多數比賽週都沒有那麼多機會。如上所述,20%的比賽有黃隊,所以在16場比賽的一周中,你只能預期有3.2場黃隊比賽。

可惜的是,兩回合-110、三回合+180、四回合6分NFL讓分盤的自由賠率似乎在2014賽季就如同渡渡鳥般銷聲匿跡了。上一個堅持不懈的「傑瑞金塊」在2014賽季降低了賠率。

請注意,2004 年是樣本期間黃牌預告表現最差的一年,並且請注意我在哪一年在Suncoast下注了上述彩票。

6.5 分即場預告

下表顯示了6.5分場外讓分盤投注的賠率,根據所選投注數量和體育博彩組別。本表中的賠率以「一比一」為基準。換句話說,如果投注獲勝,則將退還原始投注金。

6.5 分即期過關投注 — 賠率表

體育博彩
2 3 4 5 6 7 8 9 10
博伊德10至14 7點到5點12點到5點4比1 6比1 8比1 9比1
凱撒10至13 6點到5點2比1 7比2 5比1
CG技術10至13 3比2 5比2 4比1 11比2
金塊7點到5點2比1 4比1 6比1 8比1 9比1
傑瑞的金塊10至13 7點到5點2比1 7比2 5比1 6比1 9比1
米高梅10至14 7點到5點2比1 7比2 5比1 9比1 12比1
南點10至13 7點到5點12點到5點4比1 6比1 8比1 10比1
車站10至13 3比2 2比1 4比1 6比1 7比1 9比1
平流層10至13 7點到5點11點到5點4比1 11比2 8比1 9比1
金銀島10至13 6點到5點2比1 7比2 5比1
西門10至14 3比2 2比1 5比2 5比1
威廉希爾4到5 29至20 11點到5點7比2 5比1 7比1 9比1 12比1 15比1
永利10至13 3比2 5比2 4比1 11比2

下表顯示了隨機投注者在最佳6.5分過關賠率下的中獎機率和預期回報。請注意,賭場優勢在10%到54%之間。

6.5 分 OTB 讓分盤 — 隨機選擇

支付機率獲勝預期值
2 0.8 49.13% -11.57%
3 1.6 34.44% -10.47%
4 2.5 24.14% -15.52%
5 4 16.92% -15.41%
6 6 11.86% -16.99%
7 9 8.31% -16.88%
8 12 5.83% -24.26%
9 12 4.08% -46.92%
10 15 2.86% -54.21%

雖然黃牌過關盤通常指的是買入6分,但6.5分過關盤也可以做到這一點。在這種情況下,合格的讓分盤口為-9到-7.5和1到2.5。在此標準下,6.5分黃牌過關盤的勝率高達74.14%。下表顯示了它們在6.5分過關盤最佳可用賠率下的表現。

6.5 分 OTB 讓分盤 — Wong Picker

支付機率獲勝預期值
2 0.8 54.96% -1.06%
3 1.6 40.75% 5.95%
4 2.5 30.21% 5.74%
5 4 22.40% 11.99%
6 6 16.61% 16.24%
7 9 12.31% 23.11%
8 12 9.13% 18.65%
9 12 6.77% -12.04%
10 15 5.02% -19.74%

雖然上表顯示了一些強勁的玩家優勢,高達 23%,但賠率並不像 6 分黃牌預告那麼好。

7 分即場預告

下表顯示了7分場外讓分盤投注根據所選投注數量和體育博彩組別的賠付情況。本表中的賠償金以「一比一」為基準。換句話說,如果投注獲勝,則將退還原始投注金。

7 分即場過關投注 — 賠率表

體育博彩
2 3 4 5 6 7 8 9 10
博伊德2到3 6點到5點2比1 7比2 5比1 7比1 8比1
CG技術10至14 7點到5點2比1 3比1 5比1
金塊6點到5點9點到5點7比2 5比1 7比1 8比1
哈拉斯10至14 1比1 9點到5點3比1 4比1
傑瑞的金塊10至14 6點到5點8點到5點3比1 4比1 6比1 8比1
米高梅2到3 6點到5點9點到5點3比1 4比1 7比1 10比1
南點10至14 6點到5點2比1 7比2 5比1 13比2 9比1
車站10至14 6點到5點9點到5點7比2 5比1 6比1 8比1
平流層10至14 6點到5點2比1 3比1 5比1 7比1 8比1
金銀島10至14 1比1 9點到5點3比1 4比1
西門2到3 6點到5點9點到5點3比1 9點到2點
威廉希爾10至14 13至10 2比1 3比1 9點到2點6比1 8比1 10比1 12比1
永利10至14 6點到5點9點到5點3比1 5比1

下表顯示了隨機投注者在最佳7點過關賠率下的中獎機率和預期回報。請注意,賭場優勢在12%到54%之間。

7 分場外讓分盤 — 隨機選擇

支付機率獲勝預期值
2 5到7 51.35% -11.97%
3 1.4 36.80% -11.69%
4 2 26.37% -20.90%
5 3.5 18.90% -14.97%
6 5 13.54% -18.76%
7 7 9.70% -22.38%
8 10 6.95% -23.52%
9 10 4.98% -45.20%
10 12 3.57% -53.59%

既然我研究了6分和6.5分的黃牌讓分盤,那我不妨也研究一下7分的黃牌讓分盤。這樣,讓分盤的合格範圍將是-9.5到-7.5,或1到2.5。雖然可能存在,但在NFL中,0.5或-0.5的讓分盤從未出現。每場比賽的勝率均為74.61%。下表顯示了7分黃牌讓分盤的預期回報,基於所選場次的最佳勝率。

7 分 OTB 讓分盤 — Wong Picker

支付機率獲勝預期值
2 5到7 55.66% -4.58%
3 1.4 41.53% -0.34%
4 2 30.98% -7.05%
5 3.5 23.11% 4.02%
6 5 17.24% 3.47%
7 7 12.87% 2.93%
8 10 9.60% 5.59%
9 10 7.16% -21.23%
10 12 5.34% -30.54%

雖然上表顯示了一些小的優勢,但它們明顯小於 6 分黃牌預告下的大優勢。

預告卡

首先,我來解釋一下什麼是「讓分盤」。它和過關盤相同,不同之處在於:(1) 每次投注都會在讓分盤中獲得額外積分;(2) 賠率更低。它的原理與場外過關(而非讓分盤)相同,只是玩家需要填寫卡片,而不是告訴寫手每條讓分盤的賠率。讓分盤上的讓分通常為整數,並遵循「平手獲勝」的規則,即玩家贏得額外半分。

投注「讓分盤」或「過關盤」牌與投注「場外盤」牌的另一個區別是,所有牌面贏錢都是「一比一」的,而場外贏錢則是「一比一」。對於那些不明白其中差異的人來說,如果玩家贏得「贏」的賭注,他還能拿回原來的賭注,而如果是「一比一」的賭注,他則不能。

過關卡種類繁多,玩家每局可額外獲得 2.5 到 10 分。當然,玩家獲得的分數越高,獲勝的機率就越低。在本頁中,我特別分析了五種過關卡,每局分別給予玩家 2.5、5.5、6.5、8.5 和 9.5 分。我的分析表明,對於隨機抽獎者來說,每局獲勝的機率如下。

每局獲勝機率

積分可能性
2.5 58.25%
5.5 66.43%
6.5 69.92%
8.5 74.98%
9.5 77.02%

根據該表,經過一些計算,我開發了一個公式來估計隨機選擇者在給定 p 個額外積分的情況下贏得任何特定回合的機率。

巫師預告方程式

以 p 個額外點覆蓋價差的機率估計為 e 0.128×p / (1+e 0.128×p )。

對於那些不熟悉數字e的人來說,它被稱為歐拉常數,等於 1/0! + 1/1! + 1/2! + 1/3! + ... = 2.718281828…它在數學中有著廣泛的應用,尤其是微積分。僅舉四個例子:

  • c*e x ,其中 c 是任何非零常數,是唯一導數為其自身的函數。
  • 如果 x=(1/t) dt 從 1 到 y 的積分,則 e x = y。
  • 把 1 美元存入一個支付 100% 利息的銀行帳戶,無限複利,一年後將有 e 美元。

回到正題,下圖顯示了根據附加點數和 Wizard Teaser Equation 估計的機率,實際獲勝的機率。

我們來看一個例子。威廉希爾的「讓分盤口」是少數讓分總是以1/2結尾的盤口之一。有一場比賽的賠率如下:愛國者隊-4.5,比爾隊+16.5。要計算兩邊的額外分數,只需將兩個讓分相加,然後除以二即可。在這種情況下,(16.5-4.5)/2 = 6。因此,我稱之為6分讓分盤口。我的公式表明,隨機選秀獲勝的機率為e 0.128×6 /(1+e 0.128×6 ) = 68.31%。

我們再來看另一個例子。凱撒賭場有一張“讓分盤”,每個讓分都是一個整數,並且有平局獲勝規則。有一場比賽的讓分是老鷹隊 -2,閃電隊 +14。同樣,將讓分相加並除以 2:(14-2)/2 = 6。然而,平手獲勝規則相當於在讓分盤上額外獲得半分。所以,我稱之為 6.5 分讓分盤。我的公式表明,隨機抽獎獲勝的機率為 e 0.128×6.5 / (1+e 0.128×6.5 ) = 69.68%。這比我所做的精確分析結果低了 0.24%,這表明估計值只是估計值而已。

下表根據 Wizard Teaser 方程式顯示了給定 0 到 10 個額外分數時,任何給定回合獲勝的機率。

巫師預告方程式

積分獲勝機率
0 50.00%
0.5 51.60%
1 53.19%
1.5 54.78%
2 56.36%
2.5 57.93%
3 59.48%
3.5 61.01%
4 62.52%
4.5 64.00%
5 65.46%
5.5 66.90%
6 68.30%
6.5 69.66%
7 71.00%
7.5 72.30%
8 73.56%
8.5 74.78%
9 75.97%
9.5 77.12%
10 78.23%

以下是我對拉斯維加斯幾種類型的透支卡的分析,按點數從少到多排列。

2.5 分預告卡

2.5 分的讓分盤僅在米高梅賭場提供。所有點數都以 1/2 結尾,因此不可能出現平手。下表顯示了 4 至 15 個選項的獲勝機率和預期回報(假設隨機選擇)。根據巫師讓分盤公式,每局的獲勝機率為 57.93%。右列顯示賭場優勢在 32% 至 81% 之間。

2.5 分 MGM 預告卡 — 隨機選擇

挑選支付機率獲勝預期值
4 6 0.112656 -0.324062
5 9.5 0.065267 -0.379962
6 15 0.037812 -0.432815
7 21 0.021906 -0.539964
8 32.5 0.012691 -0.587528
9 50 0.007353 -0.632362
10 80 0.004260 -0.659216
11 125 0.002468 -0.691512
12 187.5 0.001430 -0.731918
十三300 0.000828 -0.751500
14 450 0.000480 -0.784048
15 700 0.000278 -0.805383

聰明的賭徒可以透過只在獲得超過2.5分和/或超過3分或7分勝率的情況下下注來降低這些莊家優勢。然而,隨機抽取的莊家優勢如此之高,我認為這些技巧很少能讓賭徒擺脫困境。

3分預告卡

3點讓分盤僅在Stratosphere系列賭場提供。所有讓分盤的尾數均為1/2,因此不會出現平手。下表顯示了假設隨機選擇,3至15個選項的獲勝機率和預期回報。根據Wizard Teaser方程式,每局的獲勝機率為59.49%。右列顯示賭場優勢在25%至83%之間。

3 分平流層預告卡 — 隨機選擇

挑選支付機率獲勝預期值
3 3.5 0.210501 -0.263246
4 6 0.125220 -0.248682
5 9 0.074489 -0.329601
6 15 0.044311 -0.335339
7 20 0.026359 -0.472822
8三十0.015680 -0.529601
9 50 0.009327 -0.533627
10 75 0.005549 -0.583857
11 100 0.003301 -0.669935
12 150 0.001963 -0.705484
十三200 0.001168 -0.766404
14 300 0.000695 -0.791563
15 400 0.000413 -0.834677

與任何過關牌一樣,透過獲得高於平均的點數和/或突破關鍵的勝率,可以顯著降低賭場優勢。然而,也有一些過關牌,玩家一開始的籌碼就沒那麼深。

3.5 分預告卡

3.5 分的讓分盤僅在 Jerry's Nugget 提供。所有讓分盤的尾數均為 1/2,因此不會出現平手。下表顯示了 4 至 15 個選項的中獎機率和預期回報(假設隨機選擇)。根據 Wizard Teaser 公式,每局的中獎機率為 61.02%。右欄顯示賭場優勢在 17% 至 68% 之間。

3.5 分傑瑞金塊預告卡 — 隨機選擇

挑選支付機率獲勝預期值
4 6 0.138635 -0.168187
5 9 0.084595 -0.238648
6十三0.051619 -0.328950
7 17 0.031498 -0.464538
8二十五0.019220 -0.519505
9 41 0.011728 -0.519159
10 61 0.007156 -0.563468
11 100 0.004367 -0.563329
12 150 0.002665 -0.600318
十三250 0.001626 -0.593527
14 325 0.000992 -0.677564
15 600 0.000605 -0.636772

再次強調,可以透過尋找超過3.5分的遊戲和/或突破3分或7分的勝率差距來降低這些賭場優勢。不過,我認為最好還是在6.5分的過關卡上運用這個策略。

5點預告卡

我看過三種 5 點預告卡,如下:

  • 金塊彩券、傑瑞金塊彩券:點差總是以 1/2 結尾。例如,泰坦隊 +1.5,閃電隊 +8.5。點數 = (1.5 + 8.5) / 2 = 5。
  • 西門:點差始終為整數,平手獲勝。例如,老鷹隊 -4,閃電隊 +13。記住,平手獲勝規則為雙方各得半分。總分 = (-4+13)/2 + 0.5 = 5。

下表顯示了每組在 5 分盤口中支付的金額。

5點預告卡-賠率表

體育博彩
3 4 5 6 7 8 9 10 11 12十三14 15
金塊2.6 4 5 8 11 16 22三十45 65 100 150 250
傑瑞的金塊4 6 8 12 16二十五三十五50 70 100 150 300
西門2.5 3.5 5.5 8 11 15 20三十40 65 100 150 250

傑瑞金塊 (Jerry's Nugget) 的賠率是三者中最高的,所以我將只分析其 5 點過關盤。根據巫師過關盤公式,每局的勝率均為 65.48%。表格顯示,隨機抽獎的賭場優勢在 26% 到 60% 之間。

5 分預告卡 — Jerry's Nugget — 隨機選擇

挑選支付機率獲勝預期值
4 4 0.183833 -0.264667
5 6 0.120373 -0.277761
6 8 0.078820 -0.369441
7 12 0.051611 -0.380669
8 16 0.033795 -0.459286
9二十五0.022129 -0.446785
10三十五0.014490 -0.492860
11 50 0.009488 -0.525610
12 70 0.006213 -0.565120
十三100 0.004068 -0.593203
14 150 0.002664 -0.600446
15 300 0.001744 -0.476748

5.5 分預告卡

這是一種常見的讓分盤投注卡,我在五個不同的體育博彩公司見過。他們叫法不同,規則也不同,具體如下:

  • 永利 — 1/2 點差盤口卡:所有點差都以一半結束,兩個點差之間的距離始終為 11,或每隊 5.5 分。
  • 南點-大轉盤特惠:所有讓分均為整數,平手,且讓分之間的差距始終為12。在整數讓分中,平手輸規則將使玩家損失半分。因此,每個讓分的平均移動分數為12/2 - 0.5 = 5.5。
  • 博伊德、車站、金銀島平手贏盤:所有讓分均為整數,平手贏,讓分之間的差距始終為10。在整數讓分盤中,平手輸盤規則使玩家獲得半分。因此,每個讓分盤平均移動的分數為10/2 + 0.5 = 5.5。

下表顯示了每個體育博彩公司在 5.5 分預告盤中支付的金額。

5.5 分預告卡 — 賠率表

體育博彩
3 4 5 6 7 8 9 10 11 12十三14 15
博伊德2.5 3.5 5 8 10 15 20三十40 60 100 150 300
南點2.5 4 6 8 10 15 20三十45 75 125 175 350
車站2.5 3.5 5 8 10 15 20三十40 60 100 150 300
平流層2.5 3.5 5 8 10 15 20三十45 65 100 150 250
金銀島2.75 4 6 8 12 16 20三十40 65 95 150 240
永利2.5 3.5 5 7 11 15 20三十45 60 90 125 200

根據巫師轉盤公式,平均投注者預期中獎率為 66.91%。下表顯示了隨機投注者的中獎機率和預期回報,並與最佳賠率表進行了比較。賭場優勢從 15% 到 46% 不等。

5.5 分預告卡 — 隨機選擇

挑選支付機率獲勝預期值
3 2.75 0.299579 -0.176157
4 4 0.200454 -0.198183
5 6 0.134128 -0.195232
6 8 0.089748 -0.282018
7 12 0.060052 -0.279376
8 16 0.040182 -0.357089
9 20 0.026887 -0.462269
10三十0.017990 -0.460290
11 45 0.012038 -0.458305
12 75 0.008055 -0.395901
十三125 0.005390 -0.326309
14 175 0.003606 -0.368908
15 350 0.002413 -0.155448

玩家可以透過尋找至少有六點的點數朝著對自己有利的方向移動的局面來降低賭場優勢。大約一半的遊戲都會有這樣的機會。例如,如果發牌者發出一張半點牌,其中每個點數都以一半結束,那麼如果原始點數也以一半結束,他就必須將其中一邊移動六點,另一邊移動五點。只選擇六點的牌,每次選擇的成功機率將從 66.91% 增加到估計的 68.31%。下表顯示了玩家只選擇六點的牌時預期的回報。回報範圍從玩家優勢 15% 到賭場優勢 35%。

5.5 分預告卡 — 6 分選擇器

挑選支付機率獲勝預期值
3 2.75 0.318804 -0.123290
4 4 0.217787 -0.128854
5 6 0.148778 -0.107332
6 8 0.101636 -0.186914
7 12 0.069431 -0.166826
8 16 0.047431 -0.241104
9 20 0.032402 -0.351963
10三十0.022135 -0.335953
11 45 0.015121 -0.319547
12 75 0.010330 -0.225263
十三125 0.007057 -0.117914
14 175 0.004821 -0.156380
15 350 0.003293 0.152615

比較以上兩張表格,我們發現賭場優勢的下降幅度從3條過關過關盤的5%到15條過關過關盤的31%。遺憾的是,我們看到的唯一優勢出現在15條過關過關盤。在NFL,一週內幾乎不可能出現15次6分機會。

6 分預告卡

威廉希爾和米高梅兩家公司提供6分讓分盤口。如下表所示,威廉希爾在各個選項上提供的賠率均與米高梅持平或更高,包括從3到20的更大範圍。

6點過關卡-賠率表

挑選威廉希爾米高梅
3 2.6
4 4 3
5 5 4.5
6 8 6.5
7 11 10
8 16 15
9 22 20
10三十三十
11 45 45
12 65 60
十三100 90
14 150 125
15 200 200
16 300
17 500
18 700
19 1000
20 1500

下表顯示了3至20個選項的中獎機率和預期回報,假設採用威廉希爾賠率表,並由隨機抽籤員進行投注。根據巫師轉盤公式,每局的中獎機率為68.31%。右列顯示,賭場優勢介於17%至34%之間。

6點預告卡 — William Hill — 隨機選擇

挑選支付機率獲勝預期值
3 3 0.318804 -0.171111
4 4 0.217787 -0.128854
5 5 0.148778 -0.256110
6 8 0.101636 -0.186914
7 11 0.069431 -0.236257
8 16 0.047431 -0.241104
9 22 0.032402 -0.287159
10三十0.022135 -0.335953
11 45 0.015121 -0.319547
12 65 0.010330 -0.328561
十三100 0.007057 -0.294331
14 150 0.004821 -0.276898
15 200 0.003293 -0.341363
16 300 0.002250 -0.325091
17 500 0.001537 -0.231574
18 700 0.001050 -0.265084
19 1,000 0.000717 -0.282788
20 1,500 0.000490 -0.265069

6.5 分預告卡

6.5分的讓分盤僅由凱撒娛樂場提供。讓分始終為整數,平手獲勝。請記住,「平手獲勝」規則價值半分。例如,有一場比賽的賠率是老鷹-2,閃電隊+14。此賠率價值為(-2+14)/2 + 0.5 = 6.5

與大多數(甚至所有)過關投注相比,這個賠率相當高。根據巫師過關投注公式,隨機投注者可以預期每筆投注的獲勝機率為 69.68%。下表顯示了 4 到 15 筆過關投注的獲勝機率和預期回報。賭場優勢在 11% 到 25% 之間。

6.5 分預告卡 — 凱薩 — 隨機選擇

挑選支付機率獲勝預期值
4 3.5 0.235779 -0.174773
5 5 0.164298 -0.178511
6 7 0.114488 -0.198587
7 10 0.079778 -0.202217
8 15 0.055592 -0.166122
9 20 0.038738 -0.225239
10三十0.026994 -0.190186
11 40 0.018810 -0.247597
12 60 0.013107 -0.213556
十三90 0.009134 -0.177974
14 130 0.006365 -0.172605
15 200 0.004435 -0.112996

這些賭場優勢夠低,足以檢驗如果玩家只在拿到7分時做出這些選擇,賠率會如何改變。如果場外(OTB)點差最終為一半,那麼發牌者就必須將一邊的點差調整為5.5分,另一邊的點差調整為6.5分,才能使兩個點差都變成整數。然後,再根據平手獲勝規則,加上另一半點差,有時就能達到7分。

如果玩家選擇的選項比場外讓分盤多7分,那麼他可以將每局的勝率從隨機選號者的69.68%提升到預估的71.02%。這將改變回報表,如下所示。

6.5 分預告卡 — 凱薩 — 額外半分選擇器

挑選支付機率獲勝預期值
4 3.5 0.254376 -0.109684
5 5 0.180653 -0.096735
6 7 0.128296 -0.101926
7 10 0.091114 -0.088864
8 15 0.064707 -0.029393
9 20 0.045954 -0.080924
10三十0.032636 -0.020935
11 40 0.023177 -0.072915
12 60 0.016460 -0.012403
十三90 0.011690 0.052059
14 130 0.008302 0.079220
15 200 0.005896 0.179140

好消息是,根據上表,選擇額外半分的玩家在15場比賽中將獲得18%的優勢。壞消息是,只有大約一半的比賽會有這樣的機會。由於NFL一周最多只有16場,因此幾乎不可能有這麼多的機會。不過,這也體現了尋找額外半分的價值。玩家可以透過利用後期盤口變動和/或突破3比7的關鍵勝率來進一步降低賭場優勢。

8分平手獲勝預告卡

Westgate 是唯一提供 8 分讓分盤的運動博彩公司。下表顯示了賠率。

8 點預告卡 — Westgate — 賠率表

4 5 6 7 8 9 10 11 12十三14 15
2 2.5 3.5 4.5 6 7.5 9.5 6 7.5 10 12.5 15

隨機投注者預期中獎率為 73.58%。下表顯示了隨機投注者的中獎機率以及與 Westgate 賠率表的預期回報。賭場優勢從 41% 到 85% 不等。

8點預告卡-隨機選擇

挑選支付機率獲勝預期值
4 2 0.293131 -0.413738
5 2.5 0.215688 -0.460779
6 3.5 0.158706 -0.444530
7 4.5 0.116777 -0.474503
8 6 0.085926 -0.484446
9 7.5 0.063225 -0.525813
10 9.5 0.046522 -0.558046
11 6 0.034231 -0.794614
12 7.5 0.025187 -0.811094
十三10 0.018533 -0.814668
14 12.5 0.013637 -0.829539
15 15 0.010034 -0.849488

8.5分平手獲勝預告卡

這種牌的點數是:同一場比賽中兩隊讓分相差16分,且始終為整數,平手獲勝。平手獲勝規則計半分,因此每方得分為16/2 + 0.5 = 8.5分。體育博彩公司是這樣稱呼它們的。

  • 凱薩 — 「平手獲勝」超級預告卡
  • 米高梅 — Ties Win 超級預告片
  • 平流層 — 超級預告卡
  • 車站——超級預告特輯

下表列出了四家提供這些服務的體育博彩公司。如您所見,三家公司並列第一,其中Station提供的賠率低於其他所有公司。

8.5 分預告卡 — 賠率表

體育博彩
4 5 6 7 8 9 10 11 12十三14 15
凱撒2 2.5 3.5 4.5 6 7.5 9.5 12 15 20二十五三十
米高梅2 2.5 3.5 4.5 6 7.5 9.5 12 15 20二十五三十
車站2 2.5 3.5 4 5.5 7 9三十
平流層2 2.5 3.5 4.5 6 7.5 9.5 12 15 20二十五三十

根據巫師轉盤公式,隨機選擇者預期中獎率為 74.81%。下表顯示了隨機選擇者的中獎機率和預期回報,並與最佳賠償表進行了比較。賭場優勢在 37% 到 60% 之間。

8.5 分預告卡 — 隨機選擇

挑選支付機率獲勝預期值
4 2 0.316065 -0.367869
5 2.5 0.236985 -0.407537
6 3.5 0.177691 -0.378081
7 4.5 0.133232 -0.400454
8 6 0.099897 -0.400616
9 7.5 0.074903 -0.438229
10 9.5 0.056162 -0.466461
11 12 0.042110 -0.494678
12 15 0.031574 -0.526388
十三20 0.023674 -0.526516
14二十五0.017751 -0.556228
15三十0.013310 -0.600713

9分平手獲勝預告卡

有兩本運動博彩書籍提供 9 分盤口,分別是 Boyd Gaming 和 Golden Nugget。

9點過關卡-賠率表

體育博彩
4 5 6 7 8 9 10 11 12十三14 15
博伊德2 2.5 3.5 4.5 6 7.5 9.5 12 15 20二十五三十
金塊2.2 2.6 3.5 4.5 5.5 7 9 11 14 18 23三十

根據巫師轉盤公式,隨機選擇者預期中獎率為 75.99%。下表顯示了隨機選擇者中獎機率以及預期回報,以及博伊德和金塊之間更高的中獎率。賭場優勢從 27% 到 51% 不等。

9點預告卡-隨機選擇

挑選支付機率獲勝預期值
4 2.2 0.333112 -0.267153
5 2.6 0.253069 -0.342022
6 3.5 0.192259 -0.327095
7 4.5 0.146061 -0.342727
8 6 0.110964 -0.334217
9 7.5 0.084300 -0.367748
10 9.5 0.064044 -0.391585
11 12 0.048655 -0.416144
12 15 0.036963 -0.445549
十三20 0.028081 -0.438371
14二十五0.021334 -0.466656
15三十0.016207 -0.513776

9.5分平手獲勝預告卡

有兩家運動博彩公司提供9.5分的讓分盤,分別是金銀島和西門。它們的賠率表如下。正如你所見,金銀島的賠率始終更高。

9.5 分預告卡 — 賠率表

體育博彩
4 5 6 7 8 9 10 11 12十三14 15
金銀島2 2.5 3.5 4 5.5 7 9 11.5 14.5 18.5 23.5三十
西門2.25 3 3.5 4.5 6 7.5 9 11十三16 20

根據巫師轉盤公式,隨機選擇者預期中獎率為 77.14%。下表顯示了隨機選擇者的中獎機率以及與金銀島賠率表的預期回報。賭場優勢在 26% 到 38% 之間。

9.5 分預告卡 — 金銀島 — 隨機選擇

挑選支付機率獲勝預期值
4 2 0.354134 -0.291732
5 2.5 0.273187 -0.317033
6 3.5 0.210742 -0.262402
7 4 0.162571 -0.349715
8 5.5 0.125411 -0.310240
9 7 0.096745 -0.322787
10 9 0.074631 -0.328321
11 11.5 0.057572 -0.337922
12 14.5 0.044412 -0.356022
十三18.5 0.034261 -0.366179
14 23.5 0.026429 -0.378910
15三十0.020388 -0.388354

10 分平手獲勝預告卡

只有威廉希爾提供10分的讓分盤。根據巫師讓分盤公式,隨機投注者預期中獎率為78.25%。下表顯示了隨機投注者的中獎機率以及預期回報與威廉希爾賠率的對比情況。賭場優勢在18%到29%之間。

9.5 分預告卡 — 金銀島 — 隨機選擇

挑選支付機率獲勝預期值
4 2.2 0.374945 -0.175120
5 2.6 0.293400 -0.237160
6 3.5 0.229589 -0.196437
7 4.5 0.179657 -0.191544
8 5.5 0.140584 -0.226788
9 7 0.110009 -0.229938
10 9 0.086083 -0.225249
11 11 0.067362 -0.259023
12 14 0.052711 -0.262042
十三18 0.041247 -0.257548
14 24 0.032277 -0.225362
15三十0.025257 -0.242294
16三十八0.019764 -0.248973
17四十八0.015465 -0.257656
18 64 0.012102 -0.225475
19 75 0.009470 -0.289754
20 100 0.007410 -0.258963

概括

對於隨機投注者來說,過關投注絕對是一個糟糕的選擇,因為賭場優勢巨大。如果你必須下注,賭場優勢雖然比常規投注少,但仍然很高。以下是一些關於如何降低過關投注賭場優勢的建議。

  • 在賠率最高的體育博彩公司下注。
  • 盡可能嘗試跨越關鍵的勝利分差,尤其是 3 分和 7 分。
  • 在牌面上和牌面外之間獲取盡可能多的分數(此建議僅適用於牌)。

如果你必須投注讓分盤,那麼最好的方法就是所謂的「黃讓分盤」 。這是一種場外讓分盤,投注範圍涵蓋3分到7分之間的特定讓分。

如果您必須下注讓分卡,那麼凱撒6.5 分卡的整體賠率是最佳的。

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