「Odds in statistics and Odds in a horse race」の版間の差分

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!style="width:50px"|Horses
 
!style="width:50px"|Horses
 
!style="width:80px"|Bettors
 
!style="width:80px"|Bettors
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!style="width:150px"|If the horse wins  
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!style="width:140px"|If the horse wins  
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!style="width:150px"|Calculation
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!style="width:130px"|Calculation
 
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|style="text-align:center"|A
 
|style="text-align:center"|A
76行目: 76行目:
 
|3 bettors
 
|3 bettors
 
|$20 into 3 bettors
 
|$20 into 3 bettors
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|$20 ÷ 3 = $6.66...
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|$20 ÷ 3 = $6.66..
 
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|-
 
|style="text-align:center"|D
 
|style="text-align:center"|D
87行目: 87行目:
 
|$20 into 1 bettor
 
|$20 into 1 bettor
 
|$20 ÷ 1 = $20
 
|$20 ÷ 1 = $20
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|}
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===From a view point of winning probabilities===
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Assumed that predictions by bettors were as precise as God, a winning probability of each horse is as follows:
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{|class="wikitable"
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|-
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!style="width:50px"|Horses
 +
!style="width:80px"|Bettors
 +
!style="width:140px"|If the horse wins
 +
!style="width:130px"|Calculation
 +
!style="width:80px"|Winning probability
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|-
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|style="text-align:center"|A
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|10 bettors
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|$20 into 10 bettors
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|$20 ÷ 10 = $2
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|10/20
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|-
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|style="text-align:center"|B
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|5 bettors
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|$20 into 5 bettors
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|$20 ÷ 5 = $4
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|5/20
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|-
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|style="text-align:center"|C
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|3 bettors
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|$20 into 3 bettors
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|$20 ÷ 3 = $6.66..
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|3/20
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|-
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|style="text-align:center"|D
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|2 bettors
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|$20 into 2 bettors
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|$20 ÷ 2 = $10
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|2/20
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|-
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|style="text-align:center"|E
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|1 bettor
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|$20 into 1 bettor
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|$20 ÷ 1 = $20
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|1/20
 
|}
 
|}

2022年11月6日 (日) 23:53時点における版

Definition of Odds in statistics

[math]\displaystyle{ Odds=\frac{probability\ that\ the\ outcome\ occurs}{probability\ that\ the\ outcome\ does\ not\ occur} }[/math]

Example of a horse rase

Assumption

In order to simplify, the bookmaker in the following scenario does not charge any betting fees

A race that 5 horses start and 10 bettors bet

Here is a horse race that 5 horses start and 20 people — 20 bettors — bet each of 5 horses.

Names of horses are A, B, C, D and E.

Horses
A
B
C
D
E

Each bettor bets $1 for one horse. All bet money are pooled ($20 pooled in total) and will be redistributed for bettors who bet a winning horse.

Now each all bettors bet as following:

Horses Bettors
A 10 bettors
B 5 bettors
C 3 bettors
D 2 bettors
E 1 bettor

Results

If each horse wins, pooled $20 are redistributed as following:

Horses Bettors If the horse wins Calculation
A 10 bettors $20 into 10 bettors $20 ÷ 10 = $2
B 5 bettors $20 into 5 bettors $20 ÷ 5 = $4
C 3 bettors $20 into 3 bettors $20 ÷ 3 = $6.66..
D 2 bettors $20 into 2 bettors $20 ÷ 2 = $10
E 1 bettor $20 into 1 bettor $20 ÷ 1 = $20

From a view point of winning probabilities

Assumed that predictions by bettors were as precise as God, a winning probability of each horse is as follows:

Horses Bettors If the horse wins Calculation Winning probability
A 10 bettors $20 into 10 bettors $20 ÷ 10 = $2 10/20
B 5 bettors $20 into 5 bettors $20 ÷ 5 = $4 5/20
C 3 bettors $20 into 3 bettors $20 ÷ 3 = $6.66.. 3/20
D 2 bettors $20 into 2 bettors $20 ÷ 2 = $10 2/20
E 1 bettor $20 into 1 bettor $20 ÷ 1 = $20 1/20
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