「Odds in statistics and Odds in a horse race」の版間の差分
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60行目: | 60行目: | ||
!style="width:50px"|Horses | !style="width:50px"|Horses | ||
!style="width:80px"|Bettors | !style="width:80px"|Bettors | ||
− | !style="width: | + | !style="width:140px"|If the horse wins |
− | !style="width: | + | !style="width:130px"|Calculation |
|- | |- | ||
|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 | ||
− | |$20 ÷ 3 = $6.66 | + | |$20 ÷ 3 = $6.66.. |
|- | |- | ||
|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 | ||
+ | |} | ||
+ | |||
+ | ===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: | ||
+ | |||
+ | {|class="wikitable" | ||
+ | |- | ||
+ | !style="width:50px"|Horses | ||
+ | !style="width:80px"|Bettors | ||
+ | !style="width:140px"|If the horse wins | ||
+ | !style="width:130px"|Calculation | ||
+ | !style="width:80px"|Winning probability | ||
+ | |- | ||
+ | |style="text-align:center"|A | ||
+ | |10 bettors | ||
+ | |$20 into 10 bettors | ||
+ | |$20 ÷ 10 = $2 | ||
+ | |10/20 | ||
+ | |- | ||
+ | |style="text-align:center"|B | ||
+ | |5 bettors | ||
+ | |$20 into 5 bettors | ||
+ | |$20 ÷ 5 = $4 | ||
+ | |5/20 | ||
+ | |- | ||
+ | |style="text-align:center"|C | ||
+ | |3 bettors | ||
+ | |$20 into 3 bettors | ||
+ | |$20 ÷ 3 = $6.66.. | ||
+ | |3/20 | ||
+ | |- | ||
+ | |style="text-align:center"|D | ||
+ | |2 bettors | ||
+ | |$20 into 2 bettors | ||
+ | |$20 ÷ 2 = $10 | ||
+ | |2/20 | ||
+ | |- | ||
+ | |style="text-align:center"|E | ||
+ | |1 bettor | ||
+ | |$20 into 1 bettor | ||
+ | |$20 ÷ 1 = $20 | ||
+ | |1/20 | ||
|} | |} |
2022年11月6日 (日) 23:53時点における版
目次
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 |