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Pari mutuel betting

Horse Racing
Index number
wager
1
1
$60.00
2
2
$140.00
3
3
$24.00
4
4
$110.00
5
5
$220.00
6
6
$94.00
7
7
$300.00
8
8
$80.00
There are no rows in this table
⁠
The total pool of money on the event is $1028.00.
For example, with a commission rate of 14.25% = $146.49. This leaves a remaining amount of $881.51.
Distributed to Outcome 4: $881.51 / $110.00 = 8.01 ≈ $8 per $1 wagered. This payout includes the $1 wagered plus an additional $7 profit.
Thus, the odds on Outcome 4 are 7-to-1 (or, expressed as
decimal odds
⁠
, 8.01).
Prior to the event, betting agencies will often provide approximates for what will be paid out for a given outcome should no more bets be accepted at the current time. Using the wagers and commission rate above (14.25%), an approximates table in decimal odds and fractional odds would be:
Outcome
Index number
Ratio
Odds
1
1
14.69
13:1
2
2
6.3
5:1
3
3
36.73
35:1
4
4
8.01
7:1
5
5
4.01
3:1
6
6
9.38
8:1
7
7
2.94
2:1
8
8
11.02
10:1
There are no rows in this table
⁠

Prediction Markets

In Automated market-maker, the market-maker will calculate and post prices for all possible states.
This allows the market organizer to immediately post prices for all states - rather than waiting for traders to post orders as in a continuous double auction.
While this mechanism is generally pari-mutuel, the value of a winning order is fixed in Hanson’s mechanism.
Bibliography:
⁠
https://en.wikipedia.org/wiki/Parimutuel_betting
⁠
⁠
⁠
https://en.wikipedia.org/wiki/Exotic_option
⁠
⁠
⁠
https://web.stanford.edu/~yyye/scpmfinal.pdf
⁠
⁠
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