Shenmue/Duck Racing

Duck Racing is a hidden game that can be found in Shenmue II. The player can either place bets on which of six ducks will win a race, or enter their own duck and attempt to win. The player can bet anywhere from HK$20 to HK$1000, with odds and probability of winning varying by race and by duck.

Ducks
There are twelve different ducks that can appear in duck races.

Names and Stats
When choosing to bet on a duck, the player can view the paddock where information on each duck will be provided. Each duck has four public characteristics: speed, stamina, guts, and personality. Speed, stamina, and guts are measured as a rank from A-D (S-C in Japanese), whereas personality is one of four descriptions: This would leave a possibility of up to 256 distinct ducks; however, there are only twelve different ducks that appear in Duck Racing. Each duck has a 50% chance of appearing in each race.
 * "Good at getting a head start." (S)
 * "Good at holding opponents down." (D)
 * "Has sharp and quick legs." (L)
 * "Strong in the home stretch." (H)

The names given to the ducks are unofficial. They were coined as mnemonics for the three main stats each duck has. Note: Downy and Legs are the only two ducks to share a set of main stats (BDD), so their names refer to their personalities instead.

Values
Each duck has a preset value which is used when calculating odds; the odds for each duck are calculated by taking the sum of the values of all ducks in the race, dividing by the value of the duck in question, and rounding down to the nearest 0.1.

For example, in a race among Ada, Bombadil, Bedbug, Bacardi, Dack, and Cobbed, the odds can be calculated as follows:

Sum = 10+8+8+6+6+5 = 43

Ada = 43/10 = 4.3

Bombadil = 43/8 = 5.3

Bedbug = 43/8 = 5.3

Bacardi = 43/6 = 7.1

Dack = 43/6 = 7.1

Cobbed = 43/5 = 8.6

Detailed information about values and calculated odds can be found in this google sheet.

Win probability and RTP
The win probabilities were calculated based on a total of 1849 races, taking a total of approximately 75 hours. The six ducks in each race, and the winner, was recorded. The win probability for each duck is simply the number of times it won a race, divided by the number of races it took part in; the RTP for each duck is the sum of its odds in each race it won, divided by the number of races it took part in.

A full list of races can be found in this pastebin file and this google sheet.

Overall RTP
Randomly choosing a duck, or choosing based on colour or number or any other factor that results in betting on all ducks equally gives an RTP of approximately 100%. With the correct strategy, this can be increased to 264.4% (at a maximum HK$1000 bet, this gives an average earnings of HK$1644 per race).

The optimal strategy is simple - bet on the duck that appears first in the list at the top of the page (i.e. the one with the highest individual RTP). For example, in a race among Bobby, Becky, Hyper, Legs, Downy, and Cissy, the optimal strategy would be to bet on Cissy.

It may seem as though it's a bad idea to bet on a duck with an RTP less than 100% in the table, but the table shows overall RTP; the actual RTP varies from race to race. For example, Becky may have a win probability of 15.6% and an RTP of 82.4% over all races, but if the other five racers are Bobby, Bedbug, Hyper, Bacardi, and Legs, her win probability increases to 31.1%; as a result, her RTP also increases to 174.4%.

With earnings of approximately HK$800 per minute, Duck Racing is the fastest way to earn money in Shenmue II without needing to mitigate losses by saving and reloading.