Dead Heat

The Setup

Eight horses are about to race. You have access to the results of 500 historical races involving these exact horses. A parimutuel betting market is open on the outcome.

Parimutuel mechanics. All money bet on a given horse is pooled. If your horse wins, you receive your proportional share of the entire pool, minus a 15% takeout by the track.

Concretely: if the total pool is $P$, the track takes $0.15P$, leaving $0.85P$. If horse $i$ received fraction $f_i$ of all bets, and you bet $b$ on horse $i$, your payout if $i$ wins is:

$\text{payout} = b \cdot \frac{0.85}{f_i}$

Your profit if $i$ wins is $\text{payout} - b$. If $i$ loses, your profit is $-b$.

Your pool is £10,000. You may allocate any amount to any combination of horses. You may not bet on multiple horses in the same race beyond your total stake (no arbing across horses — standard parimutuel rules).

The race will be simulated 10,000 times from the same underlying distributions that generated the historical data. Your score is your total profit across all 10,000 simulations, divided by 10,000 (i.e. your average profit per race in £).

Current Market

The current parimutuel pool fractions (fraction of total money currently on each horse) are:

Note: these pool fractions will remain fixed for scoring purposes — your bets are assumed to be a negligible fraction of the total pool and do not move the market.

Historical Data

Download: race_data.csv

Columns: race_id, Shadowfax, Iron Duke, Morningstar, Red Tide, Gallant Fox, Blue Streak, Copper Prince, Last Chance, winner

Each row is one historical race. Each horse column shows that horse's finishing time in seconds. The winner is the horse with the lowest finish time.

Your Submission

Enter your stake on each horse (in £) using the form below the problem statement. Stakes must be non-negative and must sum to at most £10,000. You may stake £0 on any horse.

Hints

• The historical data tells you something about each horse's true win probability. The crowd's pool fractions may or may not reflect these accurately.
• In parimutuel betting, the expected value of betting £1 on horse $i$ with true win probability $p_i$ and pool fraction $f_i$ is:

$EV = p_i \cdot \frac{0.85}{f_i} - 1$

• Bet only where your edge is positive.
• Think about how to size your bets. The Kelly criterion is worth reading about.

Background reading

• Parimutuel betting — how pool-based betting markets work.
• Favourite-longshot bias — a well-documented pattern in betting markets where longshots are overbet.

Scoring

Your submission is simulated against 10,000 races drawn from the true distributions. Score = average profit per race in £.

Higher is better. Negative scores are possible (you can lose money).