Seven horses compete in the Derby of Destiny: Thunder (A), Blaze (B), Champion (C), Dazzle (D), Eclipse (E), Flash (F), and Glory (G).
Use the following data to determine which horse is most likely to win the next racing event.
Racing Records:
- Thunder (A) beats Blaze (B) – 10 out of 10 times
- Champion (C) beats Thunder (A) – 8 out of 10 times
- Dazzle (D) beats Champion (C) – 7 out of 9 times
- Eclipse (E) beats Dazzle (D) – 6 out of 8 times
- Flash (F) beats Eclipse (E) – 5 out of 7 times
- Glory (G) beats Flash (F) – 4 out of 6 times
- Blaze (B) beats Glory (G) – 9 out of 11 times
Challenge: Using these direct and derived relationships, calculate each horse’s probability of winning the race.
View the answer
Solution:
Derived Cross-Relationships:
Based on transitive performance (if X beats Y and Y beats Z, then X’s likelihood against Z = X’s rate × Y’s rate = 7/9 × 8/10):
- Champion (C) beats Blaze (B) – 8 out of 10 times (via Thunder)
- Dazzle (D) beats Thunder (A) – 6 out of 10 times (via Champion)
- Eclipse (E) beats Champion (C) – 5 out of 9 times (via Dazzle)
- Flash (F) beats Dazzle (D) – 4 out of 8 times (via Eclipse)
- Glory (G) beats Eclipse (E) – 3 out of 7 times (via Flash)
- Blaze (B) beats Flash (F) – 6 out of 11 times (via Glory)
Analysis Method: Each horse’s overall performance is calculated by averaging their win rates against all other horses (using both direct and derived matchups).
Individual Horse Performance:
Thunder (A):
- Beats Blaze 10 out of 10 times
- Loses to Champion 2 out of 10 times
- Loses to Dazzle 4 out of 10 times
- Loses to Eclipse 1 out of 7 times
- Loses to Flash 2 out of 11 times
- Loses to Glory 1 out of 11 times
- Average win rate: 13.2%
Blaze (B):
- Loses to Thunder 0 out of 10 times
- Loses to Champion 2 out of 10 times
- Loses to Dazzle 1 out of 9 times
- Loses to Eclipse 1 out of 7 times
- Beats Flash 6 out of 11 times
- Beats Glory 9 out of 11 times
- Average win rate: 12.8%
Champion (C):
- Beats Thunder 8 out of 10 times
- Beats Blaze 8 out of 10 times
- Loses to Dazzle 2 out of 9 times
- Loses to Eclipse 5 out of 9 times
- Loses to Flash 2 out of 6 times
- Loses to Glory 4 out of 11 times
- Average win rate: 19.6%
Dazzle (D):
- Beats Thunder 6 out of 10 times
- Beats Blaze 8 out of 9 times
- Beats Champion 7 out of 9 times
- Loses to Eclipse 2 out of 8 times
- Loses to Flash 4 out of 7 times
- Loses to Glory 3 out of 6 times
- Average win rate: 20.0%
Eclipse (E):
- Beats Thunder 6 out of 7 times
- Beats Blaze 6 out of 7 times
- Beats Champion 4 out of 9 times
- Beats Dazzle 6 out of 8 times
- Loses to Flash 2 out of 7 times
- Loses to Glory 3 out of 6 times
- Average win rate: 18.0%
Flash (F):
- Beats Thunder 9 out of 11 times
- Loses to Blaze 5 out of 11 times
- Beats Champion 4 out of 6 times
- Beats Dazzle 3 out of 7 times
- Beats Eclipse 5 out of 7 times
- Loses to Glory 2 out of 6 times
- Average win rate: 18.8%
Glory (G):
- Beats Thunder 10 out of 11 times
- Loses to Blaze 2 out of 11 times
- Beats Champion 7 out of 11 times
- Beats Dazzle 3 out of 6 times
- Beats Eclipse 4 out of 6 times
- Beats Flash 4 out of 6 times
- Average win rate: 20.0%
Final Rankings:
- Dazzle (D): 20.0% – Tied for highest average win rate
- Glory (G): 20.0% – Tied for strongest overall performance
- Champion (C): 19.6% – Close third with solid matchups
- Flash (F): 18.8% – Strong mid-tier performer
- Eclipse (E): 18.0% – Decent against most opponents
- Thunder (A): 13.2% – Perfect against Blaze but poor elsewhere
- Blaze (B): 12.8% – Weakest overall record
Key Insight: Despite Thunder’s perfect record against Blaze, the transitive relationships reveal Dazzle and Glory as favorites for the coming event, showing how circular dynamics can differ from apparent perspectives.