Bragmore should lend his spare pair of goggles to his primary competitor Aprince and should play fair.
Step-by-step explanation:
Winning is very important in a competition but more than winning what matters more is playing fair and playing hard to compete with your competitors where every one is given equal chances to show their strength and capabilities.
Even though not giving goggles to his primary competitor will increase the chance of Bragmore to win the race easily and he will win the cash prize but that would not be a fair fight. So he should fight giving equal opportunities to his competitor also and give his spare goggles to his competitor.