The Wimbledon final between Nadal and Federer is about to begin! You want to spend your full budget of €100 on bets for this game. There are two different companies with their own payout ratios per player. Company A payout: Nadal 1.29 Federer 4 Company B payout: Nadal 1.2 Federer 4.7 What will your betting strategy be, and why?

First, calculate the implied probability for both players per company. If their sum is below 100%, there is an arbitrage opportunity. Company A 1/1.29 + 1/4 = 1.03, or 103%. Here, there are no arbitrage opportunities. Company B 1/1.2 + 1/4.7 = 1.05, or 105%. Again, there are no arbitrage opportunities. However, what if we combine the odds from both firms? Federer (Company A) & Nadal (Company B) 1/4 + 1/1.2 = 1.08, or 108%. Here, there are no arbitrage opportunities. Nadal (Company A) & Federer (Company B) 1/1.29 + 1/4.7 = 0.99, or 99%. Here we have an arbitrage opportunity! So, let's focus on Nadal (Company A) & Federer (Company B). The odds (Nadal 1.29 and Federer 4.7) have a ratio that's approximately equal to 21 vs 78. To let these values sum to 100, let's make it 22 vs 78. Now, let's check if betting these values would make us money: Nadal: 78*1.29 = €100.62 Federer: 22*4.7 = €103.40 Yes, we found an opportunity to always win, regardless of the outcome of the game!

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Title	Category	Subcategory	Difficulty	Status
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Parimutuel Betting	Probability and Statistics	Game Puzzle	Medium	Unlock

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