When a correlated parlay favors the bettor
A sportsbook offers a two-leg parlay and prices it the lazy way: it multiplies the two fair single-leg odds as if the legs were independent, quoting . Each leg is a true on its own. But the legs are positively correlated: when one wins, the other tends to win too, so the true probability that both win is , not .
What is the fair parlay price given the correlation, and what is the bettor's edge against the book's quote?
Show a hint
The product rule assumes independence. With positive correlation the true joint probability is higher than the product, so the fair odds are lower than . The book is paying too much.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.