Yup exactly. But other bets (surely they are not betting on the exact same thing with just different odds and even if they were they) don't influence the chances of this bet. These are independent events. Either you think you are likely to win or not. To refuse 1:1 odds on the grounds that you could make more money somewhere else means either A: you do it for the money and not the sport or B: don't have enough money to wager on all these bets but then he should ask for a lower amount or refuse with that reasoning. Maybe I am missing some other possible explanation? The reason of refusal is very important to understanding the motivation behind it.
If there are two people offering you a bet:
Person A offers you 5:1 odds in your favor saying that a random dice throw will yield a number small than 3.
Person B offers you 1:1 odds in your favor saying that a random number chosen between 1 and 10 will yield a number bigger than 6.
Thinking about the wager with Person B is independent of the wager with Person A. When deciding which bet to engage in the answer is both because in both cases you should be convinced that your chances of winning are >50%. Refusing the second bet would lower your overall expected winnings.
If there are two people offering you a bet:
Person A offers you 5:1 odds in your favor saying that a random dice throw will yield a number small than 3.
Person B offers you 1:1 odds in your favor saying that a random number chosen between 1 and 10 will yield a number bigger than 6.
Thinking about the wager with Person B is independent of the wager with Person A. When deciding which bet to engage in the answer is both because in both cases you should be convinced that your chances of winning are >50%. Refusing the second bet would lower your overall expected winnings.