If red paid 4 cents to blue’s 7 cents, it would be right to bet on red every time.
Nope.
Consider a deck of 10 cards; 7 blue and 3 red. You write down a list of 10 predictions, in order, and the cards are dealt out; for every card that matches the corresponding prediction you get a reward based on the card color.
If you make 10 blue predictions, and blue cards are worth 7 points, you get 7 correct answers and 49 points.
If you make 10 red predictions, you get 3 correct answers, and red cards have to be worth 16.33 for you to break even.
Fixed. I meant to add a cent to red after making it fair, but accidentally set it up such that the .7 chance one got the seven cents rather than the three in the fair case.
Nitpick:
Nope.
Consider a deck of 10 cards; 7 blue and 3 red. You write down a list of 10 predictions, in order, and the cards are dealt out; for every card that matches the corresponding prediction you get a reward based on the card color.
If you make 10 blue predictions, and blue cards are worth 7 points, you get 7 correct answers and 49 points.
If you make 10 red predictions, you get 3 correct answers, and red cards have to be worth 16.33 for you to break even.
Fixed. I meant to add a cent to red after making it fair, but accidentally set it up such that the .7 chance one got the seven cents rather than the three in the fair case.