Horse betting game 3 horse, racing, you could buy ticket 1 dollar to bet on each horse win. For every dollar you bet, the profit you could win from the three are 2, 4, and 6 dollars, how do you play this game?
I am thinking about let the money bet on each horse be x, y, z. And then for each scenario I would try to get the same profit:
2x - y - z = 4y - x - z = 6z - x - y
Is this the correct way to think about this? I would appreciate any help. Thank you.
Actually I found a link that talks about the exact same problem https://www.reddit.com/r/askmath/comments/8jr7lw/help_probability_interview_question_on_betting_on/, but still I don't understand it.

You can check whether this is a Dutch book.
For this you need a sum the reciprocals of returns (which is the amount that you would have to bet to get 1 return) and see if the total is above 1.
$$\frac{1}{2} + \frac{1}{4} + \frac{1}{6} = \frac{11}{12} < 1$$
So this is a Dutch book and you have a garanteed profit.
