The game of dots is played by rolling a fair die and receiving $1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?

Question

Answer: The equally likely outcomes of each roll are receiving $6, $5, $4, $3, $2, or $1. I think the answer is $3.50 since you are equally likely to win more or less than the cost. That is 3 of 6 possible outcomes are a gain for 50% chance of a gain, and 3 of 6 or 50% are a loss.
Is this answered correctly?
Thanks.

Answer 1

That's what I would say.

Answer 2

Thanks.

Answer 3

another way.

Expected value: 1/6 (6 + 5 + 4 + 3 + 2 +1)
= 1/6 (21)