Let's calculate the expected return per outcome. Let's define the following:

• is the expected return when dice are the same.
• is the probability that dice are the same.

Let's start with the case where 3 dice are the same, where you earn €16. The first dice can be any dice, but the other two dice need to be the same. So,

(1)  

(2)  

Next, consider the case where 2 dice are the same, where you earn €14. The first dice can be any dice, the second dice needs to be the same and the third dice needs to be another number. You can order this in ways. So,

(3)  

(4)  

Finally, consider the case where no dice are the same, where you lose €4. The first dice can be any dice, the second dice needs to be another number and the third dice again needs to be another number. So,

(5)  

(6)  

The expected return of this game is defined as:

(7)  

(8)  

(9)  

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