The Lucky Dice

Ray and Evangeline are playing a game named “The Lucky Dice”. In this game, each player tosses up a ‘n sided special fair dice’ alternatively. This continues for k turns(In each turn two players both roll the dice once). Then the players add all the numbers they got and the person with the higher sum wins.


This is a companion discussion topic for the original entry at https://toph.co/p/the-lucky-dices

Can you give an explaination of the editorial?

Logic:
In 1 turn you expect the highest value which is L+N-1 and you also want your opponent to have the lowest value which is L. So, you get your answer for a single play is res=L+L+N-1. And for k plays, the total sum is k*res.