The Sum Game

"The Sum Game" is a simple C++ "controlled chaos" themed game, where you simply enter two values: the limit sum score and how many times to roll a 6 sided dice. The dice is rolled n times and it must be lower than the limit. If the final sum is lower than the limit you've initially entered, you win the game. The number of dice rolls must be greater than or equal to 1/4 of the limit in order to roll the dice. I now present a challenge: can you win with the largest amount of dice rolls in order to reach a ratio of 1:3, 2:5, 4:7, or an even higher ratio?