Bro and I are trying to create mechanics for a tabletop game. First, I will explain the mechanic and then I will ask what we need to solve, please.
The game is a racing game, where the first to 100 miles/km/points wins. A player can choose from different "car builds." There are 2 stats to each car, "Acceleration" (which is the number of dice the player ADDS to your roll each turn), and "Top Speed" (which is the maximum number of dice the player can roll). The sum of Acceleration and Top Speed Stats must equal 10, and Acceleration can never be greater than Top Speed. This results in 5 possible builds: (Acceleration, Top Speed) = (5,5), (4,6), (3,7), (2,8), (1,9).
At the starting line/turn 1, Acceleration begins, and the player rolls a number of 6-sided dice equal to their Acceleration stat. On turn 2, a number of dice equal to the Acceleration stat is added to the dice already in hand (i.e., if Acceleration = 3, on turn 1 three dice are rolled, and on turn 2 six dice are rolled). On each turn, dice equal to the Acceleration stat are added to the total number UNTIL the Top Speed is reached. The number of dice equal to the Top Speed stat is used for the remaining turns. Ergo, a (5,5) build will reach it's top speed during turn 1 and it will take 20 turns to reach 100 miles/km/points at most (assuming every dice rolled only = 1 for this unlucky player). A (1,9) build will take 9 turns to reach Top Speed, but for the remainder of the game rolls 9 dice.
We are trying to figure out the most number of turns it would take each build to make it to 100, and so are assuming every dice rolled only ever results in 1. What is an equation for solving this problem, rather than adding each one individually, and could it be scaled to find then the smallest number of turns it would take for each to reach 100?
Our goal is to chart these most basic base stats to see if these builds are competitive with each other and that there are no wildly outstanding favorites before we start adding in additional player mechanics.
It has been over a decade since I did Calculus, and I need people smarter than me! Thank you for any input in advance~
The game is a racing game, where the first to 100 miles/km/points wins. A player can choose from different "car builds." There are 2 stats to each car, "Acceleration" (which is the number of dice the player ADDS to your roll each turn), and "Top Speed" (which is the maximum number of dice the player can roll). The sum of Acceleration and Top Speed Stats must equal 10, and Acceleration can never be greater than Top Speed. This results in 5 possible builds: (Acceleration, Top Speed) = (5,5), (4,6), (3,7), (2,8), (1,9).
At the starting line/turn 1, Acceleration begins, and the player rolls a number of 6-sided dice equal to their Acceleration stat. On turn 2, a number of dice equal to the Acceleration stat is added to the dice already in hand (i.e., if Acceleration = 3, on turn 1 three dice are rolled, and on turn 2 six dice are rolled). On each turn, dice equal to the Acceleration stat are added to the total number UNTIL the Top Speed is reached. The number of dice equal to the Top Speed stat is used for the remaining turns. Ergo, a (5,5) build will reach it's top speed during turn 1 and it will take 20 turns to reach 100 miles/km/points at most (assuming every dice rolled only = 1 for this unlucky player). A (1,9) build will take 9 turns to reach Top Speed, but for the remainder of the game rolls 9 dice.
We are trying to figure out the most number of turns it would take each build to make it to 100, and so are assuming every dice rolled only ever results in 1. What is an equation for solving this problem, rather than adding each one individually, and could it be scaled to find then the smallest number of turns it would take for each to reach 100?
Our goal is to chart these most basic base stats to see if these builds are competitive with each other and that there are no wildly outstanding favorites before we start adding in additional player mechanics.
It has been over a decade since I did Calculus, and I need people smarter than me! Thank you for any input in advance~
