Hi,

I am trying to make my own math game for a school project, but i want to know what all the chances are to win this game. This is the game board with the dice:

Rules:

- You start on the starting line.

- You throw the dice and if you get a color you should put your pawn on the board with the corresponding color.

- Then you must throw the dice again and if you throw the color that's one top you, you can go one stage further but if you throw another color you put your pawn on that color from the same stage.

- i didn't want to make this game to long, so if you throw the second time while this is your second stay on this stage then you can put your dice on the next stage on the square with the same color you just threw.

- White sides of the dice don't count until you are on the last stage because the end is white. So the chance's are 1/4 for every color until on the last stage. There the chance is 2/6 to throw white because there are to white sides on the dice.

Now the goal is to get to the end as fast as possible.

6 steps is perfect and 11 steps are the maximum amount steps.

I am now counting step by step what the chances are but could somebody help me to make a calculation for this game to get all the chances?

I am really dazzled, because i think this involves a combination of calculations to get a right formula.

I hope a mathgenius is able to solve this problem!

Thanks