First, start with 1 checker on the 24-point and 8-point, and 3 checkers on the 6-point and 13-point. The remaining 7 checkers will be placed randomly on these points.

We need to randomly pick 3 different numbers from 1 to 10. To generate a number, first roll one die until you don't get a 6. Then roll another die. If it is high (4, 5, or 6), add 5 to the first die. Repeat this process until 3 different numbers from 1 to 10 have been rolled.

The numbers you have generated partition the 7 other numbers 1 to 10 into 4 groups. This is how many additional checkers are placed on the 6-, 8-, 13-, and 24- points respectively. For example, if the 3 numbers randomly generated are 2, 7, and 10, then this partitions the other numbers into (1)(3 4 5 6)(8 9)(), and so 1 extra checker is placed on the 6-point, 4 extra checkers are placed on the 8-point, and the last 2 extra checkers are placed on the 13-point.

Finally, some of these stacks might be moved up one space. Roll a die. If it is high, then the stack on the 6-point starts on the 5-point instead. Roll another die. If it is high, then the stack on the 8-point starts on the 7-point instead. Roll another die. If it is high, then the stack on the 13-point starts on the 12-point instead.

Continuing the example above, if only the 13 point is shifted forward, then this would be the starting position: