Atomic Highway is a game system that uses pools of 6-sided dice to determine player successes. I'm trying to write a probability calculator for this system but have hit a snag. The rules are as follows:
- You roll 1-5 6-sided dice, counting dice that result in 6 as successes.
- Reroll the dice that rolled as a 6, keep rerolling 6es until you have no more 6es. Add the new 6es to the successes.
- You get 0-5 bonus points you can divide as you want among the dice that didn't result in 6es on the first roll. If you manage to bump up one or more dice results to 6 with this, add those to successes.
- If your total successes is equal to or higher than a treshold, the player succeeds.
I originally found a reddit thread describing a process to calculate the odds of success (thread here) and managed to program this process, but unfortunately the odds they achieve with their method are way off.
Specifically, they claim when rolling 3 dice with 2 bonus points and needing at least 2 successes, you have a 71% chance of succeeding. The rulebook however provides a table with the success chances and cites a 41% chance of success in this case. I simulated 1 million of these dice rolls and averaged the results, coming out at about 37-38% success rate.
Clearly the reddit method is wrong, and I've unfortunately not found alternatives. Can anyone here find where the reddit method goes wrong and explain how you should calculate this for a more accurate result? Thank you in advance!