Challenge: Chance Calculations

[X3M]

I was in a heated discussion on the BGDF forum about calculating the win/loss ratio for a certain dice mechanic for a board game.

Although the discussion is still going on. I feel that if we want to get to the bottom of it. We need more people to think about it. Everyone is getting different numbers as results. And I don't think that we can get rest until it is figured out.

 

Soldiers battle each other and have a different number of dice for attacking and defending.

 

The mechanic for determining the winner:

- One player has a number of dice for attacking.

- Another player has a number of dice for defending.

- After rolling, the dice are sorted from high to low.

- The first dice are compared. The highest wins.

- If there is a tie, we look at the next die and repeat.

- If one player runs out of dice after all the ties. The other player automatically wins.

- If both players run out of dice after all the ties. The defender wins.

 

What are the win/loss ratio's for 1v1, 2v1, 3v1, 4v1 etc. Then 1v2, 2v2, 3v2, 4v2 etc. 1v3, 2v3 and so on?

A nice table of 9 v 9 dice is what we seek.

[MrFlibble]

I've never been really good at math, but there have to be some works on probabilistic calculations that you might use. If you find a source that provides an explanation of such calculations in terms that can be understood by non-specialists, please post it here as this may actually be useful.

[X3M]

Well, in the last 3 days, we figured it out.

 

This one was way more complex then we though before hand. :D

But a fun example for scholars to learn why sometimes a simulation is the only choice to do.

And of course why a simulation is a good reference point to know if you calculated something right or not.