Hi math wizards,

I've got a probability question that I can't wrap my head around. I'm trying to balance decks size so that the number of rounds in my game is 10 or less regardless of the numbers of players. Below is a breakdown of how cards are drawn. Is there anyone that can help me with a formula to solve this?

The game is a 2 to 6 player game and I currently have a deck of 54 cards, with the following distribution

- 23 imps

- 16 spiders

- 10 snakes

- 5 dragons

For the first 1/3rd of the deck players draw cards equal to the number of players +1

The rest of the game players draw nests (will explain) equal to the number of players +1

A nest happens when the same monster gets drawn consecutively (they stack) and has a max stack size of 3 monsters.

Let's pretend the following cards are (in order) on top of the deck: imp, spider, spider, spider, spider, spider, dragon, dragon, imp

In a 2 player game you draw the following cards on 1 turn:

- Imp

- Spider, Spider, Spider

- Spider, Spider

In a 3 player game you draw the following cards on 1 turn:

- Imp

- Spider, Spider, Spider

- Spider, Spider

- Dragon, Dragon

etc...

I'm trying to get the game average under a maximum of 10 rounds, but am a bit clueless as to how a formula for this work. Right now I'm using brute force analysis, meaning playtesting the heck out of it and writing down what happens. It would be great if someone can save me the time and educate me on math & stats :)

That's interesting... Apparently I wasn't clear in conveying the rules, but the results you get from your script amount to the same as I'm getting from playtesting. I think I've got enough to go on though, so thanks for the help!