The Tavern

Just kidding, its not really that crazy.

Say you have a deck of 52 cards, and you have to pull n cards. On each card is a command to pull between 0 and m new cards, with each value having a given likelihood in the deck (for example 10 cards will tell you to pull two new cards).

You get a tree if you graph out a given run, but what is this cascading effect called in mathematics? I already programmed a simulater so I can play with the outcomes, so not really interested in a solutions (unless there is an explicit solution or some interesting boundary behaviors).

Reason I am curious is that I am messing around with a game I am designing and thought this might offer a means of ramping up difficulty in a natural and still somewhat randomized manner, in a way which requires zero memorization or computation (other than simple counting) from the player. You get an exponential decay curve for the total cards drawn, which you can easily tweak by altering the internal populations as well as the original number of draws.

Is the tree you get, like, a prize for the graph? A potted plant? Sounds neat.

Queuing theory, mixture models, recursive equations, convolutions, ...

Lol, no just if you graph out the branches you end up with what is called a "tree" in the study of graphs. What you actually get, is an army of variable number of units (strength) based on how you stack the deck and how many cards you force the player to start their first pull with. I've got a deck building game where I wanted to have a static method for increasing game difficulty as the player progresses, otherwise it gets pretty lame if you have a mechanic which works well in the early game, but which the player can steamroll as you get into the endgame.


Thanks, will look into this terms.

Is this what the potion of lignification is for?

This sounds like a probability question.

However I am not what you are asking.

The only trees I am familiar with are Binomial trees.

However each card would then be a branch and it would be confusing and look more like a messy bush. But yes if you graph each path they form a tree and each path is independent however some might be identical paths.

I’m not sure if this helps but maybe if you get more specific maybe someone else might be able to help

Lol did they legalize it where you are from?

I'm not entirely sure why there's so much confusion here, it seems pretty simple. Maybe if I rephrase it more simply:

Imagine a card game where you draw 3 cards a turn. But some of those cards say "draw another card immediately" on them. What we want to know how many cards the player draws in total on their turn. Simple.

In order to not draw the entire deck you'd want the average card to draw less than 1 more card, so I imagine most cards don't draw additional cards, some draw just one, and only a few draw two or more. Crawlnoob already has a simulation to play around with the variables but is interested in a more math theory solution, if one exists.

I don't know if this has a specific name in math, but it'd probably come up in courses on probability and/or repeated, independent trials?


Yes they did!

Exactly, Tasonir, and you are correct in your assumptions in the pack-design.

Check out the Galton–Watson process.

Heh cool, thanks.