(Belated) Design Diary Monday: I Am Not a Wizard With Spreadsheets

One of the many weaknesses I have with game balancing is I have an extremely poor background in statistics, and apparently statistics is all the rage as far as balancing numbers are concerned.

A few weeks ago, a certain reddit topic brought me to the use of hypergeometric distributions. My current work in progress idea surrounding deception will make heavy use of the concept of “BS” style card game and some type of melding card game.

I’ve started with this google spreadsheet. The only relevant table is the third one at the bottom that shows the probability of the player having N or more cards after drawing X cards from the deck. The one published above uses a standard deck of playing cards, and calculates the probability of having N or more cards of the same suit.

If each project type in my game idea corresponds to a single card suit and the values doesn’t matter, then the distribution would show me how many cards a player might need to complete a project on his or her own, using materials (cards) of the appropriate suit.

Just to throw it out there, a 5 card project size seems to be a reasonable number. The distribution tells me that there’s a 50% chance I’d have 5 cards of the same suit… after drawing 18 cards? That can’t be right.

The percentages are deceptive. The number tells me the percentage of all possible hand of 18 cards… but I’ve been starting with a hand of 5 cards and consciously made a decision to pursue a suit that I already have – often with 2 cards. Adjusting the starting numbers to a 47 card “deck” (since I’ve drawn 5 cards already)  and 11 cards that’d yield me the same suit (since I already have 2 in my hand) yields a much more reasonable 50% to get 3 more cards of the same suit at the 11th draw… until I realize that I’ve already drawn 5 cards in this case so technically I’d get the 50/50 at the 16th card. Replaying a few hands with a real deck of card confirms this – getting that “flush” is actually pretty darn hard.

Interestingly, there’s a 62% of having 5 cards or more of the same suit in the beginning of a 4 player game, if each player draws 5 cards to start with. If the game allows trading, the chance of getting those 5 cards would be significantly easier.

These numbers, once I mess around with it some more, can tell me a lot – it sets boundaries for quantities that are within reason, and with these guidelines I can come up with a card mix for my initial test. It’s probably a lot harder to look for the fun in those numbers, but I firmly believe that’s where the number crunching part of game design stops and the art part begins.

Tomorrow (well, later today): the promised initial numbers for the deception game. This design is going overtime!

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