I am developing a card game with a friend and I want to calculate the probability of different win conditions being achieved (I am putting together an excel sheet).
I have trouble calculating the probability of drawing a four-card straight out of fifteen cards (which is the average amount of cards you see per game). These are the relevant parameters:
120 cards in the deck Numbered cards run from 1-10. Each number is on 6 cards in the deck. (60 in total) There are fifteen joker cards which can represent any number. The remaining 45 cards are blanks for the purposes of this calculation, i.e. they can be drawn but not used to complete a straight.
I've been watching different videos on how to do this, and tried out different ways of calculating it, but have somehow ended up thoroughly confused. Could one of you help me out?
Edit to answer questions that came up:
- The 45 non-specified cards are 'action cards' that allow you to interact with your opponent's cards. For the purposes of this calculation, assume that they are blanks, i.e. can be drawn but can not be used to complete a straight.
- You can use more than one joker, so four jokers would be an automatic straight. Three jokers does not make an automatic straight, because you could draw only action cards with the remaining twelve draws (i.e. blanks for the purposes of making a straight).
- The intention is that the probability of getting to a straight will be high because there are many ways to mess with your opponent in the game. I am aware that this throws off the probabilities, but I'm just looking for baseline probabilities so we can balance the different win conditions.