Time Travelers DropBox

 

NOTE: The card backs were used simply for readability. There was no intention of its association with Hearthstone 

 

Finished: 2018

Platform: None

Description: A card game where you and your opponent take turns attempting to place a sequence of cards in a shared pool of 5 blind decks. 

Goal: Make a competitive game involving secrecy and forced actions. 

 

Secrecy:

Cards are placed face down in one of 5 also facedown piles of cards. The only way to reveal the facedown cards is to personally flip them. By doing this though, you risk the chance of losing if you view a pile of cards that has 3 police cards in it. So there is this risk to reward system based on actions you and your opponent make. Forcing players to make educated decisions. To extend the game a little longer, I added a safe peak card. This mitigates the risk but forces 

 

 

Forced Actions:

Are handled through the draw mechanic. I integrated just enough cards so that every draw has a decent chance for a police card. Used combination math to determine how many police cards needed to be in the deck so that there was an ever-present but not overwhelming chance of a drawing a police card. If the player had three police cords in their hand, they lose. So controlling when to make the decision to play a police card at all times is key. Which is close to 38%, see the math below!

How: Balancing the deck

 

1533939 = Sample space of combinations of 5 card hands (47C5)

This will be used a lot....

 

As with any card game, the numbers matter. Choosing those numbers at times can feel arbitrary at best. But with some basic philosophy and discrete math, we can easily determine the outcomes. 

 

Police card x 18:

The police cards are how the game ends. So there had to be a considerable amount of cards in the deck. If we added too many cards, we would end up making the win state impossible. So I used some combination math and basic math to determine some goals. 

 

I decided the sweet spot would be around 18, for a 38% chance to draw. 

 

To calculate the odds of 3 police cards in a hand: 

 

816 = Combination of 3 police cards in a pool of 18 (18C3)

406 = Combination of 2 other cards of 29 (29C2)

331296 = Combinations of 3 police and 2 other cards

 

331296/1533939 = .2159

 

This gives us a decent prediction of how often a player will have 3 police cards in their hand. That being 21.59%, which I believe to be a decent rate to force an action for a player. 

 

Permutations do not matter because this game doesn't consider the order. 

 

Safe Peek Cards x 8:

Basically, a get out of jail free card. So these cards needed to be limited. Giving players too many, they could safely peek every time. So we found the sweet spot to be 8 cards. With a draw rate of 17%, it forced players to make harder decisions when it comes to seeing in the deck. 

 

28 = Combinations of 2 Safe peek cards of 8

9139 = Combinations of 3 other cards  

255892 = Combinations of 2 Safe Peek and 3 other cards
255892/1533939 = .1668

 

So a 16% chance of a player having TWO safe peeks. So not too often.
 

Part Cards  x 11:

The win state of the cards. I won't keep spewing math at you, its made its point. Cards have a descending repetition of useful cards in the deck. 

 

Part 3 has 6 cards in the deck = 12% Draw Chance

Part 2 has 3 cards in the deck =  6% Draw Chance

Part 1 has 2 cards in the deck =  4% Draw Chance

 

While is attractive to assume we can combine those percentages to get a chance. It is highly likely each player will have one Part 3 card in a drop box by the time it actually matters.  

 

Trade Cards x 5:

Trade cards are one of the most powerful cards in stopping a win state. You can trade out a card and steal from their dropbox. Once they are used they cannot be redrawn into a hand again.

 

Safe Draw Two Cards x 5:

Safe Draw allows the player to increase their potential hand which gives them more options and combinations to create a win state. It specifically states you cannot draw a police card as an added benefit of it. 

 

 

How to Win:

  • Collect all three sequential time part cards and put them into a drop box. (their order does not matter, as long as you have 1-3)  

  • Flip and Reveal the drop box with all three cards in it

  • If the opponent cannot counter your win state on their turn they lose.

    • You can counter it by making the box non viable  by making a box have 3 police cards

    • Or stealing one of the part cards

    • Or use a time event

 

 

How to Lose:

  • If you unsafe peek a drop box with 3 police cards

  • If your hand has 3 police cards in it by the end of your turn. You lose!