A Dice Tower For Cards

For King and Parliament  (FK&P) is designed to be diceless (as is its parent, To the Strongest!). You can read thousands of articles by mathematicians, statisticians, game theorists and game designers about the pros and cons of both dice and cards. Here is an article that gives a simple summary: Mechanics Face Off: Dice vs. Cards.

I really like dice towers, particularly the lovely one I have. When you drop several dice (10d6 for example) through the tower, the sound is rather like the rattle of musketry!  Using well formed dice you can be assured that the results are completely random each time they are dropped.  Each die is an independent actor, the result of all other die in the same roll having zero effect* on it. The odds for any particular combination can be precisely calculated at any time. It is also possible to get extreme results. Ten ones, for example.

Playing cards are a different beast being dependent on one another. The first card draw (unless you replace it and reshuffle) slightly alters the odds for every other card in the deck and each succeeding continues the alteration. The game resolution system basically has a “memory”. In KF&P the memory gets reset at the end of each turn. I use an eighty card deck for each side but other multiples of forty can be used. Blackjack tables at Casinos typically use six or eight decks per shoe (to make card counting more difficult).

I use miniature playing cards for FK&P (Playing Cards) to take up less space in the 10cm grid I use. Because of their size, however, just keeping them in a single stack can be a trial.  I have already discribed the quick and dirty card shoes I made to keep them contained in a single stack for game play. They also turn out to be a bear to shuffle. They are slick and when I try to shuffle in the normal manner (a riffle suffle) they tend to shoot off into space.

Play with cards is much quicker than continually rolling dice but it take time to shuffle the decks between turns. After playing through several games, I was finding the shuffling rather laborious. I now  have a simple shuffle tray to do the job in less than a minute per deck (and it even captures some of the sound of a dice tower):

Suffle tray 1

I bought a four deck set of cards with each deck having a different back (I write this to explain why the cards in the above game deck have two different backs). I have since found another source and obtained matching backs. (Yes, it was annoying me that much! 😬)

I am now going to nerd out on the testing I did to satisfy myself that the suffle tray was doing a satisfactory job. This is far from a rigorous study and will NOT result in a paper for peer-review. 😄

methodology

The cards are first sorted into an ordered deck of ten sets of eight cards. This will be the starting set for each of my three trials:

Eight by Ten 1

Once the cards are spread in the tray, I swirl them for fifteen seconds, tilt from side-to-side for a fifteen count and tilt from front-to-back for another fifteen count. I again spread them over the surface of the tray and select them out in four or five batches and place in the card shoe:

Grabbing a batch

I then deal them out in ten sets of eight. One can readily “eye-ball” the distribution and see at a glanced how well they are mixed, but I wanted some sort of metric to use as well. I calculated** that in a well randomized set of eighty cards I should get around 7 pairs and 0.6 triplets.

As a further measure I also looked at the distribution of the number five cards. In the starting set, all the fives appear in a single row and in an ideal distribution I should get one five in eight of ten rows. There is a problem with the ideal distribution, however. To arrive at that outcome the deck would have to be highly ordered by sequential card numbers. Why? The ideal distribution of fives implies the other nine values have to be ideally distributed as well if we want the fives distribution to represent the entire distribution of eighty cards. So let’s say that a distribution that is void in no more than four rows is reasonably random.

The three trials are shown below. The second picture is a frequency distribution of the first forty cards (done as I prepare the start conditions for the next trial). I realize that a n=3 is close to meaningless. Prehaps more will be added later (but probably not 😄)

Trial One:

Trial 1 spread

Pairs = 7, accept 7 or less; Triples = 1, accept 1 or less; rows without fives = 4, accept 4 or less. All OK.

Trial 1 distribution

Trial Two

Trial 2 spread

Pairs = 4, accept 7 or less; Triples = 0, accept 1 or less; Rows without fives = 4, accept 4 or less. All OK.

Trial 2 distribution

Trial Three

Trial 3 spread

Pairs = 3, accept 7 or less; Triples = 0, accept 1 or less, Rows without fives = 4, accept 4 or less. All OK.

Trial 3 distribution

Conclusion

Until proven wrong, I am now happy to accept this shuffling method is capable of delivering a random set of cards each and every time. 😀

Why do I like cards over dice? If you play fair (that is to say, neither pre-programming the deck nor, to a lesser extent, using a card counting system) you still have an intuitive sense of how the results are likely to fall. A sense which improves as the turn wears on. If you recall several Aces (bad) or Tens (usually good) having been drawn, you have a clue as to the best actions to take. It is the sense that provides the “now is the time” moment that dice games can’t provide. A sense that is of extreme importance in an actual battle (based on my reading of history).

As a solo gamer the cards really expedite play (and I can see at a glance the situation on the game board, even if I am away from it for an extended period of time). Recall that only the activation cards remain on the board face-up, all the action cards (drawn from the same deck) are placed face down (and off board) as soon as a resolution occurs. You still have that overall sense of the spread of cards but can’t do exact calculations.

Cards rule!

* it can of course be argued that the number of dice simultaneously dropped effects the number of collision that occur which in turn effects outcomes. It is easier to simply think of the dice tower as a black box that spits out dice in a random manner.

** Once, a lifetime ago in world that no longer exists, I dealt with the mathematics of probability on a regular basis. I remember next to nothing, the database being extinguished through lack of practice and over-written way too many times. My calculations might be considered to be less than rigorous. 😄

7 thoughts on “A Dice Tower For Cards

  1. You don’t have to restrict yourself to two decks- maybe get half a dozen, tray shuffle and stick them in a big card shoe- should last the whole game, even for FK&P! I might even try that myself….

    Like

  2. Thanks, Simon.
    Yet another reason to like cards! You can easily alter play since you can control when to shuffle and how many cards comprise a deck. I saw somewhere a player keeping all the face cards (counting as 10) in the activation decks to REALLY move things along. (dice lovers will argue that you can use average dice or dice with a different number of faces to accomplish the same! The debate is endless).

    A downside – I found an ace of spades laying on the floor about half through a practice game! Of course the more decks the less effect of a missing card.

    Like

  3. Pingback: Chittering | In Red-coat Rags Attired

Comments are closed.