Saturday, 3 April 2010

Card-driven Turn Sequences: The latest (and hopefully last) test

Having recovered slightly from my cold, I decided to test the latest version of the card-driven turn sequence I have been working on.

As before I set up a Unit Activation Pack that had ten Red and ten Black playing cards, and the test was to consist of twenty turns. The Red commander was graded as ‘Good’ and needed to score 2 or higher when they threw a D6 whilst the Black commander was grades as ‘Poor’ and needed to throw a 4 or higher.

The results are as follows (the cards that activated a unit have an asterisk [*] next to them):
  1. Red, Black, Black, Black*, Red*, Black*, Red*, Black, Red*, Black*, Black, Red*, Red*, Red*, Black*, Black*, Black, Red*, Red*, Red* (5 Black and 9 Red [70.00%] of the cards were activated)
  2. Red, Red*, Red, Black, Black*, Black*, Black*, Black, Red*, Black*, Black, Black*, Red*, Red*, Red*, Red, Red*, Red*, Black, Black (5 Black and 7 Red [60.00%] of the cards were activated)
  3. Red*, Black*, Black, Red*, Black*, Red*, Black*, Black*, Red*, Red*, Red*, Black, Red*, Black*, Red*, Black*, Red*, Black, Red*, Black* (7 Black and 10 Red [85.00%] of the cards were activated)
  4. Red*, Red*, Red*, Black, Black, Black*, Red*, Black*, Red, Red*, Red*, Black*, Black*, Black*, Black, Red*, Black, Red, Black*, Red* (6 Black and 8 Red [70.00%] of the cards were activated)
  5. Black*, Red*, Black*, Red*, Red*, Red*, Black*, Black*, Black, Red*, Red*, Red*, Red*, Black, Black*, Red*, Red, Black, Black*, Black (6 Black and 9 Red [75.00%] of the cards were activated)
  6. Black, Black, Red*, Black, Black*, Red*, Black*, Black*, Red*, Red*, Red*, Black, Red*, Red*, Red*, Red*, Red*, Black, Black, Black (3 Black and 10 Red [65.00%] of the cards were activated)
  7. Black, Red, Black*, Black*, Red, Black*, Black, Black*, Black*, Red*, Red*, Black*, Red*, Red*, Red*, Black*, Black, Red, Red*, Red (7 Black and 6 Red [65.00%] of the cards were activated)
  8. Black*, Red*, Red*, Black, Red*, Black*, Red*, Black, Red*, Red*, Black*, Black*, Red*, Red*, Black*, Black*, Red*, Red*, Black*, Black (7 Black and 10 Red [85.00%] of the cards were activated)
  9. Red, Red*, Red, Black, Black, Red, Black*, Red*, Black*, Red*, Red*, Black, Black*, Black*, Black*, Red*, Red, Red*, Black, Black* (6 Black and 6 Red [60.00%] of the cards were activated)
  10. Black, Black*, Black, Red, Red*, Black*, Black, Red*, Red*, Black*, Red*, Red*, Red*, Red*, Black*, Black*, Red*, Black*, Red*, Black* (7 Black and 9 Red [80.00%] of the cards were activated)
  11. Red*, Black*, Black*, Black*, Red*, Black*, Red*, Black*, Red*, Black, Black*, Red*, Red*, Red*, Black, Black, Black*, Red*, Red*, Red* (7 Black and 10 Red [85.00%] of the cards were activated)
  12. Red*, Red*, Red*, Black*, Black*, Black, Black, Black*, Red*, Black, Black, Black*, Red*, Red*, Red*, Red*, Red*, Red*, Black*, Black (5 Black and 10 Red [75.00%] of the cards were activated)
  13. Red, Black, Black, Red*, Black, Red*, Black*, Black*, Red*, Red*, Red*, Black*, Red*, Black, Red*, Black, Red*, Black, Red*, Black* (4 Black and 9 Red [65.00%] of the cards were activated)
  14. Red*, Red*, Red*, Black*, Black*, Black, Red*, Black, Red, Red*, Red*, Black*, Black*, Black*, Black, Red*, Black, Red*, Black*, Red* (6 Black and 9 Red [75.00%] of the cards were activated)
  15. Black*, Red*, Black, Red, Red*, Red*, Black, Black, Black*, Red*, Red*, Red*, Red*, Black, Black*, Red*, Red*, Black*, Black, Black* (5 Black and 9 Red [70.00%] of the cards were activated)
  16. Black*, Black, Red*, Black*, Black, Red, Black*, Black, Red*, Red*, Red*, Black*, Red*, Red*, Red*, Red*, Red*, Black*, Black*, Black* (7 Black and 9 Red [80.00%] of the cards were activated)
  17. Black, Red*, Black, Black*, Red*, Black, Black, Black*, Black*, Red, Red*, Black, Red*, Red*, Red, Black*, Black*, Red*, Red*, Red* (5 Black and 8 Red [65.00%] of the cards were activated)
  18. Black*, Red*, Red*, Black, Red*, Black*, Red*, Black*, Red*, Red*, Black*, Black*, Red*, Red*, Black*, Black, Red*, Red, Black, Black (6 Black and 9 Red [75.00%] of the cards were activated)
  19. Red*, Red*, Red*, Black, Black, Red, Black*, Red*, Black*, Red*, Red*, Black, Black, Black*, Black, Red*, Red*, Red*, Black*, Black* (5 Black and 9 Red [70.00%] of the cards were activated)
  20. Black*, Black, Black*, Red*, Red*, Black*, Black, Red*, Red*, Black*, Red*, Red*, Red*, Red*, Black*, Black*, Red, Black, Red*, Black* (7 Black and 9 Red [80.00%] of the cards were activated)
Overall 58.00% of Black cards and 87.50% of Red cards resulted in a unit being activated. This compares favourably with the 50.00% and 83.33% rates of activation that the dice throws should have generated.

I now feel that I have got the balance between unpredictability and predictability about right (nothing is ever perfect, after all) and I can proceed to the next stage in the development process … adding this card-driven turn sequence to my version of Joseph Morschauser’s wargames rules and play-testing it. Only then will I know if it does what I want to it do.

4 comments:

  1. Bob,

    if I were a statistics geek (what, to some extent, I am supposed to be, and I am not), I would try to base the calculations in a spreadsheet; it should not be too hard (again, if I were a statistician...) to come up with the theoretical probabilities at each node of the drawing sequence. Of course, repeating the experiment again and again (technically, this is called a "Montecarlo" study) would approximate the results, but I am not sure it will provide you the "correct" underlying distribution of outcomes. There might be a faster way to achieve it without actually repeating "n" times the experiment.

    Here's a question. You have two game "mechanisms" at work here: the drawing of a card, and the rolling of a die. But at the very end, based on the number of units (via the cards) and the quality of the commander (via the die roll) you create ONE probability distribution... which makes me wonder: can't you achieve exactly the same result by collapsing the two mechanisms into one (a table of outcomes based on a percentile dice roll comes to mind, but it is just a possibility)? The two statistical processes (cards plus die) sound a little... gamey to me (and be that said with the utter respect.) Maybe it's because of my statistical background, but I always feel uncomfortable when rules add layers of randomness when, at the very end, the underlying probability distribution can be replicate in a more straightforward manner.
    Anyway: I love both card activation and randomness in the sequence of play (can you tell I am a Piquet player?), so I am tracking your progress with great interest! keep up with the good work!

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  2. DestoFante,

    It is nice to hear from you again. How is the family?

    One of the reasons why I began recording my results on a spreadsheet in my later tests was so that I could use the same data to test different hypotheses. Once I had designed a spreadsheet that did not just record results but also allowed me to manipulate the data (Thank God for ‘IF…’ statements, conditional formatting, and absolute cell references!), I began to make serious progress.

    To test the mechanism properly I should have conducted literally hundreds of tests (as you say, the ‘Monte Carlo’ method should iron out any extremes in the data), but I decided in the end that I had sufficient data to make a reasonable judgement. After all, this is being done for fun and not for an end of term paper!

    You are quite right that I could have collapsed the two mechanisms into one but (and this is where my prejudices come to the fore) I try to avoid using charts and percentile dice during games. The reasons are aesthetic and practical; charts usually end up on the tabletop – somewhere I definitely think that they should not be, along with all the other detritus that players litter the tabletop with if they can get away with it – and percentile dice seem to have an unenviable reputation for getting themselves ‘cocked’ (i.e. ending up where it is difficult to read the result so that the dice has to be thrown again).

    The mechanism of combining cards and dice is ‘gamey’ (but it is a game after all, isn’t it?) but it is easy to remember (turn the card, throw the die, get a result) and quick to use. It also relies on things that most gamers will have easy access to and that they will understand.

    One option that I am considering is producing a special set of cards for my own use. These would be made from laminated business cards (similar to those used in the SOLFERINO IN THIRTY MINUTES game), would be in two different ‘colours’ or ‘sets’, and might even have the dice score printed on them to remind players what score they needed to get to activate a unit.

    Thanks for your feedback and questions. Answering them helps me to formulate my thoughts and recording them makes me set them out clearly.

    All the best,

    Bob

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  3. That is an interesting idea - your own cards with a printed number as a reminder of the activation roll. In general, I am not a big fan of special set of cards, unless I find them in the game (a' la Piquet.) One (very minor) turn off in IABSM was the necessity to print out my own tailored deck. To that respect, I admire the simplicity of The Sword And the Flame (not too popular in the UK, if I understand correctly), which only requires a standard set of playing cards.

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  4. DestoFante,

    It is just an idea at the moment, but as I have done something similar before it would not be too difficult to do.

    I have never understood why TSATF has not been popular in the UK. I suspect that it might be a reflection of the 'not invented here' attitude shown by some UK wargamers.

    All the best,

    Bob

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