Friday, 26 March 2010

Card-driven Turn Sequences: More test results

For my second test I used a pack of cards that contained 8 Black cards, 6 Red cards, and 1 Joker. The results were as follows:
  1. Red, Black, Black, Black, Black, Red, Black, Black, Red, Red, Joker: 10 cards (6 x Black, 4 x Red)
  2. Red, Red, Black, Black, Black, Red, Black, Red, Black, Black, Black, Black, Red, Joker: 13 cards (8 x Black, 5 x Red)
  3. Red, Red, Red, Red, Red, Joker: 5 cards (0 x Black, 5 x Red)
  4. Black, Black, Black, Red, Joker: 4 cards (2 x Black, 2 x Red)
  5. Red, Joker: 1 card (0 x Black, 1 x Red)
  6. Black, Red, Red, Black, Red, Black, Red, Black, Black, Joker: 9 cards (5 x Black, 4 x Red)
  7. Black, Red, Red, Red, Black, Red, Red, Black, Black, Black, Red, Joker: 11 cards (5 x Black, 6 x Red)
  8. Black, Black, Red, Red, Black, Red, Red, Black, Black, Black, Red, Red, Joker: 12 cards (6 x Black, 6 x Red)
This proved to be a difficult pack to shuffle because it was too small. In addition, the results were still far too variable for my requirements.

I therefore doubled the size of the pack of cards so that it contained 16 Black cards, 12 Red cards, and 2 Jokers. The results were as follows:
  1. Red, Red, Joker: 2 cards (0 x Black, 2 x Red)
  2. Red, Black, Black, Red, Red, Red, Red, Black, Red, Black, Black, Black, Red, Red, Red, Joker: 15 cards (6 x Black, 9 x Red)
  3. Red, Black, Black, Black, Black, Black, Red, Red, Black, Black, Red, Red, Red, Black, Red, Black, Black, Black, Black, Red, Black, Black, Black, Red, Red, Red, Joker: 26 cards (15 x Black, 11 x Red)
  4. Red, Black, Black, Black, Red, Black, Black, Red, Black, Red, Black, Black, Black, Red, Red, Red, Black, Black, Red, Joker: 19 cards (11 x Black, 8 x Red)
  5. Black, Black, Red, Black, Black, Black, Joker: 6 cards (5 x Black, 1 x Red)
  6. Red, Black, Black, Red, Black, Black, Red, Red, Black, Black, Red, Red, Red, Black, Black, Red, Black, Red, Joker: 18 cards (9 x Black, 9 x Red)
  7. Red, Black, Red, Joker: 3 cards (1 x Black, 2 x Red)
  8. Black, Red, Red, Joker: 4 cards (2 x Black, 2 x Red)
Because this pack was much bigger the automatic shuffling machine had no problem shuffling the cards, which would indicate that a larger pack is going to be easier to manipulate than a smaller pack. Although the results were closer to what I want to achieve, they were still too variable in places. I therefore decided to make a minor change to the pack (i.e. remove one Joker) to see if that made any significant difference. The results were as follows:
  1. Red, Black, Black, Red, Black, Black, Red, Black, Red, Black, Joker: 10 cards (6 x Black, 4 x Red)
  2. Black, Red, Black, Black, Black, Red, Black, Black, Red, Joker: 9 cards (6 x Black, 3 x Red)
  3. Black, Joker: 1 card (1 x Black, 0 x Red)
  4. Black, Black, Red, Black, Red, Red, Red, Red, Joker: 8 cards (3 x Black, 5 x Red)
  5. Black, Black, Black, Black, Black, Red, Red, Black, Black, Black, Red, Black, Red, Black, Black, Black, Black, Red, Black, Red, Red, Black, Red, Red, Red, Black, Red, Joker: 27 cards (16 x Black, 11 x Red)
  6. Black, Black, Red, Black, Black, Black, Red, Red, Black, Black, Red, Joker: 11 cards (7 x Black, 4 x Red)
  7. Black, Black, Red, Red, Red, Black, Black, Black, Black, Black, Black, Red, Black, Red, Red, Black, Black, Black, Red, Joker: 19 cards (12 x Black, 7 x Red)
  8. Black, Red, Black, Black, Red, Joker: 5 cards (3 x Black, 2 x Red)
This looked quite promising, so I continued with another eight turns:
  1. Red, Black, Black, Black, Joker: 4 cards (3 x Black, 1 x Red)
  2. Red, Red, Black, Red, Red, Red, Black, Black, Red, Black, Red, Red, Black, Red, Black, Black, Black, Red, Joker: 18 cards (8 x Black, 10 x Red)
  3. Black, Black, Red, Black, Black, Black, Red, Black, Black, Red, Red, Red, Joker: 12 cards (7 x Black, 5 x Red)
  4. Black, Black, Black, Black, Black, Red, Red, Black, Red, Red, Black, Black, Black, Joker: 13 cards (9 x Black, 4 x Red)
  5. Red, Black, Red, Black, Black, Black, Black, Red, Black, Black, Red, Red, Black, Joker: 13 cards (8 x Black, 5 x Red)
  6. Black, Joker: 5 cards (5 x Black, 0 x Red)
  7. Black, Black, Black, Red, Black, Black, Red, Black, Red, Black, Black, Black, Joker: 12 cards (9 x Black, 3 x Red)
  8. Black, Black, Red, Black, Red, Black, Black, Red, Black, Black, Black, Black, Red, Red, Joker: 14 cards (9 x Black, 5 x Red)
The average length of a turn was 11.06 cards. This compared with 15 cards for the test I conducted yesterday and 8.125 cards and 11.625 cards for the first two of today's tests. In addition the ratio of Black to Red cards turned over was 1:0.67, which is much closer to what is should be (1:0.75) than the ratio in yesterday's test (1:0.85) and the first tests held today (1:1.03 and 1:0.9 respectively).

This still needs more testing and possibly some further modification, but I feel that I have almost got a solution that matches my criteria.

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