10 million SET games simulated using “Random among ‘most similar’ Sets”

The tabulated  simulation results.

Total games played=10000000, total rounds=259722851,
took 7204 seconds. Games that never needed 15 cards
on the table: 3124823 (31.2 percent of all games).
Games where no cards remain on the table at the end:
118583 (1.2 percent of all games).
Selection mode="Random among 'most similar' Sets" (3),
seed=112881665

In deck |   Set  | NoSet | Set:NoSet for 12 | Avg # of Sets
--------+--------+-------+------------------+-------------
     69 |9677946 |322054 |      30.1:1      | 2.78
     66 |9470146 |526289 |      18.0:1      | 2.53
     63 |9373021 |621021 |      15.1:1      | 2.43
     60 |9335349 |657731 |      14.2:1      | 2.39
     57 |9321017 |671573 |      13.9:1      | 2.38
     54 |9317330 |675273 |      13.8:1      | 2.38
     51 |9314262 |678493 |      13.7:1      | 2.38
     48 |9311388 |681061 |      13.7:1      | 2.37
     45 |9309101 |683320 |      13.6:1      | 2.37
     42 |9306497 |685766 |      13.6:1      | 2.37
     39 |9304125 |688201 |      13.5:1      | 2.36
     36 |9300767 |691513 |      13.4:1      | 2.36
     33 |9297844 |694237 |      13.4:1      | 2.36
     30 |9294812 |697142 |      13.3:1      | 2.36
     27 |9293372 |698631 |      13.3:1      | 2.35
     24 |9290828 |701190 |      13.3:1      | 2.35
     21 |9289767 |702063 |      13.2:1      | 2.35
     18 |9288336 |703590 |      13.2:1      | 2.35
     15 |9287394 |704505 |      13.2:1      | 2.35
     12 |9287464 |704377 |      13.2:1      | 2.35
      9 |9287512 |704198 |      13.2:1      | 2.35
      6 |9286622 |705358 |      13.2:1      | 2.35
      3 |9287553 |704197 |      13.2:1      | 2.35
      0 |9250663 |741608 |      12.5:1      | 2.35

In deck |   Set  | NoSet | Set:NoSet for 15 | Avg # of Sets
--------+--------+-------+------------------+-------------
     69 |      0 |     0 |        oo:1      |   -
     66 | 318489 |  3565 |      89.3:1      | 3.33
     63 | 523896 |  5958 |      87.9:1      | 3.35
     60 | 620059 |  6920 |      89.6:1      | 3.35
     57 | 657241 |  7408 |      88.7:1      | 3.36
     54 | 671586 |  7395 |      90.8:1      | 3.36
     51 | 675425 |  7245 |      93.2:1      | 3.36
     48 | 678187 |  7551 |      89.8:1      | 3.36
     45 | 681033 |  7578 |      89.9:1      | 3.36
     42 | 683162 |  7736 |      88.3:1      | 3.35
     39 | 685829 |  7673 |      89.4:1      | 3.35
     36 | 688155 |  7720 |      89.1:1      | 3.35
     33 | 691314 |  7919 |      87.3:1      | 3.34
     30 | 694110 |  8046 |      86.3:1      | 3.34
     27 | 697191 |  7997 |      87.2:1      | 3.34
     24 | 698646 |  7982 |      87.5:1      | 3.33
     21 | 701002 |  8170 |      85.8:1      | 3.34
     18 | 702159 |  8073 |      87.0:1      | 3.33
     15 | 703563 |  8101 |      86.8:1      | 3.33
     12 | 704447 |  8159 |      86.3:1      | 3.33
      9 | 704246 |  8290 |      85.0:1      | 3.33
      6 | 704468 |  8020 |      87.8:1      | 3.33
      3 | 705128 |  8250 |      85.5:1      | 3.33
      0 | 704718 |  7726 |      91.2:1      | 3.33

In deck |   Set  | NoSet | Set:NoSet for 18 | Avg # of Sets
--------+--------+-------+------------------+-------------
     69 |      0 |     0 |        oo:1      |   -
     66 |      0 |     0 |        oo:1      |   -
     63 |   3565 |     0 |        oo:1      | 5.31
     60 |   5958 |     0 |        oo:1      | 5.36
     57 |   6918 |     2 |    3459.0:1      | 5.35
     54 |   7408 |     2 |    3704.0:1      | 5.37
     51 |   7397 |     0 |        oo:1      | 5.36
     48 |   7245 |     0 |        oo:1      | 5.39
     45 |   7550 |     1 |    7550.0:1      | 5.35
     42 |   7578 |     1 |    7578.0:1      | 5.35
     39 |   7736 |     1 |    7736.0:1      | 5.33
     36 |   7674 |     0 |        oo:1      | 5.34
     33 |   7720 |     0 |        oo:1      | 5.32
     30 |   7919 |     0 |        oo:1      | 5.33
     27 |   8046 |     0 |        oo:1      | 5.29
     24 |   7997 |     0 |        oo:1      | 5.32
     21 |   7982 |     0 |        oo:1      | 5.34
     18 |   8169 |     1 |    8169.0:1      | 5.31
     15 |   8074 |     0 |        oo:1      | 5.32
     12 |   8101 |     0 |        oo:1      | 5.32
      9 |   8159 |     0 |        oo:1      | 5.32
      6 |   8290 |     0 |        oo:1      | 5.32
      3 |   8020 |     0 |        oo:1      | 5.34
      0 |   8247 |     3 |    2749.0:1      | 5.32

In deck |   Set  | NoSet | Set:NoSet for 21 | Avg # of Sets
--------+--------+-------+------------------+-------------
     69 |      0 |     0 |        oo:1      |   -
     66 |      0 |     0 |        oo:1      |   -
     63 |      0 |     0 |        oo:1      |   -
     60 |      0 |     0 |        oo:1      |   -
     57 |      0 |     0 |        oo:1      |   -
     54 |      2 |     0 |        oo:1      | 7.50
     51 |      2 |     0 |        oo:1      | 7.50
     48 |      0 |     0 |        oo:1      |   -
     45 |      0 |     0 |        oo:1      |   -
     42 |      1 |     0 |        oo:1      | 10.00
     39 |      1 |     0 |        oo:1      | 8.00
     36 |      1 |     0 |        oo:1      | 9.00
     33 |      0 |     0 |        oo:1      |   -
     30 |      0 |     0 |        oo:1      |   -
     27 |      0 |     0 |        oo:1      |   -
     24 |      0 |     0 |        oo:1      |   -
     21 |      0 |     0 |        oo:1      |   -
     18 |      0 |     0 |        oo:1      |   -
     15 |      1 |     0 |        oo:1      | 7.00
     12 |      0 |     0 |        oo:1      |   -
      9 |      0 |     0 |        oo:1      |   -
      6 |      0 |     0 |        oo:1      |   -
      3 |      0 |     0 |        oo:1      |   -
      0 |      0 |     0 |        oo:1      |   -

3 responses to “10 million SET games simulated using “Random among ‘most similar’ Sets”

  1. Hi,
    can you calculate a probability of 0,6,9,12,15,18 cards left in the end of the game? I’ve found: 1% for 0 (clean up) in your estimates, 18: 1% (93:1 for no set in 15 cards with 0 cards in deck), 15: 7% (13.5:1 for no set in 12 cards with 0 cards in deck). But I’m curios about 9,12,15 as well.

    • For 1,000,000 games played:

      21 left on table: 0 (0,0 percent of all games)
      18 left on table: 0 (0,0 percent of all games)
      15 left on table: 798 (0,1 percent of all games)
      12 left on table: 73651 (7,4 percent of all games)
      9 left on table: 447233 (44,7 percent of all games)
      6 left on table: 466554 (46,7 percent of all games)
      3 left on table: 0 (0,0 percent of all games)
      0 left on table: 11764 (1,2 percent of all games)

      If there are only 3 cards left, those 3 cards
      also form a set, therefore that value is zero
      (but you already knew that :-)).

  2. Thanks, that pretty good correlates with real data for ~10k games on my site:
    18: 0%
    15: 0.0747%
    12: 7.3936%
    9: 43.4902%
    6: 48.2325%
    0: 1.1949%
    I thought that dataset is too small for any objective result, but seems as it’s ok.

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