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    HAND LENGTH TEST - expert Pro Test shooter Smart Craps, version 1.42, by DeepNet Technologies.
    Copyright 2004. All rights reserved.
      E-mail: info@deepnettech.com
      Web: info@deepnettech.com
    This is a generated craps simulation report file.
    It describes the results of a simulation of a specified game of craps.

This program is properly registered. Thank you for purchasing Smart Craps.



SIMULATION SETUP


Craps game setup:
    Minimum table bet: $30.00
    No maximum table limit (no ceiling on bet size)
    Up to 1 times odds permitted
    Odds wagers allowed with payout over the table maximum
    Automatic odds wagers (does not apply to lay odds bets):
      - rounded up such that the payout is to the even $1.00
      (i.e. if set to $5, with single odds, the maximum odds owager on $15 original bet
      with a point roll of 6 is: $25. With 6:5 odds, a $15 bet pays $18, and $30 is
      nearest payout to $5, which is a $25 bet).
    The buy and lay bet vig/commission is: 5%
    You pay a commission/vig on lost buy/lay bets
    The vig/commission leeway on bets is $1.00
      (i.e. if set to $10 with a 5% vig, then you pay a $1 commission on bets
      up to and including $30. A $20 bet would have a $1.00 vig exactly,
      so a $10 leeway allows a $30 bet. At $31, the vig would be $2).
    The vig is computed to the nearest dollar
      (i.e. if set to the nearest 50 cents, a $30 buy bet would
      have a $1.50 commission with a 5% vig, instead of $1 or $2)
    Place bet odds for 6 and 8 are: 7 to 6
    Place bet odds for 5 and 9 are: 7 to 5
    Place bet odds for 4 and 10 are: 9 to 5
    Field bet odds for a 2 point are: 2 to 1
    Field bet odds for a 12 point are: 2 to 1
    Big 6 and 8 bets odds are: 1 to 1
    Any 7 bet odds are: 4 to 1
    Any craps bet odds are: 7 to 1
    Craps 2 bet odds are: 30 to 1
    Craps 3 bet odds are: 15 to 1
    Craps 12 bet odds are: 30 to 1
    Yo 11 bet odds are: 15 to 1
    hardway 4 and 10 odds are: 7 to 1
    hardway 6 and 8 odds are: 9 to 1

Betting modules in use:
    1) Flat Betting Module

Betting systems in use:
    1) Shooter 1 - pass
      - Betting module: Flat Betting Module
      - Bet type: pass
      - betting exactly: 30
      - following bets with maximum odds allowed (only for pass/don't pass bets)
      - point for bets (only used for certain bets types): 6
      - bet only on the come out roll
      - for applicable bet types, the bets are 'off' on the come out roll
      - come out dice set for Pro Test rolls: left die: T2F4, right die: T5F3 (all sevens)
      - 4/10 dice set for Pro Test rolls: left die: T1F5, right die: T3F5 (2V-A)
      - 5/9 dice set for Pro Test rolls: left die: T1F3, right die: T4F2 (5/9)
      - 6/8 dice set for Pro Test rolls: left die: T1F3, right die: T5F3 (3V)
      - SRR usage for come out rolls: shooter's minimum SRR
      - SRR usage for point rolls: shooter's maximum SRR

Shooters in use:
    1) Shooter 1 - Pro Test, expert:
      - Bet system: Shooter 1 - pass
      - Throw style: Pro Test
      - Total # of rolls in Pro Test: 200
      - Pro 1 passes: 106
        - Pro 1 probability: 0.922904% (low is good)
        - Minimum # of passes in 200 rolls for a 1.00% Pro 1 Test probability: 106
        - Expected # of Pro 1 passes for a random shooter (4/9th): 88.89
      - Pro 2 passes: 38
        - Pro 2 probability: 0.841179% (low is good)
        - Minimum # of passes in 200 rolls for a 1.00% Pro 2 Test probability: 38
        - Expected # of Pro 2 passes for a random shooter (1/4 of Pro 1 passes): 22.22
      Not using Pro 3 score in rolls
      - weakening the Pro score values to achieve a 95% confidence interval
        (i.e. a range of scores surrounding the actual Pro score values that has a 95%
        chance of containing the actual shooter's Pro score)
        - Pro 1 score decreased to 94.00 observe the 95% confidence interval
        - Pro 2 score descreased to 29.00 to maintain the same original proportion of
        of Pro 2 to Pro 1 passes, using the altered lower Pro 1 score, above

Table spots:
    Spot # 1 walkups:
      Walkup # 1:
        - shooter: Shooter 1 - Pro Test, expert
        - frequency: 1
          (proportionate to other walkup frequencies for this shooter)
        - duration: 50
          (# of throws walkup will stay around)
        - betting as this walkup/shooter does


SIMULATION RESULTS


Win/loss rates:
    *** Expectation: 8.471901%
      (total of all wins and losses, divided by the total of all bets made)
    Average earnings/loss per throw: $1.294073
    Average earnings/loss per betting event: $2.541570
    Average earnings/loss per hand: $11.707962
    Average earnings/loss per hour: $129.407277
    Average # of bets/hour: 50.9
      (assumes 100 throws per hour)

Simulation statistics:
    Intended # of rounds in simulation: 10,000,000
    Actual # of rounds completed: 10,000,000
    Each round is a: bet (a single betting event)
    Random seed: 12345
    Start time for simulation: Mon Apr 04 17:25:39 2005
    End time for simulation: Mon Apr 04 17:26:11 2005
    Elapsed simulation time: 00:00:32
    Total # of hands: 2,170,805
    Average # of throws/hand: 9.05
    Longest hand (in throws): 108
    50% of hands are of throw length 7.30 or more (median value)
    5% of hands are of throw length 24.92 or more
    1% of hands are of throw length 37.23 or more
    Inferred probability of hand ending per round (seven out): 12.2542%
    Distribution table of hands by length (2,170,805 hands in total):

      Hand length
      Frequency
      Prob. for hand
      Prob. hand >=
      Expected prob.
      1 0 0.00% 100.00% 100.00%
      2 223,179 10.28% 100.00% 100.00%
      3 238,561 10.99% 89.72% 87.75%
      4 216,247 9.96% 78.73% 76.99%
      5 190,640 8.78% 68.77% 67.56%
      6 165,845 7.64% 59.99% 59.28%
      7 145,546 6.70% 52.35% 52.02%
      8 127,378 5.87% 45.64% 45.64%
      9 110,824 5.11% 39.77% 40.05%
      10 96,597 4.45% 34.67% 35.14%
      11 84,637 3.90% 30.22% 30.83%
      12 72,925 3.36% 26.32% 27.06%
      13 64,230 2.96% 22.96% 23.74%
      14 56,010 2.58% 20.00% 20.83%
      15 48,559 2.24% 17.42% 18.28%
      16 42,286 1.95% 15.18% 16.04%
      17 36,613 1.69% 13.24% 14.07%
      18 32,387 1.49% 11.55% 12.35%
      19 28,002 1.29% 10.06% 10.84%
      20 24,428 1.13% 8.77% 9.51%
      21 21,439 0.99% 7.64% 8.34%
      22 18,607 0.86% 6.66% 7.32%
      23 16,177 0.75% 5.80% 6.42%
      24 13,970 0.64% 5.05% 5.64%
      25 12,175 0.56% 4.41% 4.95%
      26 10,728 0.49% 3.85% 4.34%
      27 9,547 0.44% 3.35% 3.81%
      28 8,115 0.37% 2.91% 3.34%
      29 7,187 0.33% 2.54% 2.93%
      30 6,243 0.29% 2.21% 2.57%
      31 5,448 0.25% 1.92% 2.26%
      32 4,584 0.21% 1.67% 1.98%
      33 4,179 0.19% 1.46% 1.74%
      34 3,594 0.17% 1.27% 1.52%
      35 3,080 0.14% 1.10% 1.34%
      36 2,709 0.12% 0.96% 1.17%
      37 2,330 0.11% 0.84% 1.03%
      38 2,009 0.09% 0.73% 0.90%
      39 1,766 0.08% 0.64% 0.79%
      40 1,493 0.07% 0.55% 0.70%
      41 1,340 0.06% 0.49% 0.61%
      42 1,171 0.05% 0.42% 0.54%
      43 1,030 0.05% 0.37% 0.47%
      44 871 0.04% 0.32% 0.41%
      45 824 0.04% 0.28% 0.36%
      46 689 0.03% 0.24% 0.32%
      47 564 0.03% 0.21% 0.28%
      48 492 0.02% 0.19% 0.24%
      49 444 0.02% 0.16% 0.21%
      50 406 0.02% 0.14% 0.19%
      51 339 0.02% 0.12% 0.17%
      52 307 0.01% 0.11% 0.14%
      53 268 0.01% 0.09% 0.13%
      54 211 0.01% 0.08% 0.11%
      55 200 0.01% 0.07% 0.10%
      56 181 0.01% 0.06% 0.09%
      57 153 0.01% 0.06% 0.08%
      58 118 0.01% 0.05% 0.07%
      59 132 0.01% 0.04% 0.06%
      60 101 0.00% 0.04% 0.05%
      61 90 0.00% 0.03% 0.04%
      62 65 0.00% 0.03% 0.04%
      63 68 0.00% 0.02% 0.03%
      64 48 0.00% 0.02% 0.03%
      65 44 0.00% 0.02% 0.03%
      66 45 0.00% 0.02% 0.02%
      67 39 0.00% 0.02% 0.02%
      68 38 0.00% 0.01% 0.02%
      69 29 0.00% 0.01% 0.02%
      70 27 0.00% 0.01% 0.01%
      71 23 0.00% 0.01% 0.01%
      72 23 0.00% 0.01% 0.01%
      73 18 0.00% 0.01% 0.01%
      74 14 0.00% 0.01% 0.01%
      75 10 0.00% 0.01% 0.01%
      76 14 0.00% 0.01% 0.01%
      77 12 0.00% 0.00% 0.01%
      78 18 0.00% 0.00% 0.00%
      79 4 0.00% 0.00% 0.00%
      80 8 0.00% 0.00% 0.00%
      81 8 0.00% 0.00% 0.00%
      82 7 0.00% 0.00% 0.00%
      83 3 0.00% 0.00% 0.00%
      84 4 0.00% 0.00% 0.00%
      85 3 0.00% 0.00% 0.00%
      86 2 0.00% 0.00% 0.00%
      87 4 0.00% 0.00% 0.00%
      88 2 0.00% 0.00% 0.00%
      89 1 0.00% 0.00% 0.00%
      90 0 0.00% 0.00% 0.00%
      91 3 0.00% 0.00% 0.00%
      92 3 0.00% 0.00% 0.00%
      93 2 0.00% 0.00% 0.00%
      94 3 0.00% 0.00% 0.00%
      95 0 0.00% 0.00% 0.00%
      96 2 0.00% 0.00% 0.00%
      97 1 0.00% 0.00% 0.00%
      98 0 0.00% 0.00% 0.00%
      99 0 0.00% 0.00% 0.00%
      100 1 0.00% 0.00% 0.00%
      101 1 0.00% 0.00% 0.00%
      102 0 0.00% 0.00% 0.00%
      103 0 0.00% 0.00% 0.00%
      104 0 0.00% 0.00% 0.00%
      105 0 0.00% 0.00% 0.00%
      106 1 0.00% 0.00% 0.00%
      107 1 0.00% 0.00% 0.00%
      108 1 0.00% 0.00% 0.00%


Betting statistics (wagers only, no wins or losses):
    # of betting events: 10,000,000
    Average bet size: $30.0000
    Standard deviation: $0.000000
    Variance: $0.000000
    Smallest bet size: $30.00
    Largest bet size: $30.00
    Sum of all bets: $300,000,000

Bankroll statistics (wins and losses only on bets made):
    Average earnings/loss per betting event: $2.541570
    Standard deviation: $33.018351
      (in earnings/loss dollars per betting event)
    Variance: $1090.211532
    Largest wager lost: -$30.00
    Biggest win: $60.00
    Total earnings/loss: $25,415,703.00

Dice roll statistics (by sum, all shooters):
    Number of dice rolls/throws: 19,640,088

    Roll
    # Rolled
    # Expected
    Difference
    Chi Square
    2 519911 545558.0 -25647.0 1205.6804
    3 1048078 1091116.0 -43038.0 1697.5917
    4 1646739 1636674.0 10065.0 61.8964
    5 2187291 2182232.0 5059.0 11.7281
    6 2729124 2727790.0 1334.0 0.6524
    7 3377323 3273348.0 103975.0 3302.6738
    8 2728596 2727790.0 806.0 0.2382
    9 2189231 2182232.0 6999.0 22.4477
    10 1644292 1636674.0 7618.0 35.4585
    11 1049066 1091116.0 -42050.0 1620.5449
    12 520437 545558.0 -25121.0 1156.7324

    Sum of above chi squares: 9115.6444

Dice outcome statistics (all shooters):
    Number of dice rolls/throws: 19,640,088
    # expected per outcome: 545,558

    Outcome
    # Rolled
    Difference
    Chi Square
    1|1 519911 -25647.0 1205.6804
    1|2 527639 -17919.0 588.5544
    1|3 563788 18230.0 609.1614
    1|4 569834 24276.0 1080.2228
    1|5 575898 30340.0 1687.2919
    1|6 519774 -25784.0 1218.5957
    2|1 520439 -25119.0 1156.5483
    2|2 561882 16324.0 488.4411
    2|3 526075 -19483.0 695.7781
    2|4 526406 -19152.0 672.3375
    2|5 582399 36841.0 2487.8368
    2|6 520222 -25336.0 1176.6171
    3|1 521069 -24489.0 1099.2619
    3|2 571316 25758.0 1216.1394
    3|3 577216 31658.0 1837.0713
    3|4 585759 40201.0 2962.3255
    3|5 529346 -16212.0 481.7617
    3|6 521321 -24237.0 1076.7548
    4|1 520066 -25492.0 1191.1512
    4|2 528837 -16721.0 512.4878
    4|3 586403 40845.0 3057.9957
    4|4 576761 31203.0 1784.6447
    4|5 573024 27466.0 1382.7699
    4|6 519072 -26486.0 1285.8545
    5|1 520767 -24791.0 1126.5414
    5|2 581977 36419.0 2431.1688
    5|3 525411 -20147.0 744.0118
    5|4 526171 -19387.0 688.9382
    5|5 561307 15749.0 454.6373
    5|6 520667 -24891.0 1135.6481
    6|1 521011 -24547.0 1104.4751
    6|2 576856 31298.0 1795.5283
    6|3 568715 23157.0 982.9324
    6|4 563913 18355.0 617.5439
    6|5 528399 -17159.0 539.6883
    6|6 520437 -25121.0 1156.7324

    Sum of above chi squares: 43733.1301

For shooter: 'Shooter 1 - Pro Test, expert'
    Expectation: 8.471901%
    # of betting events: 10,000,000
    Average earnings/loss per betting event: $2.541570
    Standard deviation: $33.018351
      (in earnings/loss dollars per betting event)
    Variance: $1090.211532
    Largest wager lost: -$30.00
    Biggest win: $60.00
    Total earnings/loss: $25,415,703.00
    Total # of hands: 2,170,805
    Average # of throws/hand: 9.05
    Longest hand (in throws): 108
    50% of hands are of length 7.30 or more (median value)
    5% of hands are of throw length 24.92 or more
    1% of hands are of throw length 37.23 or more
    Inferred probability of hand ending per round (seven out): 12.2542%
    Distribution table of hands by length (2,170,805 hands in total):

      Hand length
      Frequency
      Prob. for hand
      Prob. hand >=
      Expected prob.
      1 0 0.00% 100.00% 100.00%
      2 223,179 10.28% 100.00% 100.00%
      3 238,561 10.99% 89.72% 87.75%
      4 216,247 9.96% 78.73% 76.99%
      5 190,640 8.78% 68.77% 67.56%
      6 165,845 7.64% 59.99% 59.28%
      7 145,546 6.70% 52.35% 52.02%
      8 127,378 5.87% 45.64% 45.64%
      9 110,824 5.11% 39.77% 40.05%
      10 96,597 4.45% 34.67% 35.14%
      11 84,637 3.90% 30.22% 30.83%
      12 72,925 3.36% 26.32% 27.06%
      13 64,230 2.96% 22.96% 23.74%
      14 56,010 2.58% 20.00% 20.83%
      15 48,559 2.24% 17.42% 18.28%
      16 42,286 1.95% 15.18% 16.04%
      17 36,613 1.69% 13.24% 14.07%
      18 32,387 1.49% 11.55% 12.35%
      19 28,002 1.29% 10.06% 10.84%
      20 24,428 1.13% 8.77% 9.51%
      21 21,439 0.99% 7.64% 8.34%
      22 18,607 0.86% 6.66% 7.32%
      23 16,177 0.75% 5.80% 6.42%
      24 13,970 0.64% 5.05% 5.64%
      25 12,175 0.56% 4.41% 4.95%
      26 10,728 0.49% 3.85% 4.34%
      27 9,547 0.44% 3.35% 3.81%
      28 8,115 0.37% 2.91% 3.34%
      29 7,187 0.33% 2.54% 2.93%
      30 6,243 0.29% 2.21% 2.57%
      31 5,448 0.25% 1.92% 2.26%
      32 4,584 0.21% 1.67% 1.98%
      33 4,179 0.19% 1.46% 1.74%
      34 3,594 0.17% 1.27% 1.52%
      35 3,080 0.14% 1.10% 1.34%
      36 2,709 0.12% 0.96% 1.17%
      37 2,330 0.11% 0.84% 1.03%
      38 2,009 0.09% 0.73% 0.90%
      39 1,766 0.08% 0.64% 0.79%
      40 1,493 0.07% 0.55% 0.70%
      41 1,340 0.06% 0.49% 0.61%
      42 1,171 0.05% 0.42% 0.54%
      43 1,030 0.05% 0.37% 0.47%
      44 871 0.04% 0.32% 0.41%
      45 824 0.04% 0.28% 0.36%
      46 689 0.03% 0.24% 0.32%
      47 564 0.03% 0.21% 0.28%
      48 492 0.02% 0.19% 0.24%
      49 444 0.02% 0.16% 0.21%
      50 406 0.02% 0.14% 0.19%
      51 339 0.02% 0.12% 0.17%
      52 307 0.01% 0.11% 0.14%
      53 268 0.01% 0.09% 0.13%
      54 211 0.01% 0.08% 0.11%
      55 200 0.01% 0.07% 0.10%
      56 181 0.01% 0.06% 0.09%
      57 153 0.01% 0.06% 0.08%
      58 118 0.01% 0.05% 0.07%
      59 132 0.01% 0.04% 0.06%
      60 101 0.00% 0.04% 0.05%
      61 90 0.00% 0.03% 0.04%
      62 65 0.00% 0.03% 0.04%
      63 68 0.00% 0.02% 0.03%
      64 48 0.00% 0.02% 0.03%
      65 44 0.00% 0.02% 0.03%
      66 45 0.00% 0.02% 0.02%
      67 39 0.00% 0.02% 0.02%
      68 38 0.00% 0.01% 0.02%
      69 29 0.00% 0.01% 0.02%
      70 27 0.00% 0.01% 0.01%
      71 23 0.00% 0.01% 0.01%
      72 23 0.00% 0.01% 0.01%
      73 18 0.00% 0.01% 0.01%
      74 14 0.00% 0.01% 0.01%
      75 10 0.00% 0.01% 0.01%
      76 14 0.00% 0.01% 0.01%
      77 12 0.00% 0.00% 0.01%
      78 18 0.00% 0.00% 0.00%
      79 4 0.00% 0.00% 0.00%
      80 8 0.00% 0.00% 0.00%
      81 8 0.00% 0.00% 0.00%
      82 7 0.00% 0.00% 0.00%
      83 3 0.00% 0.00% 0.00%
      84 4 0.00% 0.00% 0.00%
      85 3 0.00% 0.00% 0.00%
      86 2 0.00% 0.00% 0.00%
      87 4 0.00% 0.00% 0.00%
      88 2 0.00% 0.00% 0.00%
      89 1 0.00% 0.00% 0.00%
      90 0 0.00% 0.00% 0.00%
      91 3 0.00% 0.00% 0.00%
      92 3 0.00% 0.00% 0.00%
      93 2 0.00% 0.00% 0.00%
      94 3 0.00% 0.00% 0.00%
      95 0 0.00% 0.00% 0.00%
      96 2 0.00% 0.00% 0.00%
      97 1 0.00% 0.00% 0.00%
      98 0 0.00% 0.00% 0.00%
      99 0 0.00% 0.00% 0.00%
      100 1 0.00% 0.00% 0.00%
      101 1 0.00% 0.00% 0.00%
      102 0 0.00% 0.00% 0.00%
      103 0 0.00% 0.00% 0.00%
      104 0 0.00% 0.00% 0.00%
      105 0 0.00% 0.00% 0.00%
      106 1 0.00% 0.00% 0.00%
      107 1 0.00% 0.00% 0.00%
      108 1 0.00% 0.00% 0.00%


    Dice roll statistics (by sum, for 'Shooter 1 - Pro Test, expert' - all rolls):
      Number of dice rolls/throws: 19,640,088

      Roll
      # Rolled
      # Expected
      Difference
      Chi Square
      2 519911 545558.0 -25647.0 1205.6804
      3 1048078 1091116.0 -43038.0 1697.5917
      4 1646739 1636674.0 10065.0 61.8964
      5 2187291 2182232.0 5059.0 11.7281
      6 2729124 2727790.0 1334.0 0.6524
      7 3377323 3273348.0 103975.0 3302.6738
      8 2728596 2727790.0 806.0 0.2382
      9 2189231 2182232.0 6999.0 22.4477
      10 1644292 1636674.0 7618.0 35.4585
      11 1049066 1091116.0 -42050.0 1620.5449
      12 520437 545558.0 -25121.0 1156.7324

      Sum of above chi squares: 9115.6444

    Dice outcome statistics (for 'Shooter 1 - Pro Test, expert' - all rolls):
      Number of dice rolls/throws: 19,640,088
      # expected per outcome: 545,558

      Outcome
      # Rolled
      Difference
      Chi Square
      1|1 519911 -25647.0 1205.6804
      1|2 527639 -17919.0 588.5544
      1|3 563788 18230.0 609.1614
      1|4 569834 24276.0 1080.2228
      1|5 575898 30340.0 1687.2919
      1|6 519774 -25784.0 1218.5957
      2|1 520439 -25119.0 1156.5483
      2|2 561882 16324.0 488.4411
      2|3 526075 -19483.0 695.7781
      2|4 526406 -19152.0 672.3375
      2|5 582399 36841.0 2487.8368
      2|6 520222 -25336.0 1176.6171
      3|1 521069 -24489.0 1099.2619
      3|2 571316 25758.0 1216.1394
      3|3 577216 31658.0 1837.0713
      3|4 585759 40201.0 2962.3255
      3|5 529346 -16212.0 481.7617
      3|6 521321 -24237.0 1076.7548
      4|1 520066 -25492.0 1191.1512
      4|2 528837 -16721.0 512.4878
      4|3 586403 40845.0 3057.9957
      4|4 576761 31203.0 1784.6447
      4|5 573024 27466.0 1382.7699
      4|6 519072 -26486.0 1285.8545
      5|1 520767 -24791.0 1126.5414
      5|2 581977 36419.0 2431.1688
      5|3 525411 -20147.0 744.0118
      5|4 526171 -19387.0 688.9382
      5|5 561307 15749.0 454.6373
      5|6 520667 -24891.0 1135.6481
      6|1 521011 -24547.0 1104.4751
      6|2 576856 31298.0 1795.5283
      6|3 568715 23157.0 982.9324
      6|4 563913 18355.0 617.5439
      6|5 528399 -17159.0 539.6883
      6|6 520437 -25121.0 1156.7324

      Sum of above chi squares: 43733.1301

    Dice roll statistics (by sum, for 'Shooter 1 - Pro Test, expert' - come out rolls only):
      Number of dice rolls/throws: 6,086,790

      Roll
      # Rolled
      # Expected
      Difference
      Chi Square
      2 160589 169077.5 -8488.5 426.1633
      3 322402 338155.0 -15753.0 733.8558
      4 488204 507232.5 -19028.5 713.8419
      5 652157 676310.0 -24153.0 862.5740
      6 817356 845387.5 -28031.5 929.4732
      7 1206518 1014465.0 192053.0 36358.4301
      8 815972 845387.5 -29415.5 1023.5207
      9 653194 676310.0 -23116.0 790.0955
      10 486327 507232.5 -20905.5 861.6166
      11 322929 338155.0 -15226.0 685.5764
      12 161142 169077.5 -7935.5 372.4455

      Sum of above chi squares: 43757.5930

    Dice outcome statistics (for 'Shooter 1 - Pro Test, expert' - come out rolls only):
      Number of dice rolls/throws: 6,086,790
      # expected per outcome: 169,077

      Outcome
      # Rolled
      Difference
      Chi Square
      1|1 160589 -8488.0 426.1144
      1|2 161351 -7726.0 353.0408
      1|3 161789 -7288.0 314.1465
      1|4 160791 -8286.0 406.0741
      1|5 161131 -7946.0 373.4329
      1|6 161470 -7607.0 342.2491
      2|1 161051 -8026.0 380.9902
      2|2 164981 -4096.0 99.2283
      2|3 164888 -4189.0 103.7854
      2|4 164578 -4499.0 119.7147
      2|5 221046 51969.0 15973.6508
      2|6 160850 -8227.0 400.3119
      3|1 161434 -7643.0 345.4961
      3|2 164908 -4169.0 102.7967
      3|3 164980 -4097.0 99.2767
      3|4 221196 52119.0 16065.9946
      3|5 165069 -4008.0 95.0103
      3|6 161657 -7420.0 325.6292
      4|1 161570 -7507.0 333.3100
      4|2 165112 -3965.0 92.9826
      4|3 221855 52778.0 16474.8445
      4|4 164004 -5073.0 152.2107
      4|5 165375 -3702.0 81.0566
      4|6 160592 -8485.0 425.8132
      5|1 161555 -7522.0 334.6433
      5|2 219865 50788.0 15255.8949
      5|3 164044 -5033.0 149.8198
      5|4 164791 -4286.0 108.6475
      5|5 164511 -4566.0 123.3069
      5|6 161867 -7210.0 307.4581
      6|1 161086 -7991.0 377.6746
      6|2 162005 -7072.0 295.8012
      6|3 161371 -7706.0 351.2153
      6|4 161224 -7853.0 364.7427
      6|5 161062 -8015.0 379.9466
      6|6 161142 -7935.0 372.3997

      Sum of above chi squares: 72308.7109

    Dice roll statistics (by sum, for 'Shooter 1 - Pro Test, expert' - point rolls only):
      Number of dice rolls/throws: 13,553,298

      Roll
      # Rolled
      # Expected
      Difference
      Chi Square
      2 359322 376480.5 -17158.5 782.0169
      3 725676 752961.0 -27285.0 988.7248
      4 1158535 1129441.5 29093.5 749.4250
      5 1535134 1505922.0 29212.0 566.6568
      6 1911768 1882402.5 29365.5 458.1021
      7 2170805 2258883.0 -88078.0 3434.3231
      8 1912624 1882402.5 30221.5 485.1986
      9 1536037 1505922.0 30115.0 602.2312
      10 1157965 1129441.5 28523.5 720.3472
      11 726137 752961.0 -26824.0 955.5966
      12 359295 376480.5 -17185.5 784.4800

      Sum of above chi squares: 10527.1024

    Dice outcome statistics (for 'Shooter 1 - Pro Test, expert' - point rolls only):
      Number of dice rolls/throws: 13,553,298
      # expected per outcome: 376,480

      Outcome
      # Rolled
      Difference
      Chi Square
      1|1 359322 -17158.0 781.9724
      1|2 366288 -10192.0 275.9160
      1|3 401999 25519.0 1729.7582
      1|4 409043 32563.0 2816.4815
      1|5 414767 38287.0 3893.6846
      1|6 358304 -18176.0 877.5153
      2|1 359388 -17092.0 775.9681
      2|2 396901 20421.0 1107.6744
      2|3 361187 -15293.0 621.2172
      2|4 361828 -14652.0 570.2324
      2|5 361353 -15127.0 607.8042
      2|6 359372 -17108.0 777.4215
      3|1 359635 -16845.0 753.7028
      3|2 406408 29928.0 2379.1043
      3|3 412236 35756.0 3395.9082
      3|4 364563 -11917.0 377.2176
      3|5 364277 -12203.0 395.5408
      3|6 359664 -16816.0 751.1099
      4|1 358496 -17984.0 859.0742
      4|2 363725 -12755.0 432.1346
      4|3 364548 -11932.0 378.1678
      4|4 412757 36277.0 3495.5927
      4|5 407649 31169.0 2580.4998
      4|6 358480 -18000.0 860.6035
      5|1 359212 -17268.0 792.0310
      5|2 362112 -14368.0 548.3410
      5|3 361367 -15113.0 606.6797
      5|4 361380 -15100.0 605.6364
      5|5 396796 20316.0 1096.3128
      5|6 358800 -17680.0 830.2762
      6|1 359925 -16555.0 727.9750
      6|2 414851 38371.0 3910.7885
      6|3 407344 30864.0 2530.2446
      6|4 402689 26209.0 1824.5635
      6|5 367337 -9143.0 222.0422
      6|6 359295 -17185.0 784.4354

      Sum of above chi squares: 45973.6284