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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