-------------------------------------------------------------------------- Blackjack Audit, version 2.7 ============================ This Blackjack simulation report was produced by Blackjack Audit from DeepNet Technologies. We have a complete line of Blackjack training and simulation software for Palm OS, Pocket PC, and Windows. web: www.deepnettech.com e-mail: info@deepnettech.com -------------------------------------------------------------------------- Simulation Report ================= System settings: Count system: High-Low Action table: Multi3: D8, DAS, s17, DblAny Index set: High-Low: Multi3 Casino settings: number of decks: 8 allow double after splits: yes (DAS) dealer hits soft 17: no (S17) penetration: 3/4 of shoe allow resplitting of aces: yes allow hitting of split aces: no Maximum number of player hands (max splits plus one): 3 restrict doubling to: any hand allow late surrender: no (noSUR) Dealer has a hole card (American rules) blackjack pays: 3 to 2 Simulation settings: unit bet size: 5 random seed: 1234 take insurance when Count System says to: yes use index values in Index set: yes using betting levels defined in count system true count calculation: conservative number of players at table: 1 position of counter: 1 betting spread: ============================ Final simulation statistics: ============================ Expectation[1]: 0.5148% ** Note: win/loss amounts account for the unit bet size of 5 ** Note: only hands at the counter's position are included in any statistics ** See the online help for details on any of these statistics Simulation started: Fri Nov 15 01:34:14 2002 Simulation ended: Fri Nov 15 03:06:04 2002 # rounds played: 1000000666 # shoes played: 17424973 # of player hands (at counter's position): 1028548551 # hands (dealer + all player): 2028549217 Average rounds/shoe: 57.39 Average hands/shoe (including dealer): 116.42 Average player hands/shoe (at counter's position): 59.03 Average # hands (including dealer)/round: 2.03 Average # of cards/hand: 2.700 Average ending system count: 0.0009 Total of all wagers: $11314312447.50 Average total wagers/round: $11.314 Average total earnings/round: $0.058244 Average wager/hand: $11.000 Winnings (or loss): $58243717.50 Standard deviation (per betting event[2], unit bet[4]): 3.34364 Standard deviation (per round[3], unit bet[4]): 3.42941 average win or loss (per betting event[2], unit bet[4]): 0.011283 average win or loss (per round[3], unit bet[4]): 0.011649 Maximum total loss of $2597.5 in round 18553 Best winnings for one shoe at round 347724219: $1620 Biggest loss for one shoe at round 272821940: $1635 Insurance contributions: Expectation contribution from insurance: 0.0312% # times insurance offered: 76929355 # times insurance accepted: 3855275 # times insurance won: 1332457 # times insurance lost: 2522818 Frequency of play combinations (in percent)[5]: total # of plays: 1354586104 Hand 2 3 4 5 6 7 8 9 T A ==================================================================== 8 0.16 0.16 0.16 0.16 0.16 0.16 0.15 0.15 0.56 0.10 9 0.24 0.25 0.25 0.25 0.25 0.24 0.23 0.23 0.85 0.16 10 0.26 0.27 0.27 0.27 0.27 0.26 0.25 0.25 0.92 0.17 11 0.35 0.35 0.34 0.35 0.34 0.35 0.34 0.34 1.24 0.23 12 0.60 0.60 0.58 0.57 0.57 0.61 0.58 0.59 2.22 0.43 13 0.66 0.65 0.62 0.59 0.59 0.67 0.64 0.66 2.46 0.47 14 0.59 0.57 0.51 0.50 0.51 0.62 0.63 0.64 2.41 0.46 15 0.61 0.59 0.53 0.50 0.51 0.68 0.68 0.70 2.62 0.50 16 0.54 0.52 0.46 0.45 0.44 0.65 0.66 0.68 2.54 0.49 soft 13 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.25 0.05 soft 14 0.08 0.08 0.08 0.08 0.07 0.08 0.07 0.07 0.27 0.05 soft 15 0.08 0.08 0.08 0.08 0.07 0.08 0.08 0.08 0.30 0.05 soft 15 0.09 0.09 0.09 0.08 0.08 0.09 0.09 0.09 0.33 0.06 soft 17 0.10 0.10 0.09 0.08 0.08 0.10 0.10 0.10 0.37 0.07 soft 18 0.12 0.11 0.10 0.09 0.09 0.12 0.11 0.11 0.41 0.07 soft 19 0.12 0.12 0.10 0.09 0.08 0.12 0.12 0.13 0.47 0.08 soft 20 0.12 0.11 0.09 0.08 0.08 0.12 0.12 0.13 0.47 0.08 AA 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.14 0.02 22 0.03 0.04 0.04 0.04 0.04 0.04 0.03 0.03 0.12 0.02 33 0.04 0.04 0.04 0.04 0.04 0.04 0.03 0.03 0.12 0.02 44 0.03 0.03 0.03 0.04 0.04 0.03 0.03 0.03 0.12 0.02 55 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.12 0.02 66 0.04 0.04 0.04 0.04 0.03 0.03 0.03 0.03 0.12 0.02 77 0.04 0.04 0.04 0.04 0.04 0.03 0.03 0.03 0.12 0.02 88 0.04 0.04 0.04 0.04 0.04 0.04 0.03 0.04 0.14 0.03 99 0.04 0.04 0.04 0.04 0.04 0.03 0.04 0.03 0.12 0.02 TT 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 1.95 0.37 <8 0.29 0.30 0.30 0.32 0.32 0.31 0.28 0.28 1.04 0.19 >16 1.61 1.48 1.28 1.19 1.23 2.53 2.53 2.63 9.65 2.01 ============================== Count system details: High-Low ============================== Count type: True count card: 2 3 4 5 6 7 8 9 10 A == == == == == == == == == == card values: 1 1 1 1 1 0 0 0 -1 -1 data for 1 deck(s): Initial Run Count (IRC): 0 Insure at count = 1.5 [>=count, bet]: [0, 2], [1, 3] data for 2 deck(s): Initial Run Count (IRC): 0 Insure at count = 2.5 [>=count, bet]: [-1, 1], [0, 2], [1, 4] data for 4 deck(s): Initial Run Count (IRC): 0 Insure at count = 3 [>=count, bet]: [1, 2], [2, 3], [3, 5] data for 6 deck(s): Initial Run Count (IRC): 0 Insure at count = 3 [>=count, bet]: [1, 2], [2, 4], [3, 8] data for 8 deck(s): Initial Run Count (IRC): 0 Insure at count = 3 [>=count, bet]: [1, 3], [2, 5], [3, 10] ================================================== Action table details: Multi3: D8, DAS, s17, DblAny ================================================== Hand 2 3 4 5 6 7 8 9 T A ======================== 8: H H H H H H H H H H 9: H D D D D H H H H H 10: D D D D D D D D H H 11: D D D D D D D D D H 12: H H S S S H H H H H 13: S S S S S H H H H H 14: S S S S S H H H H H 15: S S S S S H H H H H 16: S S S S S H H H H H A2: H H H D D H H H H H A3: H H H D D H H H H H A4: H H D D D H H H H H A5: H H D D D H H H H H A6: H D D D D H H H H H A7: S D D D D S S H H H A8: S S S S S S S S S S A9: S S S S S S S S S S AA: P P P P P P P P P P 22: P P P P P P H H H H 33: P P P P P P H H H H 44: H H H P P H H H H H 55: D D D D D D D D H H 66: P P P P P H H H H H 77: P P P P P P H H H H 88: P P P P P P P P P P 99: P P P P P S P P S S TT: S S S S S S S S S S =================================== Index set details: High-Low: Multi3 =================================== Hand 2 3 4 5 6 7 8 9 T A ======================================================================================================== 8: c>=9:D c>=5:D c>=3:D c>=1:D 9: c>=1:D c<0:H c<-2:H c<-4:H c<-6:H c>=3:D c>=7:D 10: c<-8:H c<-9:H c<-10:H c<-6:H c<-4:H c<-1:H c>=4:D c>=4:D 11: c<-9:H c<-6:H c<-4:H c<-4:H c>=1:D 12: c>=3:S c>=2:S c<0:H c<-1:H c<0:H 13: c<0:H c<-1:H c<-3:H c<-4:H c<-4:H 14: c<-3:H c<-4:H c<-6:H c<-7:H c<-7:H 15: c<-5:H c<-6:H c<-7:H c<-9:H c<-9:H c>=10:S c>=10:S c>=8:S c>=4:S c>=10:S 16: c<-8:H c<-10:H c>=9:S c>=7:S c>=5:S c>=0:S c>=8:S A2: c>=7:D c>=3:D c<0:H c<-1:H A3: c>=7:D c>=1:D c<-1:H c<-4:H A4: c>=7:D c<0:H c<-4:H c<-9:H A5: c>=4:D c<-2:H c<-6:H A6: c>=1:D c<-3:H c<-7:H c<-10:H A7: c>=0:D c<-2:S c<-6:S c<-8:S c<-10:S c>=1:S A8: c>=8:D c>=5:D c>=3:D c>=1:D c>=1:D A9: c>=10:D c>=8:D c>=6:D c>=5:D c>=4:D AA: c<-9:H c<-8:H c<-7:H c<-8:H c<-3:H 22: c<-3:H c<-5:H c<-7:H c<-9:H c>=5:P 33: c<0:H c<-4:H c<-7:H c<-9:H c>=4:P 44: c>=8:P c>=3:P c<-1:H c<-4:H 55: c<-8:H c<-9:H c<-10:H c<-6:H c<-4:H c<-1:H c>=4:D c>=4:D 66: c<-1:H c<-4:H c<-6:H c<-8:H c<-10:H 77: c<-9:H c>=5:P 88: c>=8:S 99: c<-2:S c<-3:S c<-5:S c<-6:S c<-6:S c>=3:P c<-8:S c<-9:S c>=3:P TT: c>=8:P c>=6:P c>=5:P c>=4:P Expectation per player hand (initial two cards for round only)[6]: Hand 2 3 4 5 6 7 8 9 T A ==================================================================================================================== 8: Action: H H H H H H H H H H Index: -- c>=9:D c>=5:D c>=3:D c>=1:D -- -- -- -- -- # rounds: 1811228 1809097 1837910 1808078 1809075 1837770 1835258 1834426 6770288 1268503 # hands: 1811228 1809097 1837910 1808078 1809075 1837770 1835258 1834426 6770288 1268503 % idx plays: -- 0.037% 1.398% 7.057% 31.751% -- -- -- -- -- Freq.: 0.181% 0.181% 0.184% 0.181% 0.181% 0.184% 0.184% 0.183% 0.677% 0.127% Avg. WL/R: -0.0144 0.0499 0.1168 0.2031 0.2757 0.1705 -0.1082 -0.4002 -0.4886 -0.3696 Exp.: -0.825% 2.854% 6.210% 8.962% 9.831% 9.394% -5.959% -22.031% -25.957% -19.910% 9: Action: H D D D D H H H H H Index: c>=1:D c<0:H c<-2:H c<-4:H c<-6:H c>=3:D c>=7:D -- -- -- # rounds: 2731659 2728496 2727119 2725440 2725190 2723098 2754031 2752393 10155838 1901475 # hands: 2731659 2728496 2727119 2725440 2725190 2723098 2754031 2752393 10155838 1901475 % idx plays: 30.966% 37.470% 8.051% 1.548% 0.252% 6.315% 0.210% -- -- -- Freq.: 0.273% 0.273% 0.273% 0.273% 0.273% 0.272% 0.275% 0.275% 1.016% 0.190% Avg. WL/R: 0.2089 0.3119 0.4352 0.5534 0.6675 0.3645 0.2046 -0.0934 -0.3002 -0.1137 Exp.: 7.347% 9.855% 12.593% 15.716% 18.905% 15.408% 10.991% -5.074% -15.716% -6.044% 10: Action: D D D D D D D D H H Index: c<-8:H c<-9:H c<-10:H -- -- c<-6:H c<-4:H c<-1:H c>=4:D c>=4:D # rounds: 2727637 2730493 2727317 2753667 2724911 2725723 2725106 2751367 10149816 1900644 # hands: 2727637 2730493 2727317 2753667 2724911 2725723 2725106 2751367 10149816 1900644 % idx plays: 0.038% 0.016% 0.006% -- -- 0.297% 1.757% 19.652% 2.491% 2.343% Freq.: 0.273% 0.273% 0.273% 0.275% 0.272% 0.273% 0.273% 0.275% 1.015% 0.190% Avg. WL/R: 0.7409 0.8371 0.9435 1.0449 1.1427 0.8360 0.6247 0.3455 0.0669 0.2014 Exp.: 20.676% 23.354% 26.331% 29.157% 31.909% 22.395% 16.790% 9.773% 3.063% 9.418% 11: Action: D D D D D D D D D H Index: -- -- -- -- -- c<-9:H c<-6:H c<-4:H c<-4:H c>=1:D # rounds: 3645852 3645388 3646439 3643781 3640845 3641137 3639450 3643664 13528374 2535615 # hands: 3645852 3645388 3646439 3643781 3640845 3641137 3639450 3643664 13528374 2535615 % idx plays: -- -- -- -- -- 0.018% 0.304% 1.790% 1.978% 24.498% Freq.: 0.365% 0.365% 0.365% 0.364% 0.364% 0.364% 0.364% 0.364% 1.353% 0.254% Avg. WL/R: 0.9376 1.0271 1.1256 1.2243 1.2962 0.9435 0.7212 0.4878 0.3947 0.3711 Exp.: 26.091% 28.581% 31.321% 34.064% 36.069% 25.202% 19.275% 13.097% 10.206% 12.074% 12: Action: H H S S S H H H H H Index: c>=3:S c>=2:S c<0:H c<-1:H c<0:H -- -- -- -- -- # rounds: 6312590 6401620 6400888 6393289 6429675 6393774 6395303 6391918 23578730 4440489 # hands: 6312590 6401620 6400888 6393289 6429675 6393774 6395303 6391918 23578730 4440489 % idx plays: 6.169% 13.219% 41.862% 19.442% 41.817% -- -- -- -- -- Freq.: 0.631% 0.640% 0.640% 0.639% 0.643% 0.639% 0.640% 0.639% 2.358% 0.444% Avg. WL/R: -0.4674 -0.4077 -0.3353 -0.2522 -0.2442 -0.4397 -0.5577 -0.6931 -0.7930 -0.7164 Exp.: -25.175% -21.945% -18.057% -13.579% -13.160% -22.691% -28.796% -35.745% -39.462% -36.160% 13: Action: S S S S S H H H H H Index: c<0:H c<-1:H c<-3:H c<-4:H c<-4:H -- -- -- -- -- # rounds: 6426013 6314387 6397771 6394556 6391071 6387870 6391069 6388364 23560870 4438089 # hands: 6426013 6314387 6397771 6394556 6391071 6387870 6391069 6388364 23560870 4438089 % idx plays: 41.792% 19.410% 4.016% 1.731% 1.735% -- -- -- -- -- Freq.: 0.643% 0.631% 0.640% 0.639% 0.639% 0.639% 0.639% 0.639% 2.356% 0.444% Avg. WL/R: -0.5091 -0.4293 -0.3440 -0.2561 -0.2481 -0.5542 -0.6625 -0.7795 -0.8821 -0.8133 Exp.: -27.397% -23.112% -18.522% -13.787% -13.364% -28.590% -34.179% -40.228% -43.897% -41.058% 14: Action: S S S S S H H H H H Index: c<-3:H c<-4:H c<-6:H c<-7:H c<-7:H -- -- -- -- -- # rounds: 5505650 5506298 5388295 5476172 5475912 5503115 5474892 5468134 20178116 3803830 # hands: 5505650 5506298 5388295 5476172 5475912 5503115 5474892 5468134 20178116 3803830 % idx plays: 4.060% 1.756% 0.292% 0.110% 0.112% -- -- -- -- -- Freq.: 0.551% 0.551% 0.539% 0.548% 0.548% 0.550% 0.547% 0.547% 2.018% 0.380% Avg. WL/R: -0.5143 -0.4299 -0.3477 -0.2557 -0.2476 -0.6617 -0.7556 -0.8706 -0.9728 -0.9066 Exp.: -27.593% -23.071% -18.666% -13.712% -13.279% -34.031% -38.859% -44.775% -48.223% -45.636% 15: Action: S S S S S H H H H H Index: c<-5:H c<-6:H c<-7:H c<-9:H c<-9:H c>=10:S c>=10:S c>=8:S c>=4:S c>=10:S # rounds: 5502731 5505917 5503630 5387205 5473014 5465660 5474897 5463067 20178822 3805307 # hands: 5502731 5505917 5503630 5387205 5473014 5465660 5474897 5463067 20178822 3805307 % idx plays: 0.744% 0.299% 0.113% 0.016% 0.018% 0.010% 0.011% 0.070% 2.234% 0.007% Freq.: 0.550% 0.551% 0.550% 0.539% 0.547% 0.547% 0.547% 0.546% 2.018% 0.381% Avg. WL/R: -0.5171 -0.4343 -0.3472 -0.2608 -0.2548 -0.7601 -0.8573 -0.9661 -1.0650 -1.0000 Exp.: -27.533% -23.139% -18.504% -13.898% -13.582% -38.809% -43.776% -49.314% -52.405% -49.980% 16: Action: S S S S S H H H H H Index: c<-8:H c<-10:H -- -- -- c>=9:S c>=7:S c>=5:S c>=0:S c>=8:S # rounds: 4584768 4586209 4583690 4582520 4468887 4557051 4582680 4552714 16790421 3174385 # hands: 4584768 4586209 4583690 4582520 4468887 4557051 4582680 4552714 16790421 3174385 % idx plays: 0.045% 0.006% -- -- -- 0.025% 0.178% 1.048% 47.030% 0.053% Freq.: 0.458% 0.459% 0.458% 0.458% 0.447% 0.456% 0.458% 0.455% 1.679% 0.317% Avg. WL/R: -0.5226 -0.4390 -0.3502 -0.2620 -0.2571 -0.8376 -0.9299 -1.0329 -1.1108 -1.0684 Exp.: -27.662% -23.223% -18.533% -13.864% -13.612% -42.510% -47.174% -52.414% -54.306% -52.999% A2: Action: H H H D D H H H H H Index: -- c>=7:D c>=3:D c<0:H c<-1:H -- -- -- -- -- # rounds: 891987 920848 918902 917977 918482 918744 918480 915546 3392411 615091 # hands: 891987 920848 918902 917977 918482 918744 918480 915546 3392411 615091 % idx plays: -- 0.193% 5.884% 43.279% 20.206% -- -- -- -- -- Freq.: 0.089% 0.092% 0.092% 0.092% 0.092% 0.092% 0.092% 0.092% 0.339% 0.062% Avg. WL/R: 0.0928 0.1511 0.2219 0.3380 0.4033 0.2056 0.0722 -0.1041 -0.2523 -0.1405 Exp.: 4.898% 7.920% 9.233% 10.081% 11.302% 10.446% 3.657% -5.275% -12.337% -6.961% A3: Action: H H H D D H H H H H Index: -- c>=7:D c>=1:D c<-1:H c<-4:H -- -- -- -- -- # rounds: 918190 889337 919448 918386 919329 917567 918874 917097 3394900 613736 # hands: 918190 889337 919448 918386 919329 917567 918874 917097 3394900 613736 % idx plays: -- 0.190% 26.789% 20.171% 1.820% -- -- -- -- -- Freq.: 0.092% 0.089% 0.092% 0.092% 0.092% 0.092% 0.092% 0.092% 0.339% 0.061% Avg. WL/R: 0.0446 0.1033 0.1854 0.3096 0.3847 0.1138 -0.0072 -0.1875 -0.3294 -0.2300 Exp.: 2.358% 5.416% 6.083% 8.669% 10.247% 5.774% -0.364% -9.508% -16.105% -11.462% A4: Action: H H D D D H H H H H Index: -- c>=7:D c<0:H c<-4:H c<-9:H -- -- -- -- -- # rounds: 917884 920359 889991 916922 916491 917441 916975 917539 3394596 614879 # hands: 917884 920359 889991 916922 916491 917441 916975 917539 3394596 614879 % idx plays: -- 0.182% 43.377% 1.798% 0.016% -- -- -- -- -- Freq.: 0.092% 0.092% 0.089% 0.092% 0.092% 0.092% 0.092% 0.092% 0.339% 0.061% Avg. WL/R: -0.0039 0.0561 0.1475 0.2995 0.3724 0.0310 -0.1014 -0.2715 -0.4129 -0.3117 Exp.: -0.205% 2.937% 4.415% 7.965% 9.858% 1.572% -5.145% -13.803% -20.166% -15.484% A5: Action: H H D D D H H H H H Index: -- c>=4:D c<-2:H c<-6:H -- -- -- -- -- -- # rounds: 919652 918637 917649 888639 919186 915117 916845 917706 3393459 614770 # hands: 919652 918637 917649 888639 919186 915117 916845 917706 3393459 614770 % idx plays: -- 2.626% 9.289% 0.302% -- -- -- -- -- -- Freq.: 0.092% 0.092% 0.092% 0.089% 0.092% 0.092% 0.092% 0.092% 0.339% 0.061% Avg. WL/R: -0.0390 0.0320 0.1543 0.2869 0.3730 -0.0531 -0.1828 -0.3475 -0.4744 -0.3868 Exp.: -2.065% 1.491% 4.182% 7.612% 9.860% -2.696% -9.260% -17.620% -23.192% -19.233% A6: Action: H D D D D H H H H H Index: c>=1:D c<-3:H c<-7:H c<-10:H -- -- -- -- -- -- # rounds: 918831 918838 918152 916747 888794 915538 917107 918015 3390520 614337 # hands: 918831 918838 918152 916747 888794 915538 917107 918015 3390520 614337 % idx plays: 26.777% 4.192% 0.113% 0.006% -- -- -- -- -- -- Freq.: 0.092% 0.092% 0.092% 0.092% 0.089% 0.092% 0.092% 0.092% 0.339% 0.061% Avg. WL/R: 0.0149 0.1459 0.2807 0.4215 0.5311 0.0979 -0.1727 -0.3312 -0.4422 -0.3879 Exp.: 0.487% 3.911% 7.434% 11.157% 14.057% 4.979% -8.772% -16.831% -21.614% -19.271% A7: Action: S D D D D S S H H H Index: c>=0:D c<-2:S c<-6:S c<-8:S c<-10:S -- -- -- -- c>=1:S # rounds: 916365 919685 917639 917573 917045 888180 915258 915828 3386075 612788 # hands: 916365 919685 917639 917573 917045 888180 915258 915828 3386075 612788 % idx plays: 52.873% 10.144% 0.334% 0.048% 0.009% -- -- -- -- 20.180% Freq.: 0.092% 0.092% 0.092% 0.092% 0.092% 0.089% 0.092% 0.092% 0.339% 0.061% Avg. WL/R: 0.2940 0.4066 0.5495 0.6769 0.8290 0.8590 0.2213 -0.2366 -0.3388 -0.1980 Exp.: 8.462% 10.604% 13.954% 17.161% 21.026% 41.727% 10.767% -11.504% -15.869% -9.412% A8: Action: S S S S S S S S S S Index: c>=8:D c>=5:D c>=3:D c>=1:D c>=1:D -- -- -- -- -- # rounds: 917359 918247 916688 916731 917215 917081 888829 916391 3389636 612709 # hands: 917359 918247 916688 916731 917215 917081 888829 916391 3389636 612709 % idx plays: 0.065% 1.054% 5.419% 24.741% 24.716% -- -- -- -- -- Freq.: 0.092% 0.092% 0.092% 0.092% 0.092% 0.092% 0.089% 0.092% 0.339% 0.061% Avg. WL/R: 0.7650 0.8073 0.8581 0.9460 1.0605 1.2893 1.2479 0.5778 0.0953 0.5874 Exp.: 38.758% 38.868% 34.401% 29.619% 33.187% 62.788% 60.636% 28.086% 4.459% 27.990% A9: Action: S S S S S S S S S S Index: c>=10:D c>=8:D c>=6:D c>=5:D c>=4:D -- -- -- -- -- # rounds: 919543 918265 916538 916927 916342 917246 918102 886621 3388953 612902 # hands: 919543 918265 916538 916927 916342 917246 918102 886621 3388953 612902 % idx plays: 0.010% 0.069% 0.442% 1.060% 2.449% -- -- -- -- -- Freq.: 0.092% 0.092% 0.092% 0.092% 0.092% 0.092% 0.092% 0.089% 0.339% 0.061% Avg. WL/R: 1.2608 1.2835 1.3110 1.3380 1.4091 1.6043 1.6394 1.5665 1.1676 1.3922 Exp.: 64.023% 64.900% 64.971% 64.543% 63.573% 78.038% 79.632% 76.267% 54.596% 66.107% AA: Action: P P P P P P P P P P Index: -- -- -- -- -- c<-9:H c<-8:H c<-7:H c<-8:H c<-3:H # rounds: 444836 444754 444963 444166 444411 444396 443948 444341 1647639 287711 # hands: 951869 951680 952276 950700 951034 950601 949478 950516 3525223 593135 % idx plays: -- -- -- -- -- 0.025% 0.069% 0.172% 0.070% 6.317% Freq.: 0.095% 0.095% 0.095% 0.095% 0.095% 0.095% 0.095% 0.095% 0.353% 0.059% Avg. WL/R: 1.3192 1.4345 1.5493 1.6623 1.7467 1.4014 1.1295 0.8223 0.7145 0.6463 Exp.: 29.956% 32.615% 35.116% 37.841% 39.687% 30.611% 24.554% 17.872% 14.968% 14.018% 22: Action: P P P P P P H H H H Index: c<-3:H c<-5:H c<-7:H c<-9:H -- -- c>=5:P -- -- -- # rounds: 418433 445937 446257 445561 445369 445254 446628 444010 1642886 307507 # hands: 876916 951358 954820 953487 952827 953129 452837 444010 1642886 307507 % idx plays: 3.437% 0.628% 0.097% 0.012% -- -- 1.248% -- -- -- Freq.: 0.088% 0.095% 0.095% 0.095% 0.095% 0.095% 0.045% 0.044% 0.164% 0.031% Avg. WL/R: -0.0736 0.0648 0.2372 0.3810 0.4981 0.0027 -0.3055 -0.4589 -0.5691 -0.4910 Exp.: -1.647% 1.410% 4.999% 7.670% 9.772% 0.058% -15.350% -25.253% -30.203% -26.500% 33: Action: P P P P P P H H H H Index: c<0:H c<-4:H c<-7:H c<-9:H -- -- c>=4:P -- -- -- # rounds: 445923 418632 445753 446573 446142 445213 444099 444571 1640154 307735 # hands: 767846 886892 953300 956018 955026 953207 458675 444571 1640154 307735 % idx plays: 36.479% 1.516% 0.096% 0.012% -- -- 2.929% -- -- -- Freq.: 0.077% 0.089% 0.095% 0.096% 0.096% 0.095% 0.046% 0.044% 0.164% 0.031% Avg. WL/R: -0.1665 0.0091 0.1764 0.3795 0.4429 -0.1021 -0.4348 -0.5700 -0.6667 -0.6045 Exp.: -4.198% 0.199% 3.655% 7.583% 8.659% -2.213% -19.394% -31.392% -35.380% -32.552% 44: Action: H H H P P H H H H H Index: -- c>=8:P c>=3:P c<-1:H c<-4:H -- -- -- -- -- # rounds: 445474 444459 417941 444822 446003 444857 444470 444892 1640291 307443 # hands: 445474 444908 451195 865063 946651 444857 444470 444892 1640291 307443 % idx plays: -- 0.092% 7.096% 16.956% 1.495% -- -- -- -- -- Freq.: 0.045% 0.044% 0.045% 0.087% 0.095% 0.044% 0.044% 0.044% 0.164% 0.031% Avg. WL/R: -0.0033 0.0474 0.1350 0.2656 0.3572 0.1729 -0.1008 -0.3894 -0.4803 -0.3696 Exp.: -0.190% 2.697% 5.008% 5.750% 7.266% 9.528% -5.556% -21.399% -25.528% -20.023% 55: Action: D D D D D D D D H H Index: c<-8:H c<-9:H c<-10:H -- -- c<-6:H c<-4:H c<-1:H c>=4:D c>=4:D # rounds: 445800 443778 444328 416219 444234 444110 444892 444039 1640984 307635 # hands: 445800 443778 444328 416219 444234 444110 444892 444039 1640984 307635 % idx plays: 0.033% 0.012% 0.005% -- -- 0.265% 1.646% 18.472% 2.641% 2.491% Freq.: 0.045% 0.044% 0.044% 0.042% 0.044% 0.044% 0.044% 0.044% 0.164% 0.031% Avg. WL/R: 0.7235 0.8111 0.9173 1.0300 1.1186 0.8208 0.6192 0.3185 0.0668 0.1983 Exp.: 20.761% 23.264% 26.321% 29.614% 32.080% 22.607% 17.029% 9.235% 3.117% 9.446% 66: Action: P P P P P H H H H H Index: c<-1:H c<-4:H c<-6:H c<-8:H c<-10:H -- -- -- -- -- # rounds: 445505 444884 445642 443265 416390 444873 444164 443660 1638775 306142 # hands: 865785 944853 952364 948627 889608 444873 444164 443660 1638775 306142 % idx plays: 17.018% 1.475% 0.258% 0.033% 0.003% -- -- -- -- -- Freq.: 0.087% 0.094% 0.095% 0.095% 0.089% 0.044% 0.044% 0.044% 0.164% 0.031% Avg. WL/R: -0.2997 -0.1186 0.0746 0.2854 0.3374 -0.4208 -0.5274 -0.6476 -0.7450 -0.6771 Exp.: -6.790% -2.455% 1.516% 5.723% 6.626% -23.261% -29.105% -35.656% -39.556% -36.635% 77: Action: P P P P P P H H H H Index: c<-9:H -- -- -- -- -- c>=5:P -- -- -- # rounds: 444755 445887 444703 443735 444462 417400 444122 443145 1639817 306313 # hands: 951888 954764 951546 949710 951181 891229 449521 443145 1639817 306313 % idx plays: 0.018% -- -- -- -- -- 1.085% -- -- -- Freq.: 0.095% 0.095% 0.095% 0.095% 0.095% 0.089% 0.045% 0.044% 0.164% 0.031% Avg. WL/R: -0.1615 0.0247 0.2212 0.4182 0.5436 -0.0959 -0.7803 -0.8964 -1.0061 -0.9252 Exp.: -3.133% 0.470% 4.150% 7.776% 10.171% -1.932% -36.555% -45.444% -49.070% -45.838% 88: Action: P P P P P P P P P P Index: -- -- -- -- -- -- -- -- c>=8:S -- # rounds: 443583 443950 444105 445083 442743 445416 415355 444342 1635764 306686 # hands: 949034 950148 950098 952712 947550 953257 886753 951350 3499699 656172 % idx plays: -- -- -- -- -- -- -- -- 0.064% -- Freq.: 0.095% 0.095% 0.095% 0.095% 0.095% 0.095% 0.089% 0.095% 0.350% 0.066% Avg. WL/R: 0.2186 0.3638 0.5064 0.6868 0.8592 0.6829 -0.0388 -0.7837 -1.0086 -0.7266 Exp.: 4.661% 7.761% 10.610% 13.987% 17.528% 13.945% -0.794% -16.163% -21.164% -15.939% 99: Action: P P P P P S P P S S Index: c<-2:S c<-3:S c<-5:S c<-6:S c<-6:S c>=3:P c<-8:S c<-9:S -- c>=3:P # rounds: 445117 444247 444097 444715 443043 444467 443990 416788 1635130 305359 # hands: 904690 928844 946701 950089 946859 472163 949842 890208 1635130 321618 % idx plays: 9.320% 4.209% 0.772% 0.309% 0.304% 5.516% 0.055% 0.018% -- 4.733% Freq.: 0.090% 0.093% 0.095% 0.095% 0.095% 0.047% 0.095% 0.089% 0.164% 0.032% Avg. WL/R: 0.4502 0.5815 0.7237 0.8695 0.9975 0.8452 0.5015 -0.1541 -0.3798 -0.1775 Exp.: 10.648% 13.474% 16.574% 19.814% 22.524% 31.677% 10.996% -3.388% -18.546% -6.790% TT: Action: S S S S S S S S S S Index: -- c>=8:P c>=6:P c>=5:P c>=4:P -- -- -- -- -- # rounds: 7278503 7271834 7273628 7265230 7265116 7267025 7265702 7266668 26377312 5055172 # hands: 7278503 7278112 7315269 7367115 7503431 7267025 7265702 7266668 26377312 5055172 % idx plays: -- 0.059% 0.390% 0.953% 2.218% -- -- -- -- -- Freq.: 0.728% 0.728% 0.732% 0.737% 0.750% 0.727% 0.727% 0.727% 2.638% 0.506% Avg. WL/R: 1.3101 1.3330 1.3604 1.4000 1.4717 1.6690 1.7087 1.6293 1.2235 1.4396 Exp.: 63.817% 64.652% 64.463% 63.822% 61.810% 77.906% 79.729% 76.044% 54.948% 65.652% # rounds: - Number of rounds where the initial two cards classified as this combination. # hands: - Number of hands where the initial two cards classified as this combination. Splitting (if any) can cause this number to be higher than the # of rounds. % idx plays: - Percentage of plays where the count caused the index play (if any) to be used. Freq.: - Percentage of rounds that classify with this combination Avg. WL/R: - The average win (or loss) per round, in bet units (divided by bet_size). Includes all hands played from this combination, including split hands (if any). Exp.: - The expectation for the hand combination: total winnings / total wagers. Includes winnings and wagers on split hands. System count statistics: See after table for explanation of columns Count Rounds Freq. Exp. Std. Avg. W/L ============================================================ -15 10 0.000% 40.91% 1.06 2.2500 -14 31 0.000% -6.25% 0.98 -0.3226 -13 208 0.000% -3.81% 1.01 -0.2043 -12 1288 0.000% -2.23% 1.05 -0.1184 -11 6173 0.001% -4.88% 1.05 -0.2612 -10 25197 0.003% -4.80% 1.06 -0.2581 -9 89956 0.009% -4.65% 1.08 -0.2526 -8 294465 0.029% -4.39% 1.08 -0.2395 -7 874905 0.087% -3.92% 1.09 -0.2143 -6 2368982 0.237% -3.51% 1.11 -0.1939 -5 5899566 0.590% -3.12% 1.11 -0.1725 -4 13761658 1.376% -2.52% 1.13 -0.1412 -3 30383946 3.038% -2.02% 1.14 -0.1137 -2 64551134 6.455% -1.48% 1.15 -0.0838 -1 134601851 13.460% -0.99% 1.15 -0.0559 0 503301006 50.330% -0.31% 1.15 -0.0174 1 129732306 12.973% 0.41% 3.49 0.0694 2 62316119 6.232% 0.98% 5.80 0.2787 3 29335819 2.934% 1.55% 11.61 0.9017 4 13296903 1.330% 2.12% 11.75 1.2658 5 5675311 0.568% 2.80% 11.85 1.6886 6 2258306 0.226% 3.41% 11.94 2.0726 7 829916 0.083% 3.94% 12.00 2.4100 8 279325 0.028% 4.36% 12.00 2.6747 9 85513 0.009% 5.52% 12.00 3.3843 10 23484 0.002% 6.19% 11.92 3.7781 11 5679 0.001% 6.87% 11.94 4.1997 12 1286 0.000% 11.70% 11.95 7.2900 13 257 0.000% 10.17% 12.08 6.3230 14 58 0.000% 6.15% 11.08 3.4483 15 5 0.000% 53.85% 9.80 35.0000 Count: - Each row covers from the count value (inclusive), to the value + 1 - The counts represent system counts, and are dependent on the 'true count calculation' setting Rounds: - Number of rounds where the round started with in this count range Freq.: - Percentage of rounds that classify with this count Exp.: - The expectation for the rows count: winnings / total wagers Std.: - Standard deviation. In betting units (divided by bet_size) Avg.: - The average win (or loss) per round, in bet units (divided by bet_size) Hand state statistics: Total number of hands: 1028548551 State # rounds % ============================== won 403090863 39.19% lost 492336494 47.87% BJ 45232199 4.40% push 87888995 8.54% Win/loss record per player hand total (all dealt hands)[7]: Hand value 2 3 4 5 6 7 8 9 T A ==================================================================================================================== 12: # hands: 1217447 1976786 5726540 7560174 5927014 596368 547332 499938 3362894 2307286 % won: 36.42% 38.73% 40.31% 42.32% 43.01% 26.17% 24.41% 22.86% 7.66% 0.47% % lost: 63.58% 61.27% 59.69% 57.68% 56.99% 73.83% 75.59% 77.14% 92.34% 99.53% % pushed: 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 13: # hands: 6057510 7991087 9174204 9298937 9442143 661725 617626 564183 3602644 2348976 % won: 35.93% 37.80% 39.70% 41.90% 42.40% 26.19% 24.42% 22.86% 8.59% 0.72% % lost: 64.07% 62.20% 60.30% 58.10% 57.60% 73.81% 75.58% 77.14% 91.41% 99.28% % pushed: 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 14: # hands: 8418027 8466074 8126805 8345426 8537024 662073 614819 564333 3460003 2202523 % won: 35.45% 37.47% 39.56% 41.87% 42.33% 26.26% 24.35% 22.86% 8.96% 0.77% % lost: 64.55% 62.53% 60.44% 58.13% 57.67% 73.74% 75.65% 77.14% 91.04% 99.23% % pushed: 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 15: # hands: 8969205 8851592 8486298 8301048 8549289 663579 615663 571505 4125634 2064206 % won: 35.41% 37.39% 39.55% 41.80% 42.27% 26.13% 24.45% 22.84% 11.77% 0.82% % lost: 64.59% 62.61% 60.45% 58.20% 57.73% 73.87% 75.55% 77.16% 88.23% 99.18% % pushed: 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 16: # hands: 8170164 8009114 7644039 7574115 7623914 665643 630531 665744 20276074 1922972 % won: 35.34% 37.39% 39.56% 41.79% 42.23% 26.20% 24.23% 22.70% 20.69% 0.91% % lost: 64.66% 62.61% 60.44% 58.21% 57.77% 73.80% 75.77% 77.30% 79.31% 99.09% % pushed: 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 17: # hands: 8289669 8122450 7808389 7748657 7915690 10509907 10282663 10464451 38816767 8950188 % won: 35.32% 37.34% 39.48% 41.68% 42.20% 26.19% 24.38% 22.89% 22.04% 13.56% % lost: 50.68% 49.15% 47.41% 46.09% 41.22% 36.86% 62.73% 65.09% 66.42% 71.12% % pushed: 14.00% 13.51% 13.11% 12.22% 16.58% 36.94% 12.89% 12.03% 11.54% 15.32% 18: # hands: 8007832 7534113 7024303 6767582 6884035 11160437 10474821 9650945 37488343 8731403 % won: 49.26% 50.83% 52.50% 53.88% 58.73% 63.11% 37.29% 34.84% 33.76% 29.30% % lost: 37.24% 36.08% 35.01% 33.85% 30.59% 23.10% 26.73% 53.32% 54.72% 55.08% % pushed: 13.49% 13.09% 12.50% 12.28% 10.68% 13.79% 35.98% 11.84% 11.52% 15.61% 19: # hands: 8333051 8167972 7734312 7435729 7562671 10484596 10652989 10734044 39137472 8756303 % won: 62.81% 63.87% 64.99% 66.11% 69.37% 76.90% 73.25% 46.68% 45.58% 45.78% % lost: 24.20% 23.57% 22.83% 22.09% 19.96% 15.24% 13.87% 18.12% 42.78% 38.35% % pushed: 12.99% 12.56% 12.18% 11.80% 10.68% 7.86% 12.88% 35.20% 11.63% 15.87% 20: # hands: 11610556 11428949 11010924 10835472 10891848 13951041 13929986 14087647 52796989 12281588 % won: 75.72% 76.42% 77.13% 77.94% 80.06% 84.70% 86.09% 81.86% 56.67% 58.44% % lost: 11.85% 11.48% 11.19% 10.81% 9.76% 7.40% 6.97% 6.09% 8.33% 26.47% % pushed: 12.43% 12.10% 11.68% 11.25% 10.18% 7.90% 6.94% 12.04% 35.00% 15.10% 21: # hands: 3483384 3295594 2874933 2734639 2861201 5915205 5848613 6035424 22224550 5310574 % won: 88.20% 88.52% 88.85% 89.24% 90.26% 92.62% 93.05% 93.91% 91.51% 73.30% % lost: 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% % pushed: 11.80% 11.48% 11.15% 10.76% 9.74% 7.38% 6.95% 6.09% 8.49% 26.70% Dealer statistics: Up card 17 18 19 20 21 BJ Bust ================================================================ 2 13.98% 13.45% 13.00% 12.40% 11.83% 0.00% 35.34% 3 13.46% 13.06% 12.54% 12.08% 11.48% 0.00% 37.39% 4 13.07% 12.46% 12.13% 11.64% 11.17% 0.00% 39.52% 5 12.20% 12.24% 11.77% 11.22% 10.80% 0.00% 41.77% 6 16.57% 10.62% 10.65% 10.16% 9.73% 0.00% 42.27% 7 36.89% 13.79% 7.86% 7.87% 7.39% 0.00% 26.20% 8 12.89% 35.96% 12.87% 6.93% 6.96% 0.00% 24.40% 9 12.03% 11.81% 35.14% 12.03% 6.09% 0.00% 22.90% T 11.19% 11.16% 11.18% 34.04% 3.48% 7.71% 21.24% A 13.04% 13.09% 13.07% 13.09% 5.36% 30.81% 11.54% Note: dealer hands are being played out. Risk of Ruin calculations[8]: ROR Required bankroll (units) Bankroll (dollars) ========================================================= 1.0% 2324.7 $11623.74 2.0% 1974.8 $9874.19 3.0% 1770.2 $8850.77 5.0% 1512.3 $7561.42 10.0% 1162.4 $5811.87 15.0% 957.7 $4788.45 20.0% 812.5 $4062.32 25.0% 699.8 $3499.09 33.3% 554.6 $2773.22 50.0% 349.9 $1749.55 Trip Risk of Ruin calculations[8][9]: # of rounds/bankroll (units) ROR 400 800 1200 2000 3000 4000 ================================================================ 2.0% 155.7 217.9 264.2 336.5 406.9 464.8 3.0% 144.8 202.3 245.5 312.9 378.6 430.4 5.0% 130.7 182.4 221.5 281.3 339.7 386.9 10.0% 109.0 152.1 183.9 233.8 281.5 320.1 15.0% 95.4 132.8 160.9 203.9 245.0 276.8 20.0% 84.9 117.4 142.8 179.3 215.8 244.4 25.0% 75.9 105.2 127.1 161.3 192.7 218.7 33.3% 63.4 87.7 106.2 134.3 160.3 182.0 50.0% 43.7 60.1 73.8 91.6 109.3 123.0 Notes: 1) Expectation = 100 * (amount won or loss) / (total amount wagered) 2) A betting event is an individual hand or insurance event. Each round has one or more betting events 3) A round is one dealing to the table from the shoe. With splits, more than one hand may be played in a round 4) A unit bet value is adjusted to account for the bet size. 5) Includes ALL hands when you have an action choice. 6) Player hand expectation is only based on the first two cards. Split hands are not classified, and insurance is not factored in. A round is classified only once, regardless of the number of hands. 7) All non-bust hands dealt to counter positions are classified, including splits and spread hands. Player hands are classified by their high value. NSince all hands are classified, you will see entries that do not correspond to basic strategy because of doubles and dealer blackjacks. 8) These ROR values are derived from the average earnings and standard deviation per round, using the ROR equations as published in Don Schlesinger's excellent book, 'Blackjack Attack'. We have verified that these equations produce results that match the empirical results from our ROR simulator. The displayed ROR numbers are not bounded by an upper bank goal. The trip ROR values correspond to the empirical results within 10% accuracy, which improves as the number of rounds and/or bankroll increases 9) The table lists bankroll requirements in units for the specified ROR and number of hands. Risk of Ruin simulation results: number of sessions: 200000 maximum rounds/session: 1200 Upper limit (profit goal): unlimited Lower limit (maximum loss): $1105 ** Risk of ruin percentage **: 100.00% Statistics for session where lower limit reached: # sessions: 9688 % sessions: 4.84% avg # rounds: 829 Statistics for session where neither limit was reached: # sessions: 190312 % sessions: 95.16% average maximum loss: $406 worst session loss: $1322 #/% of profitable sessions (winnings >= 0): 109393, 54.87% #/% of negative sessions (winnings < 0): 90257, 45.13% #/% of sessions with zero profit (winnings = 0): 350, 0.17% average rounds/session: 1183 average winnings/session: $68.61 standard deviation of winnings/session (per round, in dollars): 587.958