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Mathematics of Blackjack Discussion
Some tables
Posted By: Norm Wattenberger In Response To: Wonging (Thomas Hukk)
Date: Friday, 26 April 2002, at 7:55 a.m.
When you Wong, you spread less but use a higher minimum bet. As an example I've included two tables below. Each table shows the optimal bets, Risk of Ruin, Win Rate in unts and DI for all penetrations from 52 cards to 130 cards remaining. Both tables assume an $8,000 bankroll and full Kelly, KO Preferred, S17, DAS 8 decks. The first table is assuming play all hands and the second assumes wonging in at -7 (the correct value for KO eight deck IMO.)
Play All
Cards <=-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 >=3 Risk W/R DI 52 10 10 10 10 10 10 20 30 50 50 100 100 13.5% 1.84 4.80 53 10 10 10 10 10 10 30 30 50 50 100 100 13.8% 1.82 4.75 54 10 10 10 10 10 10 30 30 50 50 100 100 13.9% 1.80 4.71 55 10 10 10 10 10 20 30 30 50 50 100 100 14.1% 1.78 4.67 56 10 10 10 10 10 20 30 50 50 50 100 100 14.7% 1.78 4.63 57 10 10 10 10 10 20 30 50 50 50 100 100 14.8% 1.76 4.59 58 10 10 10 10 10 20 30 50 50 50 100 100 14.9% 1.74 4.54 59 10 10 10 10 10 20 30 50 50 50 100 100 15.1% 1.72 4.50 60 10 10 10 10 10 20 30 50 50 50 100 100 15.2% 1.70 4.47 61 10 10 10 10 10 20 30 50 50 50 100 100 15.3% 1.68 4.43 62 10 10 10 10 10 20 30 50 50 50 100 100 15.5% 1.65 4.39 63 10 10 10 10 10 20 30 50 50 50 100 100 15.7% 1.63 4.35 64 10 10 10 10 10 20 30 50 50 50 100 100 15.8% 1.61 4.31 65 10 10 10 10 10 20 30 50 50 50 100 100 16.0% 1.59 4.27 66 10 10 10 10 10 20 30 50 50 100 100 100 17.6% 1.66 4.24 67 10 10 10 10 10 20 30 50 50 100 100 100 17.8% 1.63 4.20 68 10 10 10 10 10 20 30 50 50 100 100 100 18.0% 1.61 4.16 69 10 10 10 10 10 30 30 50 50 100 100 100 18.3% 1.60 4.12 70 10 10 10 10 10 30 30 50 50 100 100 100 18.4% 1.58 4.08 71 10 10 10 10 10 30 30 50 50 100 100 100 18.6% 1.56 4.05 72 10 10 10 10 20 30 30 50 50 100 100 100 18.9% 1.54 4.01 73 10 10 10 10 20 30 50 50 50 100 100 100 19.4% 1.54 3.97 74 10 10 10 10 20 30 50 50 50 100 100 100 19.6% 1.52 3.94 75 10 10 10 10 20 30 50 50 50 100 100 100 19.7% 1.51 3.91 76 10 10 10 10 20 30 50 50 50 100 100 100 19.9% 1.49 3.87 77 10 10 10 10 20 30 50 50 50 100 100 100 20.1% 1.47 3.83 78 10 10 10 10 20 30 50 50 100 100 100 100 21.9% 1.52 3.80 79 10 10 10 10 20 30 50 50 100 100 100 100 22.0% 1.50 3.77 80 10 10 10 10 20 30 50 50 100 100 100 100 22.1% 1.49 3.74 81 5 5 5 5 10 15 25 25 50 50 50 50 5.0% 1.47 3.71 82 5 5 5 5 10 15 25 25 50 50 50 50 5.0% 1.45 3.68 83 5 5 5 5 15 15 25 25 50 50 50 50 5.2% 1.44 3.65 84 5 5 5 5 15 15 25 25 50 50 50 50 5.3% 1.42 3.61 85 5 5 5 5 15 15 25 25 50 50 50 50 5.3% 1.40 3.58 86 5 5 5 5 15 15 25 25 50 50 50 50 5.4% 1.38 3.55 87 5 5 5 5 15 15 25 25 50 50 50 50 5.5% 1.37 3.52 88 5 5 5 5 15 25 25 25 50 50 50 50 5.7% 1.37 3.50 89 5 5 5 10 15 25 25 25 50 50 50 50 5.8% 1.36 3.47 90 5 5 5 10 15 25 25 25 50 50 50 50 5.9% 1.34 3.45 91 5 5 5 10 15 25 25 25 50 50 50 50 6.0% 1.33 3.41 92 5 5 5 10 15 25 25 25 50 50 50 50 6.1% 1.31 3.38 93 5 5 5 10 15 25 25 25 50 50 50 50 6.2% 1.29 3.35 94 5 5 5 10 15 25 25 50 50 50 50 50 7.1% 1.34 3.33 95 5 5 5 10 15 25 25 50 50 50 50 50 7.2% 1.32 3.30 96 5 5 5 10 15 25 25 50 50 50 50 50 7.3% 1.31 3.27 97 5 5 5 10 15 25 25 50 50 50 50 50 7.3% 1.29 3.25 98 5 5 5 10 15 25 25 50 50 50 50 50 7.5% 1.27 3.21 99 5 5 5 10 25 25 25 50 50 50 50 50 7.8% 1.27 3.18 100 5 5 5 10 25 25 25 50 50 50 50 50 7.9% 1.26 3.16 101 5 5 5 10 25 25 25 50 50 50 50 50 7.9% 1.25 3.14 102 5 5 5 15 25 25 25 50 50 50 50 50 8.1% 1.24 3.11 103 5 5 5 15 25 25 25 50 50 50 50 50 8.2% 1.22 3.09 104 5 5 10 15 25 25 25 50 50 50 50 50 8.3% 1.21 3.07 105 5 5 10 15 25 25 25 50 50 50 50 50 8.4% 1.20 3.05 106 5 5 10 15 25 25 25 50 50 50 50 50 8.5% 1.18 3.02 107 5 5 10 15 25 25 25 50 50 50 50 50 8.7% 1.17 2.98 108 5 5 10 15 25 25 25 50 50 50 50 50 8.7% 1.15 2.96 109 5 5 10 15 25 25 25 50 50 50 50 50 8.8% 1.14 2.94 110 5 5 10 15 25 25 25 50 50 50 50 50 8.9% 1.13 2.92 111 5 5 10 15 25 25 25 50 50 50 50 50 9.0% 1.11 2.89 112 5 5 10 15 25 25 25 50 50 50 50 50 9.1% 1.10 2.87 113 5 5 10 15 25 25 25 50 50 50 50 50 9.2% 1.08 2.84 114 5 5 10 15 25 25 50 50 50 50 50 50 10.4% 1.12 2.82 115 5 5 10 15 25 25 50 50 50 50 50 50 10.5% 1.11 2.80 116 5 5 10 15 25 25 50 50 50 50 50 50 10.5% 1.10 2.78 117 5 5 15 15 25 25 50 50 50 50 50 50 10.8% 1.09 2.75 118 5 5 15 15 25 25 50 50 50 50 50 50 10.9% 1.08 2.73 119 5 5 15 15 25 25 50 50 50 50 50 50 11.0% 1.06 2.70 120 5 5 15 25 25 25 50 50 50 50 50 50 11.5% 1.06 2.68 121 5 5 15 25 25 25 50 50 50 50 50 50 11.6% 1.05 2.65 122 5 5 15 25 25 50 50 50 50 50 50 50 13.0% 1.08 2.63 123 5 5 15 25 25 50 50 50 50 50 50 50 13.1% 1.07 2.61 124 5 5 15 25 25 50 50 50 50 50 50 50 13.2% 1.05 2.58 125 5 10 15 25 25 50 50 50 50 50 50 50 13.4% 1.05 2.56 126 5 10 15 25 25 50 50 50 50 50 50 50 13.5% 1.04 2.55 127 5 10 15 25 25 50 50 50 50 50 50 50 13.6% 1.02 2.52 128 5 10 15 25 25 50 50 50 50 50 50 50 13.8% 1.01 2.50 129 5 10 15 25 25 50 50 50 50 50 50 50 14.0% 0.99 2.47 130 5 10 15 25 25 50 50 50 50 50 50 50 14.1% 0.94 2.40 Back-counting
Cards <=-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 >=3 Risk W/R DI 52 30 30 30 30 30 30 30 60 60 90 150 13.5% 1.17 6.61 53 30 30 30 30 30 30 30 60 60 90 150 13.5% 1.16 6.57 54 30 30 30 30 30 30 30 60 60 90 150 13.6% 1.14 6.53 55 30 30 30 30 30 30 30 60 60 90 150 13.6% 1.13 6.50 56 30 30 30 30 30 30 30 60 60 90 150 13.7% 1.12 6.46 57 30 30 30 30 30 30 30 60 60 90 150 13.7% 1.11 6.43 58 30 30 30 30 30 30 30 60 60 90 150 13.7% 1.10 6.39 59 30 30 30 30 30 30 30 60 60 90 150 13.8% 1.09 6.36 60 30 30 30 30 30 30 30 60 60 90 150 13.8% 1.08 6.33 61 30 30 30 30 30 30 30 60 60 90 150 13.8% 1.07 6.30 62 30 30 30 30 30 30 30 60 60 90 150 13.9% 1.06 6.26 63 30 30 30 30 30 30 30 60 60 90 150 13.9% 1.05 6.22 64 30 30 30 30 30 30 30 60 60 90 150 13.9% 1.04 6.19 65 30 30 30 30 30 30 30 60 60 90 150 14.0% 1.03 6.16 66 30 30 30 30 30 30 30 60 60 90 150 14.0% 1.02 6.13 67 30 30 30 30 30 30 60 60 60 90 150 14.4% 1.02 6.09 68 30 30 30 30 30 30 60 60 60 90 150 14.4% 1.01 6.06 69 30 30 30 30 30 30 60 60 60 90 150 14.5% 1.00 6.02 70 30 30 30 30 30 30 60 60 60 90 150 14.5% 0.99 5.99 71 30 30 30 30 30 30 60 60 60 90 150 14.5% 0.98 5.96 72 30 30 30 30 30 30 60 60 60 90 150 14.6% 0.97 5.92 73 30 30 30 30 30 30 60 60 60 90 150 14.6% 0.96 5.89 74 30 30 30 30 30 30 60 60 60 90 150 14.6% 0.96 5.86 75 30 30 30 30 30 30 60 60 60 90 150 14.7% 0.95 5.83 76 30 30 30 30 30 30 60 60 60 90 150 14.7% 0.94 5.80 77 30 30 30 30 30 30 60 60 60 90 150 14.8% 0.93 5.76 78 30 30 30 30 30 30 60 60 60 90 150 14.8% 0.92 5.73 79 30 30 30 30 30 30 60 60 60 90 150 14.8% 0.91 5.71 80 30 30 30 30 30 30 60 60 60 90 150 14.8% 0.90 5.68 81 30 30 30 30 30 30 60 60 60 90 150 14.8% 0.89 5.64 82 30 30 30 30 30 30 60 60 60 90 150 14.9% 0.88 5.62 83 30 30 30 30 30 30 60 60 60 90 150 14.9% 0.88 5.59 84 30 30 30 30 30 30 60 60 60 90 150 14.9% 0.87 5.56 85 30 30 30 30 30 30 60 60 60 90 150 14.9% 0.86 5.53 86 30 30 30 30 30 30 60 60 60 90 150 14.9% 0.85 5.50 87 30 30 30 30 30 30 60 60 60 90 150 15.0% 0.84 5.48 88 30 30 30 30 30 30 60 60 60 90 150 15.0% 0.84 5.45 89 30 30 30 30 30 30 60 60 60 90 150 15.0% 0.83 5.43 90 30 30 30 30 30 30 60 60 60 90 150 15.0% 0.82 5.40 91 30 30 30 30 30 30 60 60 60 90 150 15.0% 0.81 5.37 92 30 30 30 30 30 30 60 60 60 90 150 15.1% 0.80 5.34 93 30 30 30 30 30 30 60 60 90 90 150 15.6% 0.81 5.31 94 30 30 30 30 30 30 60 60 90 90 150 15.6% 0.80 5.28 95 30 30 30 30 30 30 60 60 90 90 150 15.6% 0.79 5.25 96 30 30 30 30 30 30 60 60 90 90 150 15.7% 0.79 5.22 97 30 30 30 30 30 30 60 60 90 90 150 15.7% 0.78 5.19 98 30 30 30 30 30 30 60 60 90 90 150 15.8% 0.77 5.16 99 30 30 30 30 30 30 60 60 90 90 150 15.8% 0.76 5.13 100 30 30 30 30 30 30 60 60 90 90 150 15.8% 0.76 5.11 101 30 30 30 30 30 30 60 60 90 90 150 15.8% 0.75 5.09 102 25 25 25 25 25 50 50 50 75 75 125 11.3% 0.75 5.06 103 25 25 25 25 25 50 50 50 75 75 125 11.3% 0.74 5.04 104 25 25 25 25 25 50 50 50 75 75 125 11.3% 0.74 5.01 105 25 25 25 25 25 50 50 50 75 75 125 11.3% 0.73 4.99 106 25 25 25 25 25 50 50 50 75 75 125 11.3% 0.72 4.96 107 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.71 4.92 108 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.71 4.90 109 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.70 4.88 110 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.69 4.86 111 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.69 4.83 112 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.68 4.81 113 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.67 4.78 114 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.67 4.76 115 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.66 4.74 116 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.66 4.72 117 25 25 25 25 25 50 50 50 75 75 125 11.4% 0.65 4.69 118 25 25 25 25 25 50 50 75 75 75 125 11.9% 0.65 4.67 119 25 25 25 25 25 50 50 75 75 75 125 11.9% 0.65 4.64 120 25 25 25 25 50 50 50 75 75 75 125 12.3% 0.65 4.62 121 25 25 25 25 50 50 50 75 75 75 125 12.3% 0.64 4.59 122 25 25 25 25 50 50 50 75 75 75 125 12.4% 0.64 4.56 123 25 25 25 25 50 50 50 75 75 75 125 12.4% 0.63 4.53 124 25 25 25 25 50 50 50 75 75 75 125 12.4% 0.62 4.51 125 25 25 25 25 50 50 50 75 75 75 125 12.4% 0.62 4.49 126 25 25 25 25 50 50 50 75 75 75 125 12.4% 0.61 4.47 127 25 25 25 25 50 50 50 75 75 75 125 12.4% 0.61 4.45 128 <