You may be comforted to know that 50% of the most likely deck compositions are covered by only 0.16% of all the possible permutations!
The point of my post is to indicate that discrete analysis (as opposed to random simulation) is possible, once one realizes that the overwhelming majority of deck compositions can be safely ignored.
Of course random simulation has its role in building a successful process for the player.
Below is a table indicating the number of blackjack-specific deck compositions that need to be analyzed to cover 99% of all possible permutations, for the penetration indicated. Permutations assume [T,J,Q,K] constitute a single rank.
For example, in the case of 50 card penetration, exactly 624,655,486 deck compositions need to be analyzed to cover 99% of all possible deck compositions, or 8.21% of all possible deck compositions. Thus, 91.79% of all possible deck compositions can be ignored from analysis.
Code:# of deck Pen. compositions covering 99% % of all possible of all perm. permutations ---- ------------ ------------- 10 101,137 70.79% 11 171,014 61.80% 12 308,684 59.88% 13 521,275 56.23% 14 908,498 56.25% 15 1,343,705 49.16% 16 2,058,384 45.71% 17 3,127,861 43.22% 18 4,490,142 39.52% 19 6,494,887 37.20% 20 9,174,522 34.92% 21 12,384,986 31.93% 22 17,096,413 30.41% 23 22,317,852 27.88% 24 29,149,576 26.00% 25 36,606,546 23.70% 26 46,694,700 22.28% 27 59,746,998 21.33% 28 73,099,014 19.81% 29 90,026,777 18.78% 30 107,682,735 17.53% 31 129,395,929 16.65% 32 146,625,113 15.11% 33 176,270,564 14.73% 34 200,207,182 13.73% 35 228,828,298 13.04% 36 259,482,719 12.43% 37 287,864,212 11.72% 38 332,190,727 11.63% 39 363,534,410 11.07% 40 392,981,873 10.52% 41 423,799,182 10.08% 42 458,306,042 9.79% 43 491,099,036 9.52% 44 514,662,789 9.16% 45 540,637,776 8.91% 46 556,316,400 8.59% 47 571,006,484 8.34% 48 619,998,560 8.66% 49 621,536,897 8.38% 50 624,655,486 8.21% 51 646,087,639 8.37% 52 628,347,871 8.10% 53 647,176,615 8.38% 54 625,466,863 8.22% 55 623,131,301 8.40% 56 619,998,560 8.66% 57 571,006,484 8.34% 58 556,316,400 8.59% 59 540,593,172 8.91% 60 514,662,789 9.16% 61 494,059,280 9.58% 62 458,306,042 9.79% 63 424,100,946 10.09% 64 392,981,873 10.52% 65 363,534,410 11.07% 66 330,456,715 11.57% 67 287,542,156 11.71% 68 259,482,719 12.43% 69 228,828,298 13.04% 70 200,671,366 13.76% 71 176,270,564 14.73% 72 146,625,113 15.11% 73 129,410,965 16.65% 74 107,682,735 17.53% 75 90,026,777 18.78%
Below is the same table as that above, but using 95% coverage of all possible deck compositions, instead of 99%.
Code:# of deck % of all possible Pen. compositions permutations ---- ------------ ------------- 10 73,260 51.27% 11 127,351 46.02% 12 214,436 41.60% 13 360,838 38.92% 14 575,564 35.64% 15 962,534 35.22% 16 1,428,820 31.73% 17 2,005,023 27.71% 18 2,651,519 23.34% 19 3,730,072 21.37% 20 5,462,365 20.79% 21 7,276,702 18.76% 22 10,187,029 18.12% 23 12,326,254 15.40% 24 16,471,616 14.69% 25 20,412,042 13.22% 26 23,370,956 11.15% 27 30,116,120 10.75% 28 36,657,451 9.93% 29 44,474,380 9.28% 30 53,659,991 8.73% 31 62,716,736 8.07% 32 71,043,145 7.32% 33 79,171,997 6.61% 34 96,275,464 6.60% 35 110,625,160 6.30% 36 119,178,451 5.71% 37 130,274,670 5.30% 38 139,848,468 4.90% 39 153,749,660 4.68% 40 158,534,803 4.24% 41 181,117,805 4.31% 42 196,481,153 4.20% 43 214,096,262 4.15% 44 216,436,226 3.85% 45 221,238,290 3.65% 46 225,362,201 3.48% 47 241,134,207 3.52% 48 260,540,118 3.64% 49 237,450,011 3.20% 50 250,870,421 3.30% 51 250,061,942 3.24% 52 251,486,534 3.24% 53 250,106,546 3.24% 54 250,870,421 3.30% 55 236,167,331 3.18% 56 260,540,118 3.64% 57 241,928,007 3.53% 58 226,156,001 3.49% 59 221,238,290 3.65% 60 218,624,090 3.89% 61 214,096,262 4.15% 62 193,037,573 4.12% 63 181,117,805 4.31% 64 158,534,803 4.24% 65 153,749,660 4.68% 66 139,668,162 4.89% 67 130,274,670 5.30% 68 119,199,970 5.71% 69 110,625,160 6.30% 70 96,275,464 6.60% 71 79,171,997 6.61% 72 71,043,145 7.32% 73 63,049,586 8.11% 74 53,659,991 8.73% 75 44,474,380 9.28%
Hello,
I've been away for a couple of weeks - looking into creating a freeware BJ simulation project. I'd like to discuss a few issues about this with the owner or administrator of this board. Can anyone pls tell me if that is Norm?
Also, it seems to me that the person who posts under the ID of "Norm" is Norman Watternberger and that he is the person who is the owner and developer of the CVCX software. If that is correct, I'd like to ask if it might be possible for me to send him a private message?
Thank you.
I'm guessing that Norm would probably view a freeware project to create a BJ simulation as competition for his products. I'd like to ask if he might see any way that both may co-exist without necessarily seeing the other as an adversary?
Last edited by Skyler62; 03-17-2017 at 03:38 AM.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
I apologize for the erroneous numbers I posted above. Below is a more concise table for a double deck showing correct values for 70%, 80%, 90%, 95%, and 99% coverage using the most likely deck compositions, specifically at the penetration indicated.
Code:# of possible deck 70% 80% 90% 95% 99% Pen. compositions coverage coverage coverage coverage coverage ----- ------------ --------- --------- --------- --------- --------- 15 1,262,459 3.9% 5.9% 9.9% 14.4% 26.4% 16 1,940,015 3.4% 5.2% 8.7% 12.8% 23.8% 17 2,905,760 2.9% 4.5% 7.7% 11.4% 21.5% 18 4,249,281 2.5% 4.0% 6.9% 10.3% 19.6% 19 6,075,858 2.2% 3.5% 6.2% 9.3% 17.9% 20 8,505,345 2.0% 3.1% 5.6% 8.5% 16.4% 21 11,669,700 1.7% 2.8% 5.0% 7.7% 15.2% 22 15,709,035 1.5% 2.5% 4.6% 7.1% 14.1% 23 20,766,162 1.4% 2.3% 4.2% 6.5% 13.1% 24 26,979,744 1.2% 2.1% 3.8% 6.0% 12.3% 25 34,476,321 1.1% 1.9% 3.5% 5.6% 11.6% 26 43,361,670 1.0% 1.7% 3.3% 5.2% 10.9% 27 53,712,091 0.9% 1.6% 3.0% 4.9% 10.4% 28 65,566,288 0.9% 1.5% 2.8% 4.6% 10.0% 29 78,918,535 0.8% 1.4% 2.7% 4.4% 9.6% 30 93,713,782 0.7% 1.3% 2.5% 4.2% 9.2% 31 109,845,265 0.7% 1.2% 2.4% 4.0% 8.9% 32 127,155,037 0.7% 1.2% 2.3% 3.8% 8.7% 33 145,437,633 0.6% 1.1% 2.2% 3.7% 8.5% 34 164,446,821 0.6% 1.1% 2.1% 3.6% 8.4% 35 183,905,073 0.6% 1.0% 2.1% 3.5% 8.2% 36 203,515,141 0.6% 1.0% 2.0% 3.4% 8.1% 37 222,972,943 0.5% 1.0% 2.0% 3.4% 8.1% 38 241,980,853 0.5% 0.9% 1.9% 3.3% 8.0% 39 260,260,447 0.5% 0.9% 1.9% 3.3% 8.0% 40 277,563,784 0.5% 0.9% 1.9% 3.3% 8.0% 41 293,682,397 0.5% 0.9% 1.9% 3.3% 8.1% 42 308,453,343 0.5% 0.9% 1.9% 3.2% 8.1% 43 321,761,913 0.5% 0.9% 1.9% 3.2% 8.2% 44 333,540,933 0.5% 0.9% 1.8% 3.3% 8.2% 45 343,766,869 0.5% 0.9% 1.8% 3.3% 8.3% 46 352,453,183 0.5% 0.9% 1.8% 3.3% 8.4% 47 359,641,573 0.5% 0.9% 1.8% 3.3% 8.4% 48 365,391,868 0.5% 0.9% 1.9% 3.3% 8.5% 49 369,771,439 0.5% 0.9% 1.9% 3.3% 8.5% 50 372,845,029 0.5% 0.9% 1.9% 3.3% 8.6% 51 374,665,863 0.5% 0.9% 1.9% 3.3% 8.6% 52 375,268,773 0.5% 0.9% 1.9% 3.3% 8.6% 53 374,665,863 0.5% 0.9% 1.9% 3.3% 8.6% 54 372,845,029 0.5% 0.9% 1.9% 3.3% 8.6% 55 369,771,439 0.5% 0.9% 1.9% 3.3% 8.5% 56 365,391,868 0.5% 0.9% 1.9% 3.3% 8.5% 57 359,641,573 0.5% 0.9% 1.8% 3.3% 8.4% 58 352,453,183 0.5% 0.9% 1.8% 3.3% 8.4% 59 343,766,869 0.5% 0.9% 1.8% 3.3% 8.3% 60 333,540,933 0.5% 0.9% 1.8% 3.3% 8.2% 61 321,761,913 0.5% 0.9% 1.9% 3.2% 8.2% 62 308,453,343 0.5% 0.9% 1.9% 3.2% 8.1% 63 293,682,397 0.5% 0.9% 1.9% 3.3% 8.1% 64 277,563,784 0.5% 0.9% 1.9% 3.3% 8.0% 65 260,260,447 0.5% 0.9% 1.9% 3.3% 8.0% 66 241,980,853 0.5% 0.9% 1.9% 3.3% 8.0% 67 222,972,943 0.5% 1.0% 2.0% 3.4% 8.1% 68 203,515,141 0.6% 1.0% 2.0% 3.4% 8.1% 69 183,905,073 0.6% 1.0% 2.1% 3.5% 8.2% 70 164,446,821 0.6% 1.1% 2.1% 3.6% 8.4% 71 145,437,633 0.6% 1.1% 2.2% 3.7% 8.5% 72 127,155,037 0.7% 1.2% 2.3% 3.8% 8.7% 73 109,845,265 0.7% 1.2% 2.4% 4.0% 8.9% 74 93,713,782 0.7% 1.3% 2.5% 4.2% 9.2% 75 78,918,535 0.8% 1.4% 2.7% 4.4% 9.6%
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