Good finding!Originally Posted by G Man
Sincerely,
Cac
k_cCode:_____8-8 v T, NDAS (split) HiLo RC indexes_____ 3/4 shoe 1/2 shoe 1/4 shoe Decks 1 p < 6 p < 5 unreliable 2 p < 11 p < 8 p < 5 3 p < 15 p < 11 p < 7 4 p < 19 p < 13 p < 8 5 p < 24 p < 16 p < 9 6 p < 28 p < 19 p < 11 7 p < 32 p < 22 p < 12 8 p < 36 p < 24 p < 13 _____8-8 v T, DAS (split) HiLo RC indexes______ 3/4 shoe 1/2 shoe 1/4 shoe Decks 1 p p < 7 unreliable 2 p < 16 p < 11 p < 7 3 p < 22 p < 15 p < 9 4 p < 28 p < 19 p < 11 5 p < 35 p < 23 p < 13 6 p < 41 p < 28 p < 15 7 p < 48 p < 32 p < 17 8 p < 54 p < 36 p < 19 ________8-8 v T (stand) HiLo RC indexes________ 3/4 shoe 1/2 shoe 1/4 shoe Decks 1 s >= 0 s >= 0 s >= 0 2 s >= 0 s >= 0 s >= 0 3 s >= 0 s >= 0 s >= 0 4 s >= 0 s >= 0 s >= 0 5 s >= 1 s >= 0 s >= 0 6 s >= 1 s >= 0 s >= 0 7 s >= 1 s >= 1 s >= 0 8 s >= 1 s >= 1 s >= 0
Hey Cac! Here are two examples from K_C’s CDCA. One is at 6D with 132 cards left, the other one at DD with 66 cards left in the shoe. In both cases the HiLo RC/TC is 0.
Attachments did not work so here are the deck compositions from 2 to A
66666/222/24/6
12-12-12-12-12/444/48/12
Using K_C's tool, I did explore all HiLo TCs from -6 to +6. At just about every TC, there is a ratio of 789/T that suggests not splitting 88 against Ten and 9. With 88 against any other upcard (except the ace in some cases) splitting between TC-6 and TC+6 is always the better move.
In short, I combine HiLo main indices with a second indice, the ratio of 789/Tens.
Now my question is not about finding out the exact frequency of the exact two subsets shown as not all TC0 with a ratio of 789/Tens below 25% are exactly the same, just like all TC +11 are not exactly identical.
Again, both cases are rare occurences but I believe the TC0/-25% happens more often than TC+11.
I just don’t know how to calculate the frequency of both situations. Maybe you do. Maybe it takes a very complex sim. I don’t know.
Hope it’s clearer now.
Thanks again for your interest. I hope to learn a little more about combinatorial analysis as the same process could apply to just about any situation when using double indices.
https://www.lasvegasadvisor.com/gamb...rategy-puzzle/
Awesome article !
"Don't Cast Your Pearls Before Swine" (Jesus)
I am at this stage still observing and playing mostly as a hobby, getting my feet wet, etc. Without specifying what I was watching, the site uses the same technique (Hi-Lo) for counting with the same basic strategy charts I've seen. I had not seen the 88v16 at tc 11 mentioned in this thread and when I saw this particular person stay at 88v10 at TC4 I had to check.
Looking at the different replies most seem to say similar things, but it seems overwhelming how much one can lose themselves in the statistics and probabilities and the math. For me, that's what makes Blackjack so interesting, exciting, and scary all at the same time.
Last edited by pbj; 10-11-2022 at 10:11 PM.
From what I am seeing it is not an easy task to analyze through combinatorial analysis. I can't promise you anything, maybe some 1D or 2D frequencies. 6D is impossible. Through a simulation is probably easier.
However, the degree of complexity of this system is too much for my taste. Not only do you have to keep counting through Hi-Lo, you also have to count the block of 789s and recount the tens.
On top of everything you have to calculate the ratio. It seems to me that it's too much.
On the other hand, who says that maintaining this secondary ratio is better than a secondary ace count? I suppose that if you are determined to use this system someone must have calculated
a SCORE or something, right? Anyway, I don't doubt that one can improve the efficiency of the game in some plays.
It's just my point of view.
Sincerely,
Cac
Hey Cac. If you could provide a frequency for DD that would be great.
As far as complexity, it's just a matter of training, skills and knowledge of the ratios.
There are some shorthands to simplify the process but it would be too long to explain.
I do count the aces. Basically it's a 4-count approach. HiLo/A/789/Tens
With that information you can see how easy it is to calculate the exact number of 23456s.
Now you know exactly how many Aces/789s/Tens/Lows are in the shoe.
Plus I get perfect insurance.
I don't have a SCORE yet as in order to get one, I need to do two things.
First, I have to clearly establish the Double Indices. (HiLo+ratio of 789/10s)
This part is mostly done thanks to KC's CDCA.
Second, I need a sim but besides Gronbog, and perhaps you, who can sim this HiLo Double Indice system?
Plus how do you derive double indices from a sim?
So I have to trust the CDCA with even distribution of 789s within the group.
My guess is that my SCORE will be on par with Tarzan Basic, Tarzan Advanced and Tarzan Ultimate
depending on addind key Cards to it or not.
Actually, Tarzan saw where I am getting at and told me that my results should be similar to his.
I am not saying that I can play at his level (a 5 to 7 counts process)
but my SCORE should be at least on par with Hi-Opt II and probably higher.
Bottom line is that, like Tarzan, I will deviate more often from basic strategy than a typical HiLo player.
The 88vT situation is just one example.
So 88vT at TC0 with a ratio of 789/Tens lower than 25% will probably happen more often than TC+11
I hope you can find a proper answer to this specific situation even if it doesn't correspond to your approach.
Thanks.
If you could articulate your criteria I may be able to help.
I could in theory generate every possible random shoe composition for a given number of cards remaining dealt from a given number of decks. My website isn't very organized but I do have a page that shows the number of random compositions for 1 or 2 decks
http://www.bjstrat.net/numSubsets_1_2.html.
I could theoretically display every subset for any given decks/cards remaining.
The greatest number of possible subsets occurs at mid-shoe. For single deck with 26 cards remaining there are 1868755 random compositions. For 2 decks with 52 cards remaining there are 375268773. I have a text file that list all 1868755 26 card
single deck compositions and their probabilities. At one point I tried displaying this on my website but there was too much data, so I gave up.
Placing conditions on what is displayed can reduce amount of data. For example out of the 1868755 26 card compositions for single deck there are 112695 with HiLo running count 0 and the sum of their probabilities is 0.124165.
If you can articulate your conditions I may be able to display them for you, probably for no more than 2 decks. This would only show the probability of your condition, not strategy gain or loss.
Here is a sample of 3 cards remaining dealt from a single deck. There are 220 compositions. First number is a reference number (1-220). Next 10 comma separated numbers are number of each rank (2,3,4,5,6,7,8,9,T,A). Last number (preceded by comma) is probability of composition (0.xxxxxxx). The sum of these probabilities is 1. There are no filtering conditions.
k_cCode:1 0,0,0,0,0,0,0,0,3,0,0.0253394 2 0,0,0,0,0,0,0,1,2,0,0.0217195 3 0,0,0,0,0,0,1,0,2,0,0.0217195 4 0,0,0,0,0,1,0,0,2,0,0.0217195 5 0,0,0,0,1,0,0,0,2,0,0.0217195 6 0,0,0,1,0,0,0,0,2,0,0.0217195 7 0,0,1,0,0,0,0,0,2,0,0.0217195 8 0,1,0,0,0,0,0,0,2,0,0.0217195 9 1,0,0,0,0,0,0,0,2,0,0.0217195 10 0,0,0,0,0,0,0,0,2,1,0.0217195 11 0,0,0,0,0,0,0,2,1,0,0.00434389 12 0,0,0,0,0,0,1,1,1,0,0.0115837 13 0,0,0,0,0,1,0,1,1,0,0.0115837 14 0,0,0,0,1,0,0,1,1,0,0.0115837 15 0,0,0,1,0,0,0,1,1,0,0.0115837 16 0,0,1,0,0,0,0,1,1,0,0.0115837 17 0,1,0,0,0,0,0,1,1,0,0.0115837 18 1,0,0,0,0,0,0,1,1,0,0.0115837 19 0,0,0,0,0,0,0,1,1,1,0.0115837 20 0,0,0,0,0,0,2,0,1,0,0.00434389 21 0,0,0,0,0,1,1,0,1,0,0.0115837 22 0,0,0,0,1,0,1,0,1,0,0.0115837 23 0,0,0,1,0,0,1,0,1,0,0.0115837 24 0,0,1,0,0,0,1,0,1,0,0.0115837 25 0,1,0,0,0,0,1,0,1,0,0.0115837 26 1,0,0,0,0,0,1,0,1,0,0.0115837 27 0,0,0,0,0,0,1,0,1,1,0.0115837 28 0,0,0,0,0,2,0,0,1,0,0.00434389 29 0,0,0,0,1,1,0,0,1,0,0.0115837 30 0,0,0,1,0,1,0,0,1,0,0.0115837 31 0,0,1,0,0,1,0,0,1,0,0.0115837 32 0,1,0,0,0,1,0,0,1,0,0.0115837 33 1,0,0,0,0,1,0,0,1,0,0.0115837 34 0,0,0,0,0,1,0,0,1,1,0.0115837 35 0,0,0,0,2,0,0,0,1,0,0.00434389 36 0,0,0,1,1,0,0,0,1,0,0.0115837 37 0,0,1,0,1,0,0,0,1,0,0.0115837 38 0,1,0,0,1,0,0,0,1,0,0.0115837 39 1,0,0,0,1,0,0,0,1,0,0.0115837 40 0,0,0,0,1,0,0,0,1,1,0.0115837 41 0,0,0,2,0,0,0,0,1,0,0.00434389 42 0,0,1,1,0,0,0,0,1,0,0.0115837 43 0,1,0,1,0,0,0,0,1,0,0.0115837 44 1,0,0,1,0,0,0,0,1,0,0.0115837 45 0,0,0,1,0,0,0,0,1,1,0.0115837 46 0,0,2,0,0,0,0,0,1,0,0.00434389 47 0,1,1,0,0,0,0,0,1,0,0.0115837 48 1,0,1,0,0,0,0,0,1,0,0.0115837 49 0,0,1,0,0,0,0,0,1,1,0.0115837 50 0,2,0,0,0,0,0,0,1,0,0.00434389 51 1,1,0,0,0,0,0,0,1,0,0.0115837 52 0,1,0,0,0,0,0,0,1,1,0.0115837 53 2,0,0,0,0,0,0,0,1,0,0.00434389 54 1,0,0,0,0,0,0,0,1,1,0.0115837 55 0,0,0,0,0,0,0,0,1,2,0.00434389 56 0,0,0,0,0,0,0,3,0,0,0.000180995 57 0,0,0,0,0,0,1,2,0,0,0.00108597 58 0,0,0,0,0,1,0,2,0,0,0.00108597 59 0,0,0,0,1,0,0,2,0,0,0.00108597 60 0,0,0,1,0,0,0,2,0,0,0.00108597 61 0,0,1,0,0,0,0,2,0,0,0.00108597 62 0,1,0,0,0,0,0,2,0,0,0.00108597 63 1,0,0,0,0,0,0,2,0,0,0.00108597 64 0,0,0,0,0,0,0,2,0,1,0.00108597 65 0,0,0,0,0,0,2,1,0,0,0.00108597 66 0,0,0,0,0,1,1,1,0,0,0.00289593 67 0,0,0,0,1,0,1,1,0,0,0.00289593 68 0,0,0,1,0,0,1,1,0,0,0.00289593 69 0,0,1,0,0,0,1,1,0,0,0.00289593 70 0,1,0,0,0,0,1,1,0,0,0.00289593 71 1,0,0,0,0,0,1,1,0,0,0.00289593 72 0,0,0,0,0,0,1,1,0,1,0.00289593 73 0,0,0,0,0,2,0,1,0,0,0.00108597 74 0,0,0,0,1,1,0,1,0,0,0.00289593 75 0,0,0,1,0,1,0,1,0,0,0.00289593 76 0,0,1,0,0,1,0,1,0,0,0.00289593 77 0,1,0,0,0,1,0,1,0,0,0.00289593 78 1,0,0,0,0,1,0,1,0,0,0.00289593 79 0,0,0,0,0,1,0,1,0,1,0.00289593 80 0,0,0,0,2,0,0,1,0,0,0.00108597 81 0,0,0,1,1,0,0,1,0,0,0.00289593 82 0,0,1,0,1,0,0,1,0,0,0.00289593 83 0,1,0,0,1,0,0,1,0,0,0.00289593 84 1,0,0,0,1,0,0,1,0,0,0.00289593 85 0,0,0,0,1,0,0,1,0,1,0.00289593 86 0,0,0,2,0,0,0,1,0,0,0.00108597 87 0,0,1,1,0,0,0,1,0,0,0.00289593 88 0,1,0,1,0,0,0,1,0,0,0.00289593 89 1,0,0,1,0,0,0,1,0,0,0.00289593 90 0,0,0,1,0,0,0,1,0,1,0.00289593 91 0,0,2,0,0,0,0,1,0,0,0.00108597 92 0,1,1,0,0,0,0,1,0,0,0.00289593 93 1,0,1,0,0,0,0,1,0,0,0.00289593 94 0,0,1,0,0,0,0,1,0,1,0.00289593 95 0,2,0,0,0,0,0,1,0,0,0.00108597 96 1,1,0,0,0,0,0,1,0,0,0.00289593 97 0,1,0,0,0,0,0,1,0,1,0.00289593 98 2,0,0,0,0,0,0,1,0,0,0.00108597 99 1,0,0,0,0,0,0,1,0,1,0.00289593 100 0,0,0,0,0,0,0,1,0,2,0.00108597 101 0,0,0,0,0,0,3,0,0,0,0.000180995 102 0,0,0,0,0,1,2,0,0,0,0.00108597 103 0,0,0,0,1,0,2,0,0,0,0.00108597 104 0,0,0,1,0,0,2,0,0,0,0.00108597 105 0,0,1,0,0,0,2,0,0,0,0.00108597 106 0,1,0,0,0,0,2,0,0,0,0.00108597 107 1,0,0,0,0,0,2,0,0,0,0.00108597 108 0,0,0,0,0,0,2,0,0,1,0.00108597 109 0,0,0,0,0,2,1,0,0,0,0.00108597 110 0,0,0,0,1,1,1,0,0,0,0.00289593 111 0,0,0,1,0,1,1,0,0,0,0.00289593 112 0,0,1,0,0,1,1,0,0,0,0.00289593 113 0,1,0,0,0,1,1,0,0,0,0.00289593 114 1,0,0,0,0,1,1,0,0,0,0.00289593 115 0,0,0,0,0,1,1,0,0,1,0.00289593 116 0,0,0,0,2,0,1,0,0,0,0.00108597 117 0,0,0,1,1,0,1,0,0,0,0.00289593 118 0,0,1,0,1,0,1,0,0,0,0.00289593 119 0,1,0,0,1,0,1,0,0,0,0.00289593 120 1,0,0,0,1,0,1,0,0,0,0.00289593 121 0,0,0,0,1,0,1,0,0,1,0.00289593 122 0,0,0,2,0,0,1,0,0,0,0.00108597 123 0,0,1,1,0,0,1,0,0,0,0.00289593 124 0,1,0,1,0,0,1,0,0,0,0.00289593 125 1,0,0,1,0,0,1,0,0,0,0.00289593 126 0,0,0,1,0,0,1,0,0,1,0.00289593 127 0,0,2,0,0,0,1,0,0,0,0.00108597 128 0,1,1,0,0,0,1,0,0,0,0.00289593 129 1,0,1,0,0,0,1,0,0,0,0.00289593 130 0,0,1,0,0,0,1,0,0,1,0.00289593 131 0,2,0,0,0,0,1,0,0,0,0.00108597 132 1,1,0,0,0,0,1,0,0,0,0.00289593 133 0,1,0,0,0,0,1,0,0,1,0.00289593 134 2,0,0,0,0,0,1,0,0,0,0.00108597 135 1,0,0,0,0,0,1,0,0,1,0.00289593 136 0,0,0,0,0,0,1,0,0,2,0.00108597 137 0,0,0,0,0,3,0,0,0,0,0.000180995 138 0,0,0,0,1,2,0,0,0,0,0.00108597 139 0,0,0,1,0,2,0,0,0,0,0.00108597 140 0,0,1,0,0,2,0,0,0,0,0.00108597 141 0,1,0,0,0,2,0,0,0,0,0.00108597 142 1,0,0,0,0,2,0,0,0,0,0.00108597 143 0,0,0,0,0,2,0,0,0,1,0.00108597 144 0,0,0,0,2,1,0,0,0,0,0.00108597 145 0,0,0,1,1,1,0,0,0,0,0.00289593 146 0,0,1,0,1,1,0,0,0,0,0.00289593 147 0,1,0,0,1,1,0,0,0,0,0.00289593 148 1,0,0,0,1,1,0,0,0,0,0.00289593 149 0,0,0,0,1,1,0,0,0,1,0.00289593 150 0,0,0,2,0,1,0,0,0,0,0.00108597 151 0,0,1,1,0,1,0,0,0,0,0.00289593 152 0,1,0,1,0,1,0,0,0,0,0.00289593 153 1,0,0,1,0,1,0,0,0,0,0.00289593 154 0,0,0,1,0,1,0,0,0,1,0.00289593 155 0,0,2,0,0,1,0,0,0,0,0.00108597 156 0,1,1,0,0,1,0,0,0,0,0.00289593 157 1,0,1,0,0,1,0,0,0,0,0.00289593 158 0,0,1,0,0,1,0,0,0,1,0.00289593 159 0,2,0,0,0,1,0,0,0,0,0.00108597 160 1,1,0,0,0,1,0,0,0,0,0.00289593 161 0,1,0,0,0,1,0,0,0,1,0.00289593 162 2,0,0,0,0,1,0,0,0,0,0.00108597 163 1,0,0,0,0,1,0,0,0,1,0.00289593 164 0,0,0,0,0,1,0,0,0,2,0.00108597 165 0,0,0,0,3,0,0,0,0,0,0.000180995 166 0,0,0,1,2,0,0,0,0,0,0.00108597 167 0,0,1,0,2,0,0,0,0,0,0.00108597 168 0,1,0,0,2,0,0,0,0,0,0.00108597 169 1,0,0,0,2,0,0,0,0,0,0.00108597 170 0,0,0,0,2,0,0,0,0,1,0.00108597 171 0,0,0,2,1,0,0,0,0,0,0.00108597 172 0,0,1,1,1,0,0,0,0,0,0.00289593 173 0,1,0,1,1,0,0,0,0,0,0.00289593 174 1,0,0,1,1,0,0,0,0,0,0.00289593 175 0,0,0,1,1,0,0,0,0,1,0.00289593 176 0,0,2,0,1,0,0,0,0,0,0.00108597 177 0,1,1,0,1,0,0,0,0,0,0.00289593 178 1,0,1,0,1,0,0,0,0,0,0.00289593 179 0,0,1,0,1,0,0,0,0,1,0.00289593 180 0,2,0,0,1,0,0,0,0,0,0.00108597 181 1,1,0,0,1,0,0,0,0,0,0.00289593 182 0,1,0,0,1,0,0,0,0,1,0.00289593 183 2,0,0,0,1,0,0,0,0,0,0.00108597 184 1,0,0,0,1,0,0,0,0,1,0.00289593 185 0,0,0,0,1,0,0,0,0,2,0.00108597 186 0,0,0,3,0,0,0,0,0,0,0.000180995 187 0,0,1,2,0,0,0,0,0,0,0.00108597 188 0,1,0,2,0,0,0,0,0,0,0.00108597 189 1,0,0,2,0,0,0,0,0,0,0.00108597 190 0,0,0,2,0,0,0,0,0,1,0.00108597 191 0,0,2,1,0,0,0,0,0,0,0.00108597 192 0,1,1,1,0,0,0,0,0,0,0.00289593 193 1,0,1,1,0,0,0,0,0,0,0.00289593 194 0,0,1,1,0,0,0,0,0,1,0.00289593 195 0,2,0,1,0,0,0,0,0,0,0.00108597 196 1,1,0,1,0,0,0,0,0,0,0.00289593 197 0,1,0,1,0,0,0,0,0,1,0.00289593 198 2,0,0,1,0,0,0,0,0,0,0.00108597 199 1,0,0,1,0,0,0,0,0,1,0.00289593 200 0,0,0,1,0,0,0,0,0,2,0.00108597 201 0,0,3,0,0,0,0,0,0,0,0.000180995 202 0,1,2,0,0,0,0,0,0,0,0.00108597 203 1,0,2,0,0,0,0,0,0,0,0.00108597 204 0,0,2,0,0,0,0,0,0,1,0.00108597 205 0,2,1,0,0,0,0,0,0,0,0.00108597 206 1,1,1,0,0,0,0,0,0,0,0.00289593 207 0,1,1,0,0,0,0,0,0,1,0.00289593 208 2,0,1,0,0,0,0,0,0,0,0.00108597 209 1,0,1,0,0,0,0,0,0,1,0.00289593 210 0,0,1,0,0,0,0,0,0,2,0.00108597 211 0,3,0,0,0,0,0,0,0,0,0.000180995 212 1,2,0,0,0,0,0,0,0,0,0.00108597 213 0,2,0,0,0,0,0,0,0,1,0.00108597 214 2,1,0,0,0,0,0,0,0,0,0.00108597 215 1,1,0,0,0,0,0,0,0,1,0.00289593 216 0,1,0,0,0,0,0,0,0,2,0.00108597 217 3,0,0,0,0,0,0,0,0,0,0.000180995 218 2,0,0,0,0,0,0,0,0,1,0.00108597 219 1,0,0,0,0,0,0,0,0,2,0.00108597 220 0,0,0,0,0,0,0,0,0,3,0.000180995
Thanks KC. I understand better your process and the nature of the task. Post 16 showed a 66-cards deck compo with a specific hand of 88v10 (66666/222/24/6) with me asking Cac how often we would see 88vT at DD with a 789/tens ratio of 25% or less with a least two 8s among the six neutral cards. That would be rare but would it happen more often than TC+11? That was a question about a specific hand in a specific condition.
Now in a more general way in order to elaborate the frequency of conditions, let’s do it at the 52-card depth (or as close as possible) of a double deck game. You eloquently showed that it’s way more reasonable for the task at hand.
At TC0 (see table below). the only variable is the group of 789s (3 cards at a time) but it doesn’t necessarily add up to 52 cards exactly depending on if there is a shortage or surplus of 789s. So deck compos vary from 43 to 64 cards at TC0. The number of cards would change even more if we do the range from TC-6 to TC+6.
So here what would be the conditions at TC0. Add/substract one ten per TC from TC-6 to TC+6.
Is this workable and how do you establish the frequency of specific hands such as 88vT from this?
2 3 4 5 6 7 8 9 T A Cards RC 789/T DECKS
4 4 4 4 4 4 4 4 16 4 52 0 0.750 1.00
4 4 4 4 4 3 3 3 16 4 49 0 0.563 0.94
4 4 4 4 4 2 2 2 16 4 46 0 0.375 0.88
4 4 4 4 4 1 1 1 16 4 43 0 0.188 0.83
4 4 4 4 4 5 5 5 16 4 55 0 0.938 1.06
4 4 4 4 4 6 6 6 16 4 58 0 1.125 1.12
4 4 4 4 4 7 7 7 16 4 61 0 1.313 1.17
4 4 4 4 4 8 8 8 16 4 64 0 1.500 1.23
Last edited by Secretariat; 10-13-2022 at 08:06 PM.
Secretariat:
This is my analysis for 1D and 2D up to 75% penetration, that is 39/52 and 78/104. The counting system used was Hi-Lo.
All subsets were analyzed up to the predetermined penetration and all possible TCs and their respective frequencies were calculated.
Within each TC, the frequencies of three different ratios (789/T) were analyzed. Each, in turn, was divided into two columns:
Column 1:
1) ratios <= 0.25
2) 0.25 < ratios <= 0.50
3) 0.50 < ratios <= 0.75
Column 2:
Within each ratio, it was also calculated how much each represents within each TC.
1) Single Deck
1) Double DeckCode:+------+-----------------+---------------------------------+---------------------------------+---------------------------------+ | TC | Probability | Ratio <= 0.25 | 0.25 < Ratio <= 0.50 | 0.50 < Ratio <= 0.75 | +------+-----------------+---------------------------------+---------------------------------+---------------------------------+ | 52 | 0.000000000664 | 0.000000000664 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 49 | 0.000000000009 | 0.000000000009 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 48 | 0.000000016673 | 0.000000016673 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 47 | 0.000000000000 | 0.000000000000 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 46 | 0.000000000235 | 0.000000000235 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 45 | 0.000000042115 | 0.000000042115 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 44 | 0.000000143051 | 0.000000143051 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 43 | 0.000000003198 | 0.000000002621 0.819445586225 | 0.000000000577 0.180554413775 | 0.000000000000 0.000000000000 | | 42 | 0.000000079645 | 0.000000035082 0.440482404036 | 0.000000044563 0.559517595964 | 0.000000000000 0.000000000000 | | 41 | 0.000000270618 | 0.000000111276 0.411191532531 | 0.000000159342 0.588808467469 | 0.000000000000 0.000000000000 | | 40 | 0.000000998393 | 0.000000451163 0.451888974579 | 0.000000547230 0.548111025421 | 0.000000000000 0.000000000000 | | 39 | 0.000000542369 | 0.000000340221 0.627286614431 | 0.000000202148 0.372713385569 | 0.000000000000 0.000000000000 | | 38 | 0.000001548535 | 0.000001055862 0.681845331259 | 0.000000460273 0.297231205664 | 0.000000032401 0.020923463076 | | 37 | 0.000005058793 | 0.000003400194 0.672135547629 | 0.000001266830 0.250421473882 | 0.000000391768 0.077442978489 | | 36 | 0.000000672005 | 0.000000156841 0.233392085988 | 0.000000455853 0.678348217464 | 0.000000059311 0.088259696548 | | 35 | 0.000002371404 | 0.000000529051 0.223095958199 | 0.000001561772 0.658585387607 | 0.000000280581 0.118318654194 | | 34 | 0.000007611767 | 0.000001975282 0.259503720428 | 0.000004762362 0.625657905270 | 0.000000837834 0.110070912378 | | 33 | 0.000022470099 | 0.000006856023 0.305117618298 | 0.000013481505 0.599975344792 | 0.000001700129 0.075661848507 | | 32 | 0.000010091052 | 0.000004437261 0.439722378167 | 0.000004784040 0.474087329109 | 0.000000728286 0.072171511826 | | 31 | 0.000029171857 | 0.000012831762 0.439867852984 | 0.000011473152 0.393295232694 | 0.000004237797 0.145270026987 | | 30 | 0.000015461288 | 0.000002458850 0.159032662002 | 0.000009523446 0.615954249631 | 0.000003286625 0.212571228873 | | 29 | 0.000093418921 | 0.000031296974 0.335017508063 | 0.000037815971 0.404799906800 | 0.000021486318 0.229999635652 | | 28 | 0.000019924117 | 0.000004704920 0.236141949302 | 0.000011860267 0.595271907781 | 0.000002930714 0.147093792988 | | 27 | 0.000129708145 | 0.000027150456 0.209319590188 | 0.000075217044 0.579894529747 | 0.000021331596 0.164458415830 | | 26 | 0.000315660493 | 0.000074158663 0.234931722142 | 0.000168264841 0.533056384683 | 0.000049611560 0.157167467474 | | 25 | 0.000000616073 | 0.000000005843 0.009484683209 | 0.000000423890 0.688050834502 | 0.000000175373 0.284662439371 | | 24 | 0.000353589521 | 0.000081020636 0.229137548019 | 0.000149714313 0.423412754875 | 0.000100808202 0.285099517581 | | 23 | 0.000177805244 | 0.000030736020 0.172863407601 | 0.000094912073 0.533797943111 | 0.000040049301 0.225242521194 | | 22 | 0.000682357135 | 0.000114742086 0.168155471621 | 0.000293070089 0.429496629125 | 0.000204740598 0.300049032381 | | 21 | 0.000416739404 | 0.000072068434 0.172934051639 | 0.000195198212 0.468393941542 | 0.000109816881 0.263514513065 | | 20 | 0.000881599564 | 0.000097696068 0.110816828636 | 0.000460005156 0.521784691011 | 0.000225691771 0.256002589403 | | 19 | 0.000910037799 | 0.000167485632 0.184042500369 | 0.000368533805 0.404965381838 | 0.000268981597 0.295571895553 | | 18 | 0.001910374915 | 0.000211284890 0.110598651662 | 0.000930908379 0.487290935510 | 0.000480403299 0.251470690781 | | 17 | 0.001809689511 | 0.000263364911 0.145530440213 | 0.000661094014 0.365307977134 | 0.000623884960 0.344746961441 | | 16 | 0.002046837880 | 0.000129422794 0.063230603057 | 0.000955063253 0.466604249565 | 0.000621924876 0.303846671011 | | 15 | 0.002223757171 | 0.000268767122 0.120861722588 | 0.000839714904 0.377610880997 | 0.000777417010 0.349596178924 | | 14 | 0.004273385492 | 0.000221674151 0.051873193084 | 0.001693499914 0.396289994613 | 0.001540253655 0.360429373392 | | 13 | 0.006754910124 | 0.000566277861 0.083832034910 | 0.002430554441 0.359820396744 | 0.002366928584 0.350401195672 | | 12 | 0.004287524116 | 0.000224054560 0.052257329302 | 0.001715986854 0.400227918839 | 0.001448329697 0.337800944870 | | 11 | 0.007545408185 | 0.000638647581 0.084640560907 | 0.002389478290 0.316679791444 | 0.002900406384 0.384393569254 | | 10 | 0.010286781948 | 0.000421425052 0.040967627589 | 0.003383401399 0.328907661917 | 0.003972450319 0.386170362993 | | 9 | 0.012616971866 | 0.000579707897 0.045946674336 | 0.003726324514 0.295342222615 | 0.005112762203 0.405228945391 | | 8 | 0.014641456886 | 0.000462164998 0.031565506212 | 0.003952561390 0.269956836980 | 0.006496780382 0.443724994918 | | 7 | 0.018900523261 | 0.000398150274 0.021065568841 | 0.005083720437 0.268972470564 | 0.007977766476 0.422092360396 | | 6 | 0.027868413882 | 0.000850381557 0.030514171382 | 0.006986084360 0.250681089697 | 0.011552725645 0.414545502812 | | 5 | 0.028993410471 | 0.000628467895 0.021676232116 | 0.005385488200 0.185748696416 | 0.013903497504 0.479539911953 | | 4 | 0.038536406680 | 0.000409063290 0.010614982696 | 0.006362929971 0.165114771176 | 0.020507950150 0.532170794245 | | 3 | 0.052524728761 | 0.001082918537 0.020617308496 | 0.007744213737 0.147439385586 | 0.025515570410 0.485782049933 | | 2 | 0.075565383662 | 0.000895143349 0.011845944607 | 0.008563775623 0.113329347485 | 0.040414512138 0.534828385433 | | 1 | 0.098316857699 | 0.000127818714 0.001300069151 | 0.006312589583 0.064206584006 | 0.057893809655 0.588849267660 | | 0 | 0.173638334617 | 0.001597615381 0.009200821836 | 0.014764047487 0.085027580572 | 0.089617667926 0.516116836319 | | -2 | 0.101351781972 | 0.000094272420 0.000930150596 | 0.004639574184 0.045776937456 | 0.040613847141 0.400721589214 | | -3 | 0.072530459389 | 0.000626131061 0.008632663654 | 0.005308150956 0.073185128029 | 0.022115150712 0.304908460507 | | -4 | 0.057227968852 | 0.000945171169 0.016515895780 | 0.004666664266 0.081545166811 | 0.015508039958 0.270987076237 | | -5 | 0.033833166588 | 0.000215020046 0.006355303609 | 0.002556400309 0.075559002212 | 0.008278820238 0.244695400194 | | -6 | 0.031060137217 | 0.000187254532 0.006028773496 | 0.002587499616 0.083306123148 | 0.007552175849 0.243146892616 | | -7 | 0.025801687136 | 0.000620431750 0.024046169815 | 0.002071499885 0.080285443104 | 0.006042261018 0.234180849751 | | -8 | 0.020730459196 | 0.000198464334 0.009573561876 | 0.002303000244 0.111092582293 | 0.003669829287 0.177025952598 | | -9 | 0.012811520951 | 0.000139306121 0.010873503763 | 0.000931830887 0.072733822226 | 0.002515886338 0.196376866401 | | -10 | 0.013568393226 | 0.000256436560 0.018899552465 | 0.001218831577 0.089828733306 | 0.002387878426 0.175988297647 | | -11 | 0.009335360588 | 0.000107397492 0.011504375370 | 0.001049418391 0.112413267962 | 0.001350858693 0.144703429519 | | -12 | 0.008114786524 | 0.000286215698 0.035270884432 | 0.000604336538 0.074473498050 | 0.001149948378 0.141710243996 | | -13 | 0.007022003107 | 0.000141757357 0.020187595269 | 0.000567981241 0.080885928463 | 0.001206053760 0.171753521309 | | -14 | 0.003742574672 | 0.000143620998 0.038374918589 | 0.000264218949 0.070598177036 | 0.000429794833 0.114839347364 | | -15 | 0.003981863613 | 0.000092925596 0.023337212231 | 0.000301351849 0.075681107694 | 0.000790265163 0.198466155591 | | -16 | 0.002361297217 | 0.000010753992 0.004554272797 | 0.000273613377 0.115874179476 | 0.000126686170 0.053651090359 | | -17 | 0.001909297834 | 0.000086240887 0.045168902316 | 0.000045648779 0.023908673484 | 0.000371699274 0.194678518803 | | -18 | 0.001867628348 | 0.000019915001 0.010663257020 | 0.000225954927 0.120984952426 | 0.000184636405 0.098861427653 | | -19 | 0.001852436078 | 0.000088664460 0.047863708194 | 0.000111185117 0.060021027551 | 0.000175193873 0.094574854957 | | -20 | 0.000931739716 | 0.000010000255 0.010732884524 | 0.000090161521 0.096766853503 | 0.000111240242 0.119389825261 | | -21 | 0.000859897646 | 0.000034059002 0.039608204294 | 0.000056443106 0.065639331024 | 0.000045850028 0.053320332348 | | -22 | 0.000423914934 | 0.000006576832 0.015514507799 | 0.000025683382 0.060586170394 | 0.000056032864 0.132179501189 | | -23 | 0.000675181605 | 0.000022283300 0.033003416322 | 0.000018904728 0.027999471822 | 0.000094071554 0.139327780047 | | -24 | 0.000179881837 | 0.000001873557 0.010415487127 | 0.000010629371 0.059090852387 | 0.000018650699 0.103683055930 | | -25 | 0.000351512928 | 0.000008368538 0.023807197433 | 0.000008723157 0.024816035847 | 0.000045234775 0.128685948825 | | -26 | 0.000316150226 | 0.000002641104 0.008353952589 | 0.000036100532 0.114187905269 | 0.000017155120 0.054262559130 | | -27 | 0.000000126340 | 0.000000000023 0.000185634392 | 0.000000000002 0.000012035636 | 0.000000002752 0.021781101946 | | -28 | 0.000129819473 | 0.000000744645 0.005736005958 | 0.000012716920 0.097958494936 | 0.000005889582 0.045367473493 | | -29 | 0.000019812788 | 0.000000185000 0.009337423528 | 0.000000167800 0.008469295239 | 0.000001816974 0.091707155004 | | -30 | 0.000093438884 | 0.000002780171 0.029753898476 | 0.000003922752 0.041982005832 | 0.000000016745 0.000179212515 | | -31 | 0.000015441324 | 0.000000027597 0.001787197075 | 0.000001135570 0.073540948993 | 0.000000482753 0.031263687265 | | -32 | 0.000029174782 | 0.000000823862 0.028238832515 | 0.000000291289 0.009984287696 | 0.000000116783 0.004002863012 | | -33 | 0.000010088127 | 0.000000218652 0.021674195240 | 0.000000065015 0.006444668517 | 0.000000023915 0.002370652460 | | -34 | 0.000022470436 | 0.000000051541 0.002293737588 | 0.000003518083 0.156564978784 | 0.000000004504 0.000200429903 | | -35 | 0.000007611430 | 0.000000010583 0.001390466111 | 0.000001039794 0.136609589007 | 0.000000000044 0.000005840220 | | -36 | 0.000002371433 | 0.000000001848 0.000779342954 | 0.000000276421 0.116562923912 | 0.000000000002 0.000000836829 | | -37 | 0.000000671976 | 0.000000000264 0.000392204586 | 0.000000065232 0.097074756634 | 0.000000000000 0.000000000000 | | -38 | 0.000005058794 | 0.000000336001 0.066419226049 | 0.000000013415 0.002651867791 | 0.000000000000 0.000000000000 | | -39 | 0.000001981606 | 0.000000099258 0.050089751544 | 0.000000002677 0.001350832202 | 0.000000000000 0.000000000000 | | -40 | 0.000000109296 | 0.000000003333 0.030496132408 | 0.000000000037 0.000334321104 | 0.000000000000 0.000000000000 | | -41 | 0.000000998393 | 0.000000000536 0.000536540992 | 0.000000000003 0.000002838845 | 0.000000000000 0.000000000000 | | -42 | 0.000000270618 | 0.000000000078 0.000286565923 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -43 | 0.000000079645 | 0.000000000001 0.000006389748 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -44 | 0.000000003198 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -45 | 0.000000143051 | 0.000000017978 0.125677862694 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -46 | 0.000000042115 | 0.000000004253 0.100978499619 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -47 | 0.000000000235 | 0.000000000012 0.051255629573 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -48 | 0.000000000000 | 0.000000000000 0.011537030145 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -49 | 0.000000016673 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -50 | 0.000000000009 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -52 | 0.000000000664 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | +------+-----------------+---------------------------------+---------------------------------+---------------------------------+
Code:+------+-----------------+---------------------------------+---------------------------------+---------------------------------+ | TC | Probability | Ratio <= 0.25 | 0.25 < Ratio <= 0.50 | 0.50 < Ratio <= 0.75 | +------+-----------------+---------------------------------+---------------------------------+---------------------------------+ | 52 | 0.000000000000 | 0.000000000000 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 50 | 0.000000000000 | 0.000000000000 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 49 | 0.000000000000 | 0.000000000000 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 48 | 0.000000000000 | 0.000000000000 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 47 | 0.000000000000 | 0.000000000000 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 46 | 0.000000000000 | 0.000000000000 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 45 | 0.000000000000 | 0.000000000000 1.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | 44 | 0.000000000004 | 0.000000000004 0.997239636658 | 0.000000000000 0.002760363342 | 0.000000000000 0.000000000000 | | 43 | 0.000000000002 | 0.000000000002 0.775007534328 | 0.000000000001 0.224992465672 | 0.000000000000 0.000000000000 | | 42 | 0.000000000033 | 0.000000000022 0.663302546401 | 0.000000000011 0.336697453599 | 0.000000000000 0.000000000000 | | 41 | 0.000000000017 | 0.000000000013 0.741689759821 | 0.000000000004 0.258310240179 | 0.000000000000 0.000000000000 | | 40 | 0.000000000224 | 0.000000000172 0.764988257021 | 0.000000000053 0.235011742979 | 0.000000000000 0.000000000000 | | 39 | 0.000000000399 | 0.000000000176 0.440505913909 | 0.000000000223 0.559278286101 | 0.000000000000 0.000215799990 | | 38 | 0.000000001099 | 0.000000000490 0.446137221401 | 0.000000000606 0.551614609857 | 0.000000000002 0.002248168742 | | 37 | 0.000000001949 | 0.000000001105 0.567028948154 | 0.000000000814 0.417632122878 | 0.000000000030 0.015338928968 | | 36 | 0.000000005389 | 0.000000002761 0.512325773670 | 0.000000002498 0.463425058428 | 0.000000000131 0.024249167902 | | 35 | 0.000000009849 | 0.000000002906 0.295074712293 | 0.000000006723 0.682672609623 | 0.000000000219 0.022237255179 | | 34 | 0.000000032190 | 0.000000011138 0.346025105278 | 0.000000019809 0.615401244633 | 0.000000001232 0.038265105988 | | 33 | 0.000000031776 | 0.000000011925 0.375281625056 | 0.000000017698 0.556965636979 | 0.000000002113 0.066487892166 | | 32 | 0.000000122906 | 0.000000036052 0.293332676609 | 0.000000077850 0.633412827843 | 0.000000008783 0.071462664184 | | 31 | 0.000000158775 | 0.000000038442 0.242117403540 | 0.000000107492 0.677010524568 | 0.000000012523 0.078870319821 | | 30 | 0.000000433868 | 0.000000102045 0.235197810993 | 0.000000283542 0.653520645586 | 0.000000046687 0.107606772177 | | 29 | 0.000000566365 | 0.000000123463 0.217992538857 | 0.000000367516 0.648903814121 | 0.000000071797 0.126767578946 | | 28 | 0.000001385428 | 0.000000260195 0.187808391118 | 0.000000923274 0.666417847964 | 0.000000190136 0.137239794581 | | 27 | 0.000001641055 | 0.000000277036 0.168815931501 | 0.000001084193 0.660668093526 | 0.000000264549 0.161206358986 | | 26 | 0.000008422364 | 0.000001308277 0.155333727606 | 0.000005351530 0.635395280458 | 0.000001623337 0.192741312084 | | 25 | 0.000010203587 | 0.000001214350 0.119012106156 | 0.000006659277 0.652640750000 | 0.000002092865 0.205110668283 | | 24 | 0.000011862547 | 0.000001489724 0.125582129683 | 0.000007146272 0.602423064592 | 0.000002924345 0.246519119727 | | 23 | 0.000026158219 | 0.000003260565 0.124647809069 | 0.000014952304 0.571610161214 | 0.000007046065 0.269363337633 | | 22 | 0.000034651452 | 0.000002788778 0.080480835826 | 0.000021431017 0.618473840029 | 0.000009130875 0.263506264441 | | 21 | 0.000069673511 | 0.000005207433 0.074740504579 | 0.000041527944 0.596036327146 | 0.000019656615 0.282124646430 | | 20 | 0.000089702667 | 0.000007439167 0.082931395106 | 0.000048204402 0.537379813171 | 0.000029376998 0.327493025993 | | 19 | 0.000174982987 | 0.000014379279 0.082175299021 | 0.000088980395 0.508508834103 | 0.000059905415 0.342349939480 | | 18 | 0.000179608240 | 0.000008633239 0.048067056761 | 0.000096122405 0.535178147952 | 0.000061686253 0.343448905401 | | 17 | 0.000387560120 | 0.000019122681 0.049341199579 | 0.000194875834 0.502827364026 | 0.000139179104 0.359116163463 | | 16 | 0.000580667862 | 0.000027349022 0.047099252077 | 0.000270667322 0.466131053875 | 0.000226506697 0.390079616223 | | 15 | 0.000817258634 | 0.000040020473 0.048969164813 | 0.000351997816 0.430705533825 | 0.000333020034 0.407484265418 | | 14 | 0.001112359132 | 0.000037634558 0.033833100052 | 0.000463696120 0.416858284823 | 0.000474599453 0.426660274833 | | 13 | 0.002210715002 | 0.000069944716 0.031638956715 | 0.000875868358 0.396192343780 | 0.000944256943 0.427127396366 | | 12 | 0.002061321482 | 0.000048208228 0.023387049485 | 0.000743459738 0.360671416183 | 0.000959592330 0.465522888482 | | 11 | 0.003698825450 | 0.000085370120 0.023080332213 | 0.001282028193 0.346604134268 | 0.001682083511 0.454761527339 | | 10 | 0.004747368409 | 0.000087817795 0.018498205218 | 0.001465819710 0.308764684694 | 0.002331571101 0.491129168815 | | 9 | 0.006902876047 | 0.000107032444 0.015505485417 | 0.001939465848 0.280964895620 | 0.003450319286 0.499837931686 | | 8 | 0.009864559724 | 0.000112287780 0.011382949019 | 0.002494221142 0.252846676591 | 0.005114762965 0.518498859331 | | 7 | 0.013788715683 | 0.000157699929 0.011436883091 | 0.003116164101 0.225993788886 | 0.007158142643 0.519130483782 | | 6 | 0.018082851676 | 0.000108147163 0.005980647562 | 0.003411565179 0.188663007378 | 0.010013249695 0.553742842935 | | 5 | 0.027286425722 | 0.000189715005 0.006952724670 | 0.004458493532 0.163396026207 | 0.014977180422 0.548887588817 | | 4 | 0.035805426803 | 0.000111044034 0.003101318551 | 0.004357719843 0.121705569013 | 0.020899449224 0.583695017498 | | 3 | 0.051405396461 | 0.000199703050 0.003884865477 | 0.005379455403 0.104647678522 | 0.029137907340 0.566825846037 | | 2 | 0.069004460823 | 0.000073492621 0.001065041602 | 0.004463927841 0.064690424176 | 0.041148071580 0.596310312245 | | 1 | 0.113333602550 | 0.000235872065 0.002081219157 | 0.006156096868 0.054318372744 | 0.065118899866 0.574577163356 | | 0 | 0.200128106169 | 0.000196408615 0.000981414449 | 0.006715965775 0.033558333727 | 0.112466834836 0.561974212365 | | -1 | 0.077579012427 | 0.000001859752 0.000023972356 | 0.001045493511 0.013476499359 | 0.034690971048 0.447169536740 | | -2 | 0.114232001076 | 0.000177477839 0.001553661294 | 0.004383735761 0.038375724141 | 0.041451110360 0.362867760083 | | -3 | 0.067909151401 | 0.000042944782 0.000632385791 | 0.002249423398 0.033124009825 | 0.022068959903 0.324977701055 | | -4 | 0.053310202931 | 0.000099804976 0.001872155250 | 0.002515516390 0.047186396821 | 0.015673275400 0.294001420716 | | -5 | 0.033605045277 | 0.000042123082 0.001253474946 | 0.001394777026 0.041504988738 | 0.008861641279 0.263699727413 | | -6 | 0.027231417285 | 0.000080511881 0.002956580647 | 0.001448623614 0.053196776318 | 0.006740502251 0.247526677768 | | -7 | 0.017863451835 | 0.000034237312 0.001916612302 | 0.000848878515 0.047520407750 | 0.004055425847 0.227023639332 | | -8 | 0.014234528319 | 0.000039304334 0.002761196776 | 0.000751001759 0.052759160117 | 0.003037511292 0.213390371920 | | -9 | 0.009232425873 | 0.000024697147 0.002675044170 | 0.000475935435 0.051550420430 | 0.001783913925 0.193222664252 | | -10 | 0.006845385420 | 0.000024914702 0.003639634704 | 0.000340331010 0.049716851414 | 0.001271206135 0.185702638645 | | -11 | 0.004707590464 | 0.000011278055 0.002395717165 | 0.000223123239 0.047396484691 | 0.000805704058 0.171149989360 | | -12 | 0.003815907270 | 0.000016830287 0.004410559653 | 0.000207591461 0.054401599901 | 0.000612670871 0.160557064825 | | -13 | 0.002690671221 | 0.000009383219 0.003487315428 | 0.000130700101 0.048575277370 | 0.000409653180 0.152249437449 | | -14 | 0.001416079361 | 0.000007141066 0.005042842779 | 0.000057699160 0.040745711037 | 0.000203139410 0.143451995698 | | -15 | 0.001107898619 | 0.000003928524 0.003545923708 | 0.000045935378 0.041461715737 | 0.000149456305 0.134900704798 | | -16 | 0.000840764529 | 0.000002982463 0.003547322576 | 0.000041552402 0.049422164060 | 0.000094510782 0.112410524462 | | -17 | 0.000553880487 | 0.000002329723 0.004206183093 | 0.000023733269 0.042849078875 | 0.000059374708 0.107197688921 | | -18 | 0.000387094877 | 0.000001597328 0.004126450977 | 0.000014175268 0.036619622229 | 0.000042363644 0.109439950216 | | -19 | 0.000179414613 | 0.000000596968 0.003327308662 | 0.000004603309 0.025657380215 | 0.000018459316 0.102886357146 | | -20 | 0.000177714578 | 0.000000761095 0.004282683122 | 0.000007596672 0.042746478433 | 0.000013546763 0.076227643074 | | -21 | 0.000086867757 | 0.000000308866 0.003555590698 | 0.000003295329 0.037935009140 | 0.000005743748 0.066120598222 | | -22 | 0.000069664028 | 0.000000142007 0.002038460441 | 0.000002538025 0.036432359254 | 0.000004228240 0.060694731781 | | -23 | 0.000034648420 | 0.000000053412 0.001541534893 | 0.000001074380 0.031008061292 | 0.000001849246 0.053371731657 | | -24 | 0.000026331339 | 0.000000130814 0.004968014610 | 0.000000784469 0.029792215691 | 0.000001869783 0.071009781751 | | -25 | 0.000011688273 | 0.000000048679 0.004164801861 | 0.000000307609 0.026317715622 | 0.000000746258 0.063846734775 | | -26 | 0.000014731638 | 0.000000030217 0.002051130775 | 0.000000506703 0.034395564348 | 0.000000429284 0.029140262098 | | -27 | 0.000003894234 | 0.000000025451 0.006535675272 | 0.000000051588 0.013247152314 | 0.000000297450 0.076382183043 | | -28 | 0.000001646839 | 0.000000008721 0.005295822006 | 0.000000017592 0.010682023439 | 0.000000111920 0.067960430187 | | -29 | 0.000001379640 | 0.000000003837 0.002780969959 | 0.000000042396 0.030729736951 | 0.000000050560 0.036647566421 | | -30 | 0.000000566365 | 0.000000001207 0.002131395686 | 0.000000014790 0.026114556954 | 0.000000017287 0.030522184957 | | -31 | 0.000000433868 | 0.000000003441 0.007931769055 | 0.000000005377 0.012392517290 | 0.000000026322 0.060667381088 | | -32 | 0.000000158870 | 0.000000001004 0.006321000368 | 0.000000002057 0.012944916063 | 0.000000007695 0.048433408764 | | -33 | 0.000000122811 | 0.000000000519 0.004226763993 | 0.000000002800 0.022796740531 | 0.000000005947 0.048422480843 | | -34 | 0.000000031776 | 0.000000000064 0.002019468523 | 0.000000000849 0.026707980283 | 0.000000001116 0.035117483540 | | -35 | 0.000000032190 | 0.000000000214 0.006633900805 | 0.000000000600 0.018633082630 | 0.000000000416 0.012914549804 | | -36 | 0.000000009849 | 0.000000000071 0.007190247430 | 0.000000000127 0.012873043304 | 0.000000000030 0.003050102673 | | -37 | 0.000000005389 | 0.000000000021 0.003843071898 | 0.000000000008 0.001551574941 | 0.000000000307 0.057003423766 | | -38 | 0.000000001949 | 0.000000000005 0.002752227688 | 0.000000000000 0.000224819650 | 0.000000000110 0.056685852733 | | -39 | 0.000000001390 | 0.000000000000 0.000217709927 | 0.000000000047 0.033858278950 | 0.000000000008 0.005610074373 | | -40 | 0.000000000107 | 0.000000000000 0.000021709435 | 0.000000000003 0.026996815342 | 0.000000000000 0.000785113912 | | -41 | 0.000000000224 | 0.000000000001 0.006680635657 | 0.000000000000 0.000653548089 | 0.000000000000 0.000013602017 | | -42 | 0.000000000017 | 0.000000000000 0.004502826862 | 0.000000000000 0.000054923862 | 0.000000000000 0.000000595462 | | -43 | 0.000000000033 | 0.000000000000 0.000016454331 | 0.000000000002 0.054908909722 | 0.000000000000 0.000000000024 | | -44 | 0.000000000002 | 0.000000000000 0.000000836519 | 0.000000000000 0.041696755935 | 0.000000000000 0.000000000000 | | -45 | 0.000000000004 | 0.000000000000 0.017380866392 | 0.000000000000 0.000025524972 | 0.000000000000 0.000000000000 | | -46 | 0.000000000000 | 0.000000000000 0.010488459227 | 0.000000000000 0.000000057238 | 0.000000000000 0.000000000000 | | -47 | 0.000000000000 | 0.000000000000 0.000000082089 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -48 | 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -49 | 0.000000000000 | 0.000000000000 0.060273957907 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -50 | 0.000000000000 | 0.000000000000 0.022742940815 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -51 | 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | | -52 | 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | 0.000000000000 0.000000000000 | +------+-----------------+---------------------------------+---------------------------------+---------------------------------+
Enjoy!
Sincerely,
Cac
This is awesome Cac and this is a smart way to break it down.
The frequency within each TC is really helpful.
I will take a close look at those numbers and keep them close.
Just one quick question.
1) If we were to do the same process with a surplus of 789s.
Would the frequencies at ratios 1.0 and 1.25 be similar to .50 and .25 respectively?
Last edited by Secretariat; 10-13-2022 at 10:05 PM.
Yes, I can do those calculations but first I have some doubts based on the examples you posted:
2D) 6 6 6 6 6 6 2 2 2 24 = 66 cards remaining
6D) 12 12 12 12 12 12 4 4 4 48 = 132 cards remaining
In both cases we have TC zero which is fine but I am not clear about the ratio.
In the posted tables, I calculated the ratio as follows:
2D) ratio = (2 + 2 + 2) / 24 = 0.33
6D) ratio = (4 + 4 + 4) / 48 = 0.25
But this is based on the remaining composition and not on the cards that we've already seen.
I understand that we have to keep two counts, one of 789s and another of Tens that have already
been seen and not that are left in the pack.
For me this is the calculation that should be done in the two examples:
2D) ratio = (6 + 6 + 6) / 8 = 2.25
6D) ratio = (20 + 20 + 20) / 48 = 1.25
Or, instead of calculating the ratio as 789/T do it the other way around as T/789
2D) ratio = 8 / (6 + 6 + 6) = 0.44
6D) ratio = 48 / (20 + 20 + 20) = 0.80
What do you think? I'll be looking forward to your response.
Sincerely,
Cac
Posting Permissions
Reply With Quote
Bookmarks