The cost of systematically using an index to generously
This is a true count frequency chart for HILO 8 decks cut 1.5 (Blackjack Attack ed3 p217):
TC +10 or higher, 0.14% 0.14% cumulative
TC +9, 0.10% 0.24% cumulative
TC +8, 0.24% 0.48% cum
TC +7, 0.32% 0.8% cum
TC +6, 0.73% 1.53% cum
TC +5, 1.03% 2.56% cum
TC +4, 2.23% 4.79% cum
TC +3, 3.27% 8.06%cum
TC +2, 6.95% 15.01% cum
TC +1, 11.33% 26.34% cum
TC 0, 27.63% 53.97% cum
TC less than 0, 46.03% 100% cum
Notice the cumulative frequencies as compared to the frequency on the next lowest TC (line below it). They are almost equal for high TC. If we assume linearity of gain in the table above an index of +8 has a frequency of 0.48% of proper use. If you have a systematic error that has you us it at +7 the frequency you use it at disadvantage is 0.32%. If the index is +8 exactly with the assumption of linear gain you can subtract TC +8 frequency from TC +7 as equal advantage and disadvantage. That leaves a frequency of 0.16 of disadvantage you still have to make up. If we assume the TC +9 has twice the advantage you divide this frequency by 2 to have 0.08%, subtract it from 0.10%, the frequency of TC +9, thats 4/5 of the advantage at TC +9. By making this mistake the closest equivalent TC index to +7 rather than +8 (our systematic mistake) is +10. You have given away most of your advantage for this index by being too aggressive.
The mistake always using a TC index of +8 at TC +7 instead of +8 is almost the same net gain in advantage as using a TC index of TC +10. This is a very costly mistake at your highest bets that gives away most of your advantage. As you can see an error of 1 TC cost you the advantage gained for the first two TCs after the index is exceeded. Look at the other high frequency cumulative versus frequency of the next lowest TC and how far up you need to go to recoup your lost advantage of employing indices before they are profitable using the method above. That is the point I have been trying to make.
Thanks for trying Aslan. The numbers are arbitrary the point is that the frequency of the count 1 less than a proper index, say+8, is almost as high as the sum of the frequencies of all the TCs +8 or above. Assuming linearity for the advantage gained around the index of TC +8, the advantage gained at TC +8 is less than what you loss by always using the +8 index prematurely at +7. The remainder of what you gave up by always using +7 takes most or all of the advantage gained at +9. An index mistake at high count not only affects your highest bets but the frequency of the incorrect play is higher than the frequency of almost all of the correct use of the index. As you use negative indices the bets are small and this same generous (using at 1 TC error to disadvantage) use of an index is a tiny fraction of the correct use of the index. Think of what the TC frequency bell curve looks like. These high TCs are in the tail of the curve. High indices must be used conservatively. Systematic mistakes on the liberal side are very costly.aslan said:
This is a true count frequency chart for HILO 8 decks cut 1.5 (Blackjack Attack ed3 p217):
TC +10 or higher, 0.14% 0.14% cumulative
TC +9, 0.10% 0.24% cumulative
TC +8, 0.24% 0.48% cum
TC +7, 0.32% 0.8% cum
TC +6, 0.73% 1.53% cum
TC +5, 1.03% 2.56% cum
TC +4, 2.23% 4.79% cum
TC +3, 3.27% 8.06%cum
TC +2, 6.95% 15.01% cum
TC +1, 11.33% 26.34% cum
TC 0, 27.63% 53.97% cum
TC less than 0, 46.03% 100% cum
Notice the cumulative frequencies as compared to the frequency on the next lowest TC (line below it). They are almost equal for high TC. If we assume linearity of gain in the table above an index of +8 has a frequency of 0.48% of proper use. If you have a systematic error that has you us it at +7 the frequency you use it at disadvantage is 0.32%. If the index is +8 exactly with the assumption of linear gain you can subtract TC +8 frequency from TC +7 as equal advantage and disadvantage. That leaves a frequency of 0.16 of disadvantage you still have to make up. If we assume the TC +9 has twice the advantage you divide this frequency by 2 to have 0.08%, subtract it from 0.10%, the frequency of TC +9, thats 4/5 of the advantage at TC +9. By making this mistake the closest equivalent TC index to +7 rather than +8 (our systematic mistake) is +10. You have given away most of your advantage for this index by being too aggressive.
The mistake always using a TC index of +8 at TC +7 instead of +8 is almost the same net gain in advantage as using a TC index of TC +10. This is a very costly mistake at your highest bets that gives away most of your advantage. As you can see an error of 1 TC cost you the advantage gained for the first two TCs after the index is exceeded. Look at the other high frequency cumulative versus frequency of the next lowest TC and how far up you need to go to recoup your lost advantage of employing indices before they are profitable using the method above. That is the point I have been trying to make.
