Blackjack Therapy
By Clarke Cant
Appendix B
Showing the maximum profit and BJF for continuous shuffle machine games
(1-EC) is your reduction in gains for effective penetrations being nullified by the probability of having cards reappear before your assumed latency—latency is a players choice when playing against the newer King and Quick 5 CS machines. For the BJF the terms BA, PA and RA are functions of C^2 where each is proportional to C^2. Profits from counting are reduced by (1-EC) and are proportional to C^2; profits overall are: (1-EC)*(EC^2) or EC^2-EC^3. The maximum profit point is the inflection point or the non trivial answer to the first derivative =0, or 2*EC-3*EC^2=0 . That answer is EC=2/3.
The terms BA, PA and RA are functions of C^2 but are also approximations of the average of all possible BA, PA and RA terms up to the shuffle point C. These terms are approximations of 3 functions that are integrals of three functions of C^2 ….or 1/3*C^3. But playing at the depth C (in this case at EC depth) for all hands the actual profits would be ~C^3 and approximated by 3*(BA+PA+RA), making the BJF for CS games: SA+(1-EC)*3*(BA+PA+RA).
The above only applies to machines that actually DO have close to normal distribution of both the inserted used cards and ALSO randomly extract segments and randomly reinsert them. Then the delay for a card reappearing would have this latency. This is definitely NOT the case with what is known about the CSMs now in use. They appear to ONLY insert the used cards at random, making for the even greater potential latency mentioned in the text, where a CSM that inserts a used card (or card block) deep into the pack, will take 64 rounds to turn over the pack, and deal deeply inserted cards, as opposed to 8 rounds with a CSM that puts all used cards to the back of the pack.
With such inertion patterns the greatest goof of the casinos is at hand. A player can DEFINITELY follow accurate basic strategy, and a positive progression and have an actual edge. It hurts to say it, but the progression player is correct about being able to beat the newer CSMs.
The reason for this is that there now really is a reason for wins to follow wins more often and losses follow losses. Consider what happens to a large discard pack and a smaller discard pack. From the studies of the cut-card effect, the large pack of discards has more plus count valued cards. The smaller more minus cards. If both are placed deep, by the CSM mechanism, the smaller pack pushes the remainders less forward, while the larger pushes more. The larger pack even is more plus count overall than the smaller pack. Over time, and the longer cards are in play, the better the cards are for the players.
You can still make banger and other plays with the CSMs too.
But the type of progression player that bets, for example, in fibinacci sequence, where the next entry is the total of the previous two entries, is actually acchieving a CSM edge. The cards that are typically part of a player winning sequence, and the contiuation of a player winning sequence, IS, but ONLY for, CSMs a VALID indication of future winnings. A winning sequence is a valid indication that a small block of cards has been moved deep.
At least with all other shoes and in pitch games the player has to count to achieve some edge. Instead of saying don’t play, we SHOULD point progression players, who play accurate basic strategy to the CSMs. Their edge is low compared to counting, and a counter who keys plus valued card rounds, and bets high until such cards begin to reappear, would not have a much higher edge unless also using banger playing tactics, but the edge for the casino can be definitely driven into the minus range. It is only a .4-.6% edge swing to these progressions, and limted opportunity for experation counting, beyond that (which is uncertain in that few CSMs actually give normal latency distribution), but the ability for far more people to learn accurate basic and a progression, than to count or make hole and location plays, can wipeout casino earnings on these games.
The fact that they are licensed as providing normal distribution of cards is false, and actionable, except as described above. You cannot license a CSM ON THE CONDITION of providing a normal distribution, WHICH ALL ARE, when it is so easy to prove that they do not! The question of Nevada regulations having a prohibitive regulation about putting bent cards through any shuffle machine, and then only giving an AMELIORATIVE regulation to only RELATIVELY relieve non-compliance, as cards are banger bent as well, should also be taken up. It is strange too that progression players only play their systems where they DO NOT work and not on the CSMs where they DO!
CSMs are perhaps the dumbest casino countermeasure since the panic Las Vegas rule changes when the second edition of Beat the Dealer came out in 1966!!!!
APPENDIX A – Ruin and Distribution
APPENDIX C – Estimating Bankroll Requirements
Last Update: 04/19/05