[From Blackjack Forum<\/em> Vol. XXVI #1, Winter 2007]
\u00a9 2007 Carlos Zilzer<\/strong><\/p>\n\n\n\n
[In 2007, Carlos Zilzer provided his \u201cAdvanced OPP,\u201d that he revved up by incorporating T. Hopper\u2019s \u201ccounter basic strategy.\u201d If you\u2019re tempted to play the OPP Count, use the advanced version, which is just as easy as the original version once you learn T. Hopper\u2019s new basic strategy.\u00a0\u2013 A.S.]<\/em><\/p>\n\n\n\n It’s been about a year since I first presented the OPP count to the public. The Easy OPP is the simplest card counting system available, and the easiest to learn. Since the publication of my article presenting the OPP, I have learned a lot, but the most rewarding thing has been the hundreds of letters and emails from grateful people who are now going to the casinos with a different view of the game.<\/p>\n\n\n\n In this article, I will provide information on how to improve the efficiency of the Easy OPP count without increasing the difficulty of use. The proposals and simulations in this article are oriented to six-deck shoe games. I will present the data for eight-deck games in a future article.<\/p>\n\n\n\n One of the simplest ways to make the Easy OPP more powerful is to use a different basic strategy geared toward the card counter. A counter-oriented basic strategy increases winnings by making the strategy correct for when the counters’ biggest bets are placed. For example, standard basic strategy calls for a player to hit his 16 versus a dealer’s 10 of the dealer. In more advanced card counting systems, playing strategies call for players to stand on a 16 versus a dealer’s 10 once the count reaches a certain level.<\/p>\n\n\n\n A counters-oriented basic strategy will call for you to stand all the time on 16 versus a dealer’s 10, because the counter’s winnings at high counts will be larger than the losses at low counts for this play. Many other deviations from standard basic strategy have the same effect.<\/p>\n\n\n\n Card-counting analyst T. Hopper has developed a basic strategy that optimizes the winnings for card counters without changing strategy with the count. At the end of this article, you will find charts of T. Hopper’s counters-oriented basic strategy from his free e-book T-H Basic Blackjack<\/em>. The charts for T. Hopper’s counters’ basic strategy are below.<\/p>\n\n\n\n A simulation of one billion rounds using standard 6 deck S17 rules shows an increase of return on investment (ROI or “score”) in the range of 15.2% to 16.7% (depending on the bet spread) for using T. Hopper’s counters’-oriented basic strategy rather than standard basic strategy. This represents an increase in winnings of greater than 0.2 units\/100 rounds.<\/p>\n\n\n\n Although the OPP does not count the 10-value cards, for counts equal to or greater than +11 in six-deck games (or +17 if starting the count from +6 as my original article suggests), the insurance bet is recommended. Taking insurance at these counts will increase your ROI (or score) 4% more.<\/p>\n\n\n\n One thing I have learned about the OPP from the feedback I’ve received from players is that, with the OPP, there is more risk to high bets early in a shoe. For example, with the Red7 count, it is possible to make a true count conversion or true edge adjustment using fractional methods to estimate the true count or true edge at any running count in any part of the shoe. But with the OPP, this is a very difficult task because the OPP does not have a “pivot” that equates to the same edge at any level of penetration.<\/p>\n\n\n\n With the OPP, the counter’s edge will increase different amounts at the same count at different levels of penetration. A running count of 12 (starting the count at 6 as recommended in my first article) will represent a larger edge after 3 decks out of 6 have been played than the same running count of 12 if it happens at the beginning of the shoe. At the end of the simulation I got six charts indicating the running OPP count, the number of rounds played in that count, the edge for that count and the variance for that count per deck played. The simulation also returned a seventh chart with the overall results of the one billion rounds. All the simulations were run using T. Hopper’s counters’ basic strategy, and insurance at counts of 11 (17) and above.<\/p>\n\n\n\n The tables below are extracts of these simulation results, showing the part of the tables for running counts 0 to 11. The running count numbers assume an initial count of 0 (not 6).<\/p>\n\n\n\n One thing I learned from the simulation results was that even in the first deck, there is an edge at counts of +5 and higher (or +11, if starting from 6). However, closer analysis of the simulation results shows that the edge is too small to justify a bet increase. This is typical behavior for any unbalanced count: There is an edge at the pivot, no matter the number of decks played. But what we really want to know is when that edge justifies a bet increase.<\/p>\n\n\n\n A look at the numbers indicates that the count at which a player obtains an edge equal or greater to 1% gets lower with the number of decks played. In the first deck, the running count (RC) must be 14 to get a win rate of 1%; in the second you get that edge at an RC of 11; and in the third deck you get it at an RC of 9. In the fourth deck you have a 1% edge at an RC of 8, while in the fifth and last deck the 1% edge comes at 6.<\/p>\n\n\n\n Another way of looking at this is to say that the deeper we are in the shoe, the higher a win rate any particular RC represents. So, the counter’s basic strategy, with insurance and a deck-dependent bet ramp, provide an increase of 40% in score from the simplest version of the OPP. As you can see, there is very little cost to this simpler betting method.<\/p>\n\n\n\n The next step was to find a simpler optimal bet ramp and an easy way to remember it, keeping in mind that the principal objective of the OPP count was that it should be exceptionally easy to learn and to implement. The following is an easy-to-remember table using multiples of 2 units that are shifted up with each deck played.<\/p>\n\n\n\n This simpler betting ramp returns a score (now is better to call it ROI because it is a real-life rather than \u201coptimal\u201d bet ramp) of $27, a win rate of 3 units\/100 rounds and a standard deviation of 59.7. HITTING AND STANDING<\/strong><\/p>\n\n\n\n Hitting or standing is considered only after all other options (surrender, split, and\/or double down) have been exhausted.<\/strong><\/p>\n\n\n\n DOUBLING DOWN<\/strong><\/p>\n\n\n\nCard Counters’ Basic Strategy to Increase the OPP Count’s Power<\/h5>\n\n\n\n
Insurance Bet for the Advanced OPP Card Counting System<\/h5>\n\n\n\n
The Penetration Effect on the Power of the OPP Count<\/h5>\n\n\n\n
Kim Lee’s article, “On the Math Behind the OPP<\/a>“, helped me to understand many things about the differences between the OPP and other card counting systems. Even though the OPP is an unbalanced count, it is very different from an unbalanced count like the Red7.<\/p>\n\n\n\n
Some time ago, I began suggesting to players to avoid any bet increase until the first deck was in the discard tray; it was easy to explain that a deck is approximately the width of the middle finger. After that I started to receive good reports from the same people telling me that they had noticed a significant increase in their winnings after applying that simple rule.
Now I will present a more comprehensive analysis and advice.
To develop advice for improving the performance of the OPP, I modified ET Fan’s PowerSim Card Counting Simulation Software to report sim results deck by deck. Then I ran simulations of 6-deck shoe games with a very deep penetration (the maximum possible to avoid shoe overflow with a 1 billion round simulation).<\/p>\n\n\n\nResults for the First Deck<\/th><\/tr> RC<\/th> Frequency<\/th> Win Rate<\/th> Variance<\/th><\/tr> 0<\/td> 45099453<\/td> -0.0048985<\/td> 1.385056<\/td><\/tr> 1<\/td> 22533049<\/td> -0.0039873<\/td> 1.382429<\/td><\/tr> 2<\/td> 17437729<\/td> -0.0023652<\/td> 1.378858<\/td><\/tr> 3<\/td> 12403039<\/td> -0.0015394<\/td> 1.373733<\/td><\/tr> 4<\/td> 8301513<\/td> -0.0005589<\/td> 1.371465<\/td><\/tr> 5<\/td> 5292419<\/td> 0.0026138<\/td> 1.368379<\/td><\/tr> 6<\/td> 3205931<\/td> 0.0021953<\/td> 1.364121<\/td><\/tr> 7<\/td> 1847678<\/td> 0.0033142<\/td> 1.359199<\/td><\/tr> 8<\/td> 1012187<\/td> 0.0059672<\/td> 1.356724<\/td><\/tr> 9<\/td> 525366<\/td> 0.0073825<\/td> 1.354168<\/td><\/tr> 10<\/td> 258580<\/td> 0.0048979<\/td> 1.351327<\/td><\/tr> 11<\/td> 121608<\/td> 0.0085356<\/td> 1.346574<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Results for the 2nd Deck<\/th><\/tr> RC<\/th> Frequency<\/th> Win Rate<\/th> Variance<\/th><\/tr> 0<\/td> 15544347<\/td> -0.0061163<\/td> 1.388518<\/td><\/tr> 1<\/td> 15711450<\/td> -0.0041119<\/td> 1.384026<\/td><\/tr> 2<\/td> 15128594<\/td> -0.0030499<\/td> 1.380121<\/td><\/tr> 3<\/td> 13898680<\/td> -0.0011779<\/td> 1.375426<\/td><\/tr> 4<\/td> 12198110<\/td> 0.0003807<\/td> 1.370685<\/td><\/tr> 5<\/td> 10220651<\/td> 0.0023369<\/td> 1.367378<\/td><\/tr> 6<\/td> 8189436<\/td> 0.0038852<\/td> 1.362689<\/td><\/tr> 7<\/td> 6268648<\/td> 0.0044798<\/td> 1.358611<\/td><\/tr> 8<\/td> 4596761<\/td> 0.0059538<\/td> 1.352943<\/td><\/tr> 9<\/td> 3225899<\/td> 0.0086714<\/td> 1.351015<\/td><\/tr> 10<\/td> 2166535<\/td> 0.00917<\/td> 1.346022<\/td><\/tr> 11<\/td> 1395226<\/td> 0.0113644<\/td> 1.342142<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Results for the 3rd Deck<\/th><\/tr> RC<\/th> Frequency<\/th> Win Rate<\/th> Variance<\/th><\/tr> 0<\/td> 13068780<\/td> -0.0079109<\/td> 1.392763<\/td><\/tr> 1<\/td> 13538813<\/td> -0.0056508<\/td> 1.387848<\/td><\/tr> 2<\/td> 13543243<\/td> -0.0033995<\/td> 1.381609<\/td><\/tr> 3<\/td> 13059870<\/td> -0.0017427<\/td> 1.376070<\/td><\/tr> 4<\/td> 12164731<\/td> 0.0003312<\/td> 1.370765<\/td><\/tr> 5<\/td> 10936276<\/td> 0.0029875<\/td> 1.365025<\/td><\/tr> 6<\/td> 9491670<\/td> 0.0046452<\/td> 1.359720<\/td><\/tr> 7<\/td> 7953935<\/td> 0.0066228<\/td> 1.354781<\/td><\/tr> 8<\/td> 6429897<\/td> 0.0076003<\/td> 1.349389<\/td><\/tr> 9<\/td> 5017369<\/td> 0.0103951<\/td> 1.343530<\/td><\/tr> 10<\/td> 3776907<\/td> 0.0112456<\/td> 1.339024<\/td><\/tr> 11<\/td> 2745790<\/td> 0.0125243<\/td> 1.332236<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Results for the 4th Deck<\/th><\/tr> RC<\/th> Frequency<\/th> Win Rate<\/th> Variance<\/th><\/tr> 0<\/td> 12302783<\/td> -0.0099998<\/td> 1.400835<\/td><\/tr> 1<\/td> 13067271<\/td> -0.0069178<\/td> 1.394555<\/td><\/tr> 2<\/td> 13400161<\/td> -0.0039155<\/td> 1.385639<\/td><\/tr> 3<\/td> 13286241<\/td> -0.0012346<\/td> 1.378854<\/td><\/tr> 4<\/td> 12721486<\/td> 0.0010927<\/td> 1.370608<\/td><\/tr> 5<\/td> 11766974<\/td> 0.0040554<\/td> 1.363121<\/td><\/tr> 6<\/td> 10512181<\/td> 0.0067284<\/td> 1.356291<\/td><\/tr> 7<\/td> 9060393<\/td> 0.0084723<\/td> 1.348629<\/td><\/tr> 8<\/td> 7545402<\/td> 0.0124984<\/td> 1.341781<\/td><\/tr> 9<\/td> 6061063<\/td> 0.0135348<\/td> 1.333774<\/td><\/tr> 10<\/td> 4700803<\/td> 0.0157303<\/td> 1.326587<\/td><\/tr> 11<\/td> 3518665<\/td> 0.0186512<\/td> 1.320435<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Results for the 5th Deck<\/th><\/tr> RC<\/th> Frequency<\/th> Win Rate<\/th> Variance<\/th><\/tr> 0<\/td> 12344303<\/td> -0.0164626<\/td> 1.41875<\/td><\/tr> 1<\/td> 13715205<\/td> -0.0112253<\/td> 1.406535<\/td><\/tr> 2<\/td> 14617344<\/td> -0.0065245<\/td> 1.393547<\/td><\/tr> 3<\/td> 14920325<\/td> -0.0019819<\/td> 1.381162<\/td><\/tr> 4<\/td> 14603698<\/td> 0.0031037<\/td> 1.36922<\/td><\/tr> 5<\/td> 13679086<\/td> 0.0070817<\/td> 1.356935<\/td><\/tr> 6<\/td> 12269032<\/td> 0.0109532<\/td> 1.345168<\/td><\/tr> 7<\/td> 10531009<\/td> 0.0148428<\/td> 1.333483<\/td><\/tr> 8<\/td> 8639179<\/td> 0.0177164<\/td> 1.322816<\/td><\/tr> 9<\/td> 6785582<\/td> 0.0210233<\/td> 1.312948<\/td><\/tr> 10<\/td> 5090888<\/td> 0.0241871<\/td> 1.301468<\/td><\/tr> 11<\/td> 3656873<\/td> 0.0268388<\/td> 1.290593<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Results for the 6th Deck<\/th><\/tr> RC<\/th> Frequency<\/th> Win Rate<\/th> Variance<\/th><\/tr> 0<\/td> 5964172<\/td> -0.0295393<\/td> 1.455209<\/td><\/tr> 1<\/td> 7198634<\/td> -0.019633<\/td> 1.431447<\/td><\/tr> 2<\/td> 8166379<\/td> -0.0105634<\/td> 1.409773<\/td><\/tr> 3<\/td> 8695839<\/td> -0.0020113<\/td> 1.387818<\/td><\/tr> 4<\/td> 8699057<\/td> 0.0051575<\/td> 1.365654<\/td><\/tr> 5<\/td> 8156422<\/td> 0.0122596<\/td> 1.34639<\/td><\/tr> 6<\/td> 7158520<\/td> 0.0183577<\/td> 1.326588<\/td><\/tr> 7<\/td> 5888341<\/td> 0.024383<\/td> 1.307584<\/td><\/tr> 8<\/td> 4525689<\/td> 0.0287781<\/td> 1.289022<\/td><\/tr> 9<\/td> 3252617<\/td> 0.0318885<\/td> 1.272016<\/td><\/tr> 10<\/td> 2180576<\/td> 0.0360891<\/td> 1.255976<\/td><\/tr> 11<\/td> 1362531<\/td> 0.0408519<\/td> 1.240604<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n When to Increase Your Bet with the Advanced OPP Count<\/h5>\n\n\n\n
As modifications to the SCOCALC program to calculate the optimal bet ramp from the data by deck was a major work, I introduced the data into a spread sheet and used a recursive trial and error macro in Visual Basic to determine the optimal bet ramp and score.
The optimal bet ramp shown below rounds the optimal bet to the nearest whole number.<\/p>\n\n\n\n1:16 Optimal Bet Ramp<\/th><\/tr> RC<\/th> 1st deck<\/th> 2nd deck<\/th> 3rd deck<\/th> 4th deck<\/th> 5th deck<\/th> 6th deck<\/th><\/tr> <4<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td><\/tr> 4<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td> 3<\/td> 5<\/td><\/tr> 5<\/td> 2<\/td> 2<\/td> 3<\/td> 4<\/td> 6<\/td> 11<\/td><\/tr> 6<\/td> 2<\/td> 3<\/td> 4<\/td> 6<\/td> 10<\/td> 16<\/td><\/tr> 7<\/td> 3<\/td> 4<\/td> 6<\/td> 8<\/td> 13<\/td> 16<\/td><\/tr> 8<\/td> 5<\/td> 5<\/td> 7<\/td> 11<\/td> 16<\/td> 16<\/td><\/tr> 9<\/td> 7<\/td> 8<\/td> 9<\/td> 12<\/td> 16<\/td> 16<\/td><\/tr> 10<\/td> 4<\/td> 8<\/td> 10<\/td> 14<\/td> 16<\/td> 16<\/td><\/tr> 11<\/td> 8<\/td> 10<\/td> 11<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 12<\/td> 6<\/td> 10<\/td> 14<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 13<\/td> 3<\/td> 14<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 14<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 15<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> >16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Using the same spread sheet I tested my initial recommendation to my readers to avoid increasing the bet until after the first deck had been dealt (bet 1 unit during the first deck). The results were as follows:<\/p>\n\n\n\nIRC= 6 IRC=0 1:16 Optimal Bet Ramp<\/th><\/tr> RC<\/th> 1st deck<\/th> 2nd deck<\/th> 3rd deck<\/th> 4th deck<\/th> 5th deck<\/th> 6th deck<\/th><\/tr> <4<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td><\/tr> 4<\/td> 1<\/td> 1<\/td> 1<\/td> 2<\/td> 4<\/td> 6<\/td><\/tr> 5<\/td> 1<\/td> 1<\/td> 2<\/td> 4<\/td> 6<\/td> 8<\/td><\/tr> 6<\/td> 1<\/td> 2<\/td> 4<\/td> 6<\/td> 8<\/td> 10<\/td><\/tr> 7<\/td> 2<\/td> 4<\/td> 6<\/td> 8<\/td> 10<\/td> 12<\/td><\/tr> 8<\/td> 4<\/td> 6<\/td> 8<\/td> 10<\/td> 12<\/td> 14<\/td><\/tr> 9<\/td> 6<\/td> 8<\/td> 10<\/td> 12<\/td> 14<\/td> 16<\/td><\/tr> 10<\/td> 8<\/td> 10<\/td> 12<\/td> 14<\/td> 16<\/td> 16<\/td><\/tr> 11<\/td> 10<\/td> 12<\/td> 14<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 12<\/td> 12<\/td> 14<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 13<\/td> 14<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 14<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 15<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr> >16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td> 16<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
As a final test, and in order to compare \u201capples with apples\u201d, I performed a simulation of the same game, same penetration, same seed but using the Red 7 count with the counter basic strategy and only the insurance index. The SCORE of that game is $42.5631. So we can say that the OPP with the proposed bet ramp and strategy has 63% of the performance of Red7 in the same conditions, which is much better that the 47.9% performance of standard OPP.
There are other variations to OPP that return higher scores but they mean modification of the tag values of the cards. These more advanced options will be presented in my next article. \u2660<\/p>\n\n\n\nT. Hopper’s Card Counters’ Basic Strategy<\/strong><\/h5>\n\n\n\n
\n\n\n\nStand<\/strong><\/th> 2<\/th> 3<\/th> 4<\/th> 5<\/th> 6<\/th> 7<\/th> 8<\/th> 9<\/th> X<\/th> A S17<\/th> A H17<\/th><\/tr> 17<\/th> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td><\/tr> 16<\/th> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> H<\/td> H<\/td> H<\/td> S<\/td> H<\/td> H<\/td><\/tr> 15<\/th> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> H<\/td> H<\/td> H<\/td> H<\/td> H<\/td> H<\/td><\/tr> 14<\/th> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> H<\/td> H<\/td> H<\/td> H<\/td> H<\/td> H<\/td><\/tr> 13<\/th> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> H<\/td> H<\/td> H<\/td> H<\/td> H<\/td> H<\/td><\/tr> 12<\/th> H<\/td> S<\/td> S<\/td> S<\/td> S<\/td> H<\/td> H<\/td> H<\/td> H<\/td> H<\/td> H<\/td><\/tr> A7<\/th> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> S<\/td> H<\/td> H<\/td> S<\/td> H<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n RULES FOR HARD HANDS<\/th><\/tr> Always stand on 17 or higher.
Always stand on 12-16 vs. 2-6 and hit 12-16 vs. 7-A except:Hit 12 vs. 2Stand on 16 vs. 10<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nRULES FOR SOFT HANDS<\/strong><\/th><\/tr> Always hit soft 17 or lower.
Always stand on soft 18 or higher, except:Hit soft 18 vs. 9 and 10Hit soft 18 vs. Ace if the dealer hits soft 17<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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