Per the request of zengrifter, I prepared a simulation to compare the two said counts. Here is my write up of the simulation:
Zen Count Vs. Hi-Opt II
The purpose of this simulation is to see how the Hi-Opt II (with no ace side-count) fares against the Zen Count. For obvious reasons, the Zen Count will be victorious in near any game, so I will be using a set of house rules that gives the Hi-Opt II (with no ace-side count) the best possible chance of winning in today’s playing environment. Clearly, if Hi-Opt were to win this, it would be because of its superior playing efficiency. Therefore, I will give it a game where BS deviations are very important. Let’s say we stumbled across a juicy single-deck game in some dust joint that just opened. The rules are as follows:
1D, H17, 3:2 BJ, No RSPA, SP to 2, .65 Pen, DAS, DD 9-11, No Surrender, 1 Card to split aces, face-down, head-on.
The games REALLY do not come better than this one. If you find one that doesn’t assign a pit-boss to stand behind EVERY player's chair, do PM me.
To give Hi-Opt II even more advantage, we will use a conservative betting range of 1-2. (Any higher betting ranges would surely give the win to the Zen Count because of it’s superior BC).
When comparing two systems, it is ideal to have the two systems jump their bet when they have the exact same advantage. At a TC of +2, the Zen Count has a TBA of +0.797%, while Hi-Opt II has an advantage of 0.784%. These are close enough for all practical purposes, so I will set each system to jump their bet to two units at a TC of +2 or higher.
A note on indexes. I am not using all of the Hi-Opt II indexes for this sim. I am using about 90 of them, which is many more than most players use. To further disadvantage the Zen Count, I am not even going to use the indexes that were made for the Zen Count. I am going to use the same ones that the Hi-Opt II uses, which are quite different in some cases because of the fact that Hi-Opt neglects Aces, while Zen counts them as a large card, which is incorrect for the purpose of most BS deviations. However, I will still set Zen’s Insurance index to +4 (remember single-deck) as it should be.
The results are as follows.
(1 Billion Hands)
Hi-Opt II: +0.590%
Zen Count: +0.633%
As you can see, the Zen count still beats the Hi-Opt II (with no Ace-side count), even when HO2 had every conceivable advantage.
Zen Count Vs. Hi-Opt II (No Ace Side-Count): DD and 6 Deck Games
First off, it should be mentioned that this comparison is going to give the HO2 an inherent advantage, for I will not include Wonging in these simulations. The reason this is disadvantageous to the Zen-Count is that the Zen-Count would be able to more effectively indicate when the deck is poor, as a direct result of its superior BC. The reason it is not feasible to program this simulation to include Wonging is that in order to make this a fair comparison, one would have to somehow tell the program “wong-out when the deck is unfavorable by x%.” Intuition might tell you that it would be fair to simply program the simulation to have both the Zen and HO2 counts to wong-out at -2, for example. This would be an erroneous assumption, however, as one count might be wonging out at a higher frequency than the other due to differences in their count. Intuition tells me that the HO2 would be wonging out more frequently because it seems that the magnitude of its TC (and RC) ranges greater than that of the Zen Count. This would give the HO2 a significant advantage because it would be playing less hands total, effectively eliminating more unfavorable situations than would the Zen Count. If you don’t believe that the magnitude of HO2‘s counts become greater than that of Zen Count, compare the indexes of the two counts. You’ll find that the indexes for HO2 are consistently higher than those of the Zen Count. Therefore, because of the difficulty associated in comparing the counts with wonging included, I will neglect the effect that it will have in the comparison. However, do keep in mind that Zen-Count is even better than the simulation depicts because it has the potential to more accurately tell the player when to wong out.
For the two-deck game, the spread we will be using is a 1-5 spread. This spread is somewhat conservative, in my opinion, from my “kitchen table” that is. Increasing the spread to 1-7, which is what I would have probably recommended, would increase the Zen-Count’s advantage because of its superior BC. However, for this simulation, we will only use a 1-5 spread. As I have mentioned in previous posts, to make a worthwhile comparison, you must have the two counts being examined jumping their bets when the deck is equally advantageous to both counts. Fortunately, these two counts experience near the exact same advantage at a TC of +3, which happens to be in the neighborhood of TBA = .495-.500%. So, the two counts will jump their bets to 5 units at a TC of +3, while betting only 1 unit during all other counts.
On the subject of indexes, the Zen Count will be further disadvantaged; both systems will be using the same set of 90 or so indexes. These indexes, however, were designed for HO2, not the Zen Count. The only indexes that will differ are the system’s respective insurance indexes and soft 18 v. A. The second index is not important at all.
The rules for the DD game will be as follows:
2D, H17, 3:2 BJ, No RSPA, SP to 2, .60 Pen, DAS, DOA2, No Surrender, 1 Card to split aces, face-down, head-on.
The results are as follows:
(1 Billion Hands)
Zen-Count: +0.671%
Hi-Opt II (no ace side-count): +0.622%
Again, the Zen-Count is victorious, even though it was at a disadvantage in this sim.
Next, I will run a similar simulation comparing the two system’s performance in six-deck games.
For the six-deck game, the spread we will be using is a 1-8 spread. This spread is somewhat conservative, in my opinion, from my “kitchen table” that is. Increasing the spread to 1-10 or even 1-20, which is what I would have probably recommended, would increase the Zen-Count’s advantage because of its superior BC. However, for this simulation, we will only use a 1-8 spread. As I have mentioned in previous posts, to make a worthwhile comparison, you must have the two counts being examined jumping their bets when the deck is equally advantageous to both counts. These two counts experience near the exact same advantage at a TC of +7 (Zen Count: TBA = +1.320%; HO2: TBA = +1.402%). So, the two counts will jump their bets to 8 units at a TC of +7, while betting only 1 unit during all other counts.
Indexes will be handled the same way as mentioned above.
For reasons mentioned above there will be no wonging for this simulation. A condition that once again is to the disadvantage of Zen.
The Rules for the Six-deck game will be as follows:
6D, H17, 3:2 BJ, No RSPA, RSP to 3, .67 Pen, DAS, DOA2, No Surrender, 1 Card to split aces, face-up, head-on.
The results are as follows:
(1 Billion Hands)
Zen-Count: +0.093%
Hi-Opt II (no ace side-count): +0.003%
Once again, the Zen Count is victorious. Although the difference between the two counts may seem small, keep in mind that this comparison is quite biased in the favor of HO2. Adding wonging, a more realistic betting spread and giving the Zen Count its proper indexes would increase the difference significantly.
Now to see if LS and restricted indices changes anything. For these simulations, each count will be getting their proper indices. A note on surrender indices. Arnold Snyder did not bother to provide Surrender indices (at least this is what CVData tells me; his complete strategy indicates that one should surrender 16 v. 9, v. 10 and v. A, regardless of the count. Humble on the other hand, provides NUMEROUS surrender indices. He even goes as far to tell you that you should surrender 12 v.9 at a TC of 29 and 13 v. 7 at a TC of 34. Yeah, O.K. Lance, I’ll keep these things in mind. As you can see, adding the LS is going to give HO2 a big advantage because of the fact that it has much more detailed indices for the surrender play. This is quite significant for the hand-held games, especially since I am programming the game to be head-on. An index generator would be the solution to finding all the indices that Snyder didn’t provide. I, however, don’t feel the motive to bust out the old index generator for this purpose.
The rules will be as follows for the first simulation:
1D, H17, 3:2 BJ, No RSPA, SP to 2, .65 Pen, DAS, DD 9-11, LS, 1 Card to split aces, face-down, head-on.
Each count will range its bets 1-2, betting two units on TC’s greater than 2. There will be no wonging.
Results:
(1 Billion Hands)
HO2 (no ASC, full indices): +0.822%
Zen Count (Full indices): +0.672%
HO2 (No ASC) is the clear winner here. There is absolutely no question about this. The detailed surrender indices gave HO2 a huge edge in this game, on top of it’s superior PE. However, I don’t think single-deck, 3:2 games with 65% pen and LS exist. If they do, I highly doubt you’d have the luxury of playing head-on, regardless of the time of day.
Next, we’ll move to the DD game and see how LS affects this game.
The rules will be:
2D, H17, 3:2 BJ, No RSPA, SP to 2, .60 Pen, DAS, DOA2, LS Card to split aces, face-down, head-on.
Each count will be spreading 1-5., betting 5 units on TC’s greater than or equal to 3, while betting 1 unit on all other hands. There, again, will be no wonging.
Results:
(1 Billion Hands)
HO2 (no ASC, full indices): +0.849%
Zen Count (Full indices): +0.755%
Again the HO2 (no ASC) beats Zen by more than a small margin. Perhaps for similar reasons as explained for the single-deck. Do they offer DD games with LS? I doubt it, though a few casinos might.
Now let’s see what happens when we look at a shoe game.
The rules will be as follows:
6D, H17, 3:2 BJ, No RSPA, RSP to 3, .67 Pen, DAS, DOA2, No Surrender, 1 Card to split aces, face-up, head-on.
Each count will spread its bets 1-8, betting 8 units on TC’s greater than or equal to 7, while betting 1 unit on all other hands. There again will be no wonging. This overly conservative spread and lack of wonging will prove to give the HO2 a sizable advantage over the Zen.
Results:
(1 Billion Hands)
HO2 (full indices, no ASC): +.203%
Zen (Full indices): +0.177%
Again HO2 is victorious. Finding a game like this would be a lot easier to do. Playing with this sort of spread without wonging would be a mistake, however. Adding a larger spread and / or wonging would be to Zen’s advantage.
Zen Count Vs. Hi-Opt II
The purpose of this simulation is to see how the Hi-Opt II (with no ace side-count) fares against the Zen Count. For obvious reasons, the Zen Count will be victorious in near any game, so I will be using a set of house rules that gives the Hi-Opt II (with no ace-side count) the best possible chance of winning in today’s playing environment. Clearly, if Hi-Opt were to win this, it would be because of its superior playing efficiency. Therefore, I will give it a game where BS deviations are very important. Let’s say we stumbled across a juicy single-deck game in some dust joint that just opened. The rules are as follows:
1D, H17, 3:2 BJ, No RSPA, SP to 2, .65 Pen, DAS, DD 9-11, No Surrender, 1 Card to split aces, face-down, head-on.
The games REALLY do not come better than this one. If you find one that doesn’t assign a pit-boss to stand behind EVERY player's chair, do PM me.
To give Hi-Opt II even more advantage, we will use a conservative betting range of 1-2. (Any higher betting ranges would surely give the win to the Zen Count because of it’s superior BC).
When comparing two systems, it is ideal to have the two systems jump their bet when they have the exact same advantage. At a TC of +2, the Zen Count has a TBA of +0.797%, while Hi-Opt II has an advantage of 0.784%. These are close enough for all practical purposes, so I will set each system to jump their bet to two units at a TC of +2 or higher.
A note on indexes. I am not using all of the Hi-Opt II indexes for this sim. I am using about 90 of them, which is many more than most players use. To further disadvantage the Zen Count, I am not even going to use the indexes that were made for the Zen Count. I am going to use the same ones that the Hi-Opt II uses, which are quite different in some cases because of the fact that Hi-Opt neglects Aces, while Zen counts them as a large card, which is incorrect for the purpose of most BS deviations. However, I will still set Zen’s Insurance index to +4 (remember single-deck) as it should be.
The results are as follows.
(1 Billion Hands)
Hi-Opt II: +0.590%
Zen Count: +0.633%
As you can see, the Zen count still beats the Hi-Opt II (with no Ace-side count), even when HO2 had every conceivable advantage.
Zen Count Vs. Hi-Opt II (No Ace Side-Count): DD and 6 Deck Games
First off, it should be mentioned that this comparison is going to give the HO2 an inherent advantage, for I will not include Wonging in these simulations. The reason this is disadvantageous to the Zen-Count is that the Zen-Count would be able to more effectively indicate when the deck is poor, as a direct result of its superior BC. The reason it is not feasible to program this simulation to include Wonging is that in order to make this a fair comparison, one would have to somehow tell the program “wong-out when the deck is unfavorable by x%.” Intuition might tell you that it would be fair to simply program the simulation to have both the Zen and HO2 counts to wong-out at -2, for example. This would be an erroneous assumption, however, as one count might be wonging out at a higher frequency than the other due to differences in their count. Intuition tells me that the HO2 would be wonging out more frequently because it seems that the magnitude of its TC (and RC) ranges greater than that of the Zen Count. This would give the HO2 a significant advantage because it would be playing less hands total, effectively eliminating more unfavorable situations than would the Zen Count. If you don’t believe that the magnitude of HO2‘s counts become greater than that of Zen Count, compare the indexes of the two counts. You’ll find that the indexes for HO2 are consistently higher than those of the Zen Count. Therefore, because of the difficulty associated in comparing the counts with wonging included, I will neglect the effect that it will have in the comparison. However, do keep in mind that Zen-Count is even better than the simulation depicts because it has the potential to more accurately tell the player when to wong out.
For the two-deck game, the spread we will be using is a 1-5 spread. This spread is somewhat conservative, in my opinion, from my “kitchen table” that is. Increasing the spread to 1-7, which is what I would have probably recommended, would increase the Zen-Count’s advantage because of its superior BC. However, for this simulation, we will only use a 1-5 spread. As I have mentioned in previous posts, to make a worthwhile comparison, you must have the two counts being examined jumping their bets when the deck is equally advantageous to both counts. Fortunately, these two counts experience near the exact same advantage at a TC of +3, which happens to be in the neighborhood of TBA = .495-.500%. So, the two counts will jump their bets to 5 units at a TC of +3, while betting only 1 unit during all other counts.
On the subject of indexes, the Zen Count will be further disadvantaged; both systems will be using the same set of 90 or so indexes. These indexes, however, were designed for HO2, not the Zen Count. The only indexes that will differ are the system’s respective insurance indexes and soft 18 v. A. The second index is not important at all.
The rules for the DD game will be as follows:
2D, H17, 3:2 BJ, No RSPA, SP to 2, .60 Pen, DAS, DOA2, No Surrender, 1 Card to split aces, face-down, head-on.
The results are as follows:
(1 Billion Hands)
Zen-Count: +0.671%
Hi-Opt II (no ace side-count): +0.622%
Again, the Zen-Count is victorious, even though it was at a disadvantage in this sim.
Next, I will run a similar simulation comparing the two system’s performance in six-deck games.
For the six-deck game, the spread we will be using is a 1-8 spread. This spread is somewhat conservative, in my opinion, from my “kitchen table” that is. Increasing the spread to 1-10 or even 1-20, which is what I would have probably recommended, would increase the Zen-Count’s advantage because of its superior BC. However, for this simulation, we will only use a 1-8 spread. As I have mentioned in previous posts, to make a worthwhile comparison, you must have the two counts being examined jumping their bets when the deck is equally advantageous to both counts. These two counts experience near the exact same advantage at a TC of +7 (Zen Count: TBA = +1.320%; HO2: TBA = +1.402%). So, the two counts will jump their bets to 8 units at a TC of +7, while betting only 1 unit during all other counts.
Indexes will be handled the same way as mentioned above.
For reasons mentioned above there will be no wonging for this simulation. A condition that once again is to the disadvantage of Zen.
The Rules for the Six-deck game will be as follows:
6D, H17, 3:2 BJ, No RSPA, RSP to 3, .67 Pen, DAS, DOA2, No Surrender, 1 Card to split aces, face-up, head-on.
The results are as follows:
(1 Billion Hands)
Zen-Count: +0.093%
Hi-Opt II (no ace side-count): +0.003%
Once again, the Zen Count is victorious. Although the difference between the two counts may seem small, keep in mind that this comparison is quite biased in the favor of HO2. Adding wonging, a more realistic betting spread and giving the Zen Count its proper indexes would increase the difference significantly.
Now to see if LS and restricted indices changes anything. For these simulations, each count will be getting their proper indices. A note on surrender indices. Arnold Snyder did not bother to provide Surrender indices (at least this is what CVData tells me; his complete strategy indicates that one should surrender 16 v. 9, v. 10 and v. A, regardless of the count. Humble on the other hand, provides NUMEROUS surrender indices. He even goes as far to tell you that you should surrender 12 v.9 at a TC of 29 and 13 v. 7 at a TC of 34. Yeah, O.K. Lance, I’ll keep these things in mind. As you can see, adding the LS is going to give HO2 a big advantage because of the fact that it has much more detailed indices for the surrender play. This is quite significant for the hand-held games, especially since I am programming the game to be head-on. An index generator would be the solution to finding all the indices that Snyder didn’t provide. I, however, don’t feel the motive to bust out the old index generator for this purpose.
The rules will be as follows for the first simulation:
1D, H17, 3:2 BJ, No RSPA, SP to 2, .65 Pen, DAS, DD 9-11, LS, 1 Card to split aces, face-down, head-on.
Each count will range its bets 1-2, betting two units on TC’s greater than 2. There will be no wonging.
Results:
(1 Billion Hands)
HO2 (no ASC, full indices): +0.822%
Zen Count (Full indices): +0.672%
HO2 (No ASC) is the clear winner here. There is absolutely no question about this. The detailed surrender indices gave HO2 a huge edge in this game, on top of it’s superior PE. However, I don’t think single-deck, 3:2 games with 65% pen and LS exist. If they do, I highly doubt you’d have the luxury of playing head-on, regardless of the time of day.
Next, we’ll move to the DD game and see how LS affects this game.
The rules will be:
2D, H17, 3:2 BJ, No RSPA, SP to 2, .60 Pen, DAS, DOA2, LS Card to split aces, face-down, head-on.
Each count will be spreading 1-5., betting 5 units on TC’s greater than or equal to 3, while betting 1 unit on all other hands. There, again, will be no wonging.
Results:
(1 Billion Hands)
HO2 (no ASC, full indices): +0.849%
Zen Count (Full indices): +0.755%
Again the HO2 (no ASC) beats Zen by more than a small margin. Perhaps for similar reasons as explained for the single-deck. Do they offer DD games with LS? I doubt it, though a few casinos might.
Now let’s see what happens when we look at a shoe game.
The rules will be as follows:
6D, H17, 3:2 BJ, No RSPA, RSP to 3, .67 Pen, DAS, DOA2, No Surrender, 1 Card to split aces, face-up, head-on.
Each count will spread its bets 1-8, betting 8 units on TC’s greater than or equal to 7, while betting 1 unit on all other hands. There again will be no wonging. This overly conservative spread and lack of wonging will prove to give the HO2 a sizable advantage over the Zen.
Results:
(1 Billion Hands)
HO2 (full indices, no ASC): +.203%
Zen (Full indices): +0.177%
Again HO2 is victorious. Finding a game like this would be a lot easier to do. Playing with this sort of spread without wonging would be a mistake, however. Adding a larger spread and / or wonging would be to Zen’s advantage.
Last edited: