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# Thread: Which deviations are most valuable?

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Originally Posted by aceside
I do every calculation myself. Let me show you that the player 16v10 is a lot more frequent than dealer Aces. Frequency of the player 16v10 is 42%*4/13=13% for six-decks. Frequency of the dealer Aces is 5%*1/13=0.4%. Therefore, 16v10 is a lot more frequent that insurance offers. I do not believe publications. The 16v10 must be the most important deviation. Besides, the surrender option will make this deviation more important. You cite of wizard of odds "late surrender adds 0.07%" is not correct for card counting. It should be 7% when counting. However, your calculation earning when flat bet with solely play deviation is very helpful for me. Thank you.
It's good to be sceptical of published data. I am that way myself. However, some sources have proven themselves to be reliable. The Wizard of Odds is one of those sources and the CV software is state of the art for our game.

It's also good to do you own research. However:

1. Your calculation for frequency of a dealer ace is incorrect. The probability off the top of the deck/shoe is simply 1/13~=7.7%
2. Your calculation of the occurrence of 16 vs T is also incorrect. 4/13 is correct for a dealer face card but what is the 42%? The correct probability for 16 vs T is 3.5% according to BJA3 (another irrefutable source).
3. An additional player edge of 7% is grossly high for surrender when counting. There is no complete card counting system which furnishes an edge even remotely this high.
4. You stated in an earlier post that surrender makes 16 vs T even more valuable. The opposite is actually true. This is because you would then surrender all initial 16 vs T hands at counts of -3 and higher and would hit at counts below -3. You would only have the opportunity to stand on 16 vs T for multicard hands and hands occurring after splitting. That is, the frequency of the hit/stand decision for 16 vs T drops dramatically.

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Originally Posted by Gronbog
It's good to be sceptical of published data. I am that way myself. However, some sources have proven themselves to be reliable. The Wizard of Odds is one of those sources and the CV software is state of the art for our game.

It's also good to do you own research. However:

1. Your calculation for frequency of a dealer ace is incorrect. The probability off the top of the deck/shoe is simply 1/13~=7.7%
2. Your calculation of the occurrence of 16 vs T is also incorrect. 4/13 is correct for a dealer face card but what is the 42%? The correct probability for 16 vs T is 3.5% according to BJA3 (another irrefutable source).
3. An additional player edge of 7% is grossly high for surrender when counting. There is no complete card counting system which furnishes an edge even remotely this high.
4. You stated in an earlier post that surrender makes 16 vs T even more valuable. The opposite is actually true. This is because you would then surrender all initial 16 vs T hands at counts of -3 and higher and would hit at counts below -3. You would only have the opportunity to stand on 16 vs T for multicard hands and hands occurring after splitting. That is, the frequency of the hit/stand decision for 16 vs T drops dramatically.
What he said!

Actually, as Norm and I have already stated in this thread, it turns out that we are independently working (I, along with Gronbog) on ranking indices according to their incremental value to SCORE. The process is computationally intensive work if it is to be done properly, and, when it comes to that, I think that the membership here is aware of our standards for publishing research.

That said, unfortunately, most of what our new junior member, aceside, has stated is simply not correct. He's excused. If this stuff were easy, everyone would be doing it! Gronbog and I have already produced a prototype for this sort of endeavor, and simply as a reply to aceside, no, 16 vs. T is not twice or more as important as insurance. And, as Gronbog stated above, your frequencies are badly mistaken. While the new research may shuffle things a bit, you surely have the correct frequencies for making a departure with 16 vs. T or insurance from p. 62, column 6 of BJA3. You have to consider not only the frequency of the holding and the dealer upcard but also the frequency of the count at which the departure is made.

Finally, you can't possibly rank "surrender" as a single value or contribution to overall SCORE. Surrender is a rules variation, not a single index departure. Rather, surrender comprises an entire collection of (very important) departures. Taken together, they are worth a great deal. You can see that easily from the BJA3 summary charts that precede each group of tables. Just look at any given rules set and then compare the SCORE to that of the same rules set with surrender added. But, in this case, "surrender" means the Fab 4. Obviously, if you use even more surrender indices, their collective value and ultimate contribution to SCORE is magnified.

Frankly, I can't censor or suppress further discussion of this topic here or anywhere else, but I would simply ask you to be patient as we continue to work on this.

Don

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Originally Posted by DSchles
unfortunately, most of what our new junior member, aceside, has stated is simply not correct.
I am glad I joined this forum. You are all very helpful. I am a blackjack player not a mathematician. This is some reason I joined this forum to seek help from you. I would like to learn from you, especially Don, Gronbog, Norm, and G man and more. I played a lot that is why I trust my intuitions. However, I made some mistakes in my calculation of blackjack hand frequencies. Let me correct them one by one. But firstly, let me simplify the math first. We assume it is a 6-deck game without surrender and consider only the player’s first two cards.

1. Player makes a stand/hit decision at 16v10 at a frequency of 42%*(13/169)*(4/13)=1.0%. Here the 42% is the frequency of true count +0.
2. Player makes insurance/no decision at dealer Ace at a frequency of 5%*1/13=0.4%. Here the 5% is the frequency of true count +3.
3. I overestimated the contribution from surrender option. I don’t know how to get a number here.
4. I totally agree with Don “you can't possibly rank "surrender" as a single value or contribution to overall SCORE”. I always combine surrender into the hit/stand option.

Finally, I will read more into your books to learn and expect to see more research results on this optic.

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OK, so you are factoring in the frequency of making the departure from basic strategy in each case. That's correct. However, your frequencies are still not right.

For 16 vs T, (13/169)*(4/13) = (1/13)*(4/13) is correct for being dealt 6,T from an infinite deck off the top but you need to multiply by 2 to allow for T,6 and you also need to consider all of the many, many other ways that you can end up with 16 vs T. For the 6 deck game you've been referencing, the probability of 6,T or T,6 is more correctly (24/312)x(96/311)x2, but that still doesn't account for the other ways to end up with 16 and how often they each occur when you're playing the correct strategy for your count.

• 42% is not the frequency of TC=0 nor the frequency of TC>=0. For a six deck game with 4.5/6 decks of penetration, deck estimates accurate to the nearest 1/2 deck and flooring used to resolve to an integer, the frequency of TC=0 is about 27.7% and the frequency of TC>=0 is about 55.0%.
• For the same game, the frequency of TC>=+3 is not 5%. It is about 8.7%.

These numbers have been determined by simulation and you can verify them using CVCX and/or CVData. The point is that these calculations can be very tricky so simulation is actually the easiest way to obtain these numbers.

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To simplify the math, we assume a game of infinite decks game without the surrender option and consider only the player’s first two cards. Player only is allowed to have two cards. To let me make corrections again:

1. Player makes a stand/hit decision when 16vs10 at a frequency of 55%*(13/169)*(4/13)=1.3%. Here the 55% is the frequency of TC>=+0.
2. Player makes an insurance/no decision at dealer Ace at a frequency of 8.7%*(1/13)=0.7%. Here the 8.7% is the frequency of TC>=+3.

The (6,T) and (T,6) permutations have been considered, and all other combinations (7,9), (8,8) for two-card 16 have been considered too. Thank you for your insight.

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Originally Posted by aceside
I am glad I joined this forum. You are all very helpful. I am a blackjack player not a mathematician. This is some reason I joined this forum to seek help from you. I would like to learn from you, especially Don, Gronbog, Norm, and G man and more. I played a lot that is why I trust my intuitions. However, I made some mistakes in my calculation of blackjack hand frequencies. Let me correct them one by one. But firstly, let me simplify the math first. We assume it is a 6-deck game without surrender and consider only the player’s first two cards.

1. Player makes a stand/hit decision at 16v10 at a frequency of 42%*(13/169)*(4/13)=1.0%. Here the 42% is the frequency of true count +0.
2. Player makes insurance/no decision at dealer Ace at a frequency of 5%*1/13=0.4%. Here the 5% is the frequency of true count +3.
3. I overestimated the contribution from surrender option. I don’t know how to get a number here.
4. I totally agree with Don “you can't possibly rank "surrender" as a single value or contribution to overall SCORE”. I always combine surrender into the hit/stand option.

Finally, I will read more into your books to learn and expect to see more research results on this optic.
A few more clarifications. The TC is >=+3 8.69% of the time for 4.5/6, not the 5% that you mention. And the frequency of all holdings of 16 vs. T is the 3.5% given on p. 62 of BJA3. So, yes, you will make a departure of standing on 16 vs. T (.035 x 0.55 = 0.0192) 1.92% of the time, or about twice very 100 hands you are dealt. You will take insurance 0.077 x 0.0869 = 0.67% of the time, or once very 150 hands. So, you use the standing index 2.87 times more frequently than you take insurance. But that's just the beginning of the story.

Next, you have to consider your average bet that you have on the table when you make each play. And, it is here that you will find the insurance wager to be more than three times as large, with, say, a 1-12 spread. So, this is how insurance "catches up" to 16 vs. T in importance. Finally, and it's much too complicated to explain here, but I do it in the book, you have to consider the page 62, column 9 calculation that takes into account how efficient your particular count (in this case, Hi-Lo) is in actually detecting and correlating to the play under discussion. So that impacts the importance of the index as well.

Many people skip right to all the charts in my book without reading all of the preceding material as to how the charts were generated and the logic and math behind them. To each his own, but to me, understanding the concepts is important and shouldn't be skipped.

Bottom line: insurance and 16 vs. T are the two most important deviations in the game, and their importance and contributions to SCORE are very close to each other -- so much so that, under certain game conditions, 16 vs. T can be more important.

Enough for now.

Don

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Originally Posted by DSchles
Bottom line: insurance and 16 vs. T are the two most important deviations in the game, and their importance and contributions to SCORE are very close to each other -- so much so that, under certain game conditions, 16 vs. T can be more important.
If insurance is the most important skill for making money, I just do not see any future of AP. This conclusion does not justify our education. Thank you somuch for you instruction. Happy New Year!

8. Did you find this post helpful? Yes | No
Originally Posted by aceside
If insurance is the most important skill for making money, I just do not see any future of AP. This conclusion does not justify our education.
Someone who is in the very early stages in development in forming a solid foundation regarding the learning stages of a game should not be making uninformed conclusions.

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Originally Posted by BoSox
Someone who is in the very early stages in development in forming a solid foundation regarding the learning stages of a game should not be making uninformed conclusions.
I meant to say is that the chance of taking insurance is only once every 150 hands. So, how is possible for you guys to make money?

10. Did you find this post helpful? Yes | No
Originally Posted by aceside
I meant to say is that the chance of taking insurance is only once every 150 hands. So, how is possible for you guys to make money?
Knowing when to take insurance is only one tool in a large tool box.

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