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Thread: Shuffle Tracking For Imbeciles PART 1-2

  1. #1

    Default Shuffle Tracking For Imbeciles PART 1-2

    Originally posted by 'Sonny' at Ken Smith's BJINFO HERE

    Shuffle Tracking For Imbeciles – Part 1

    Okay, so maybe the title needs some work. If I were Arnold Snyder, perhaps it would be titled “Algebraic Approximations of Normal Distributions in Single-Pass Riffle Co-Minglings and Disbursements of Cards in the game of 21.” Maybe my title isn’t so bad.

    I’ve read several “Shuffle Tracking For Dummies” type articles, but have always found the techniques to be too difficult to apply in a casino nvironment. I decided to start looking for a way to simplify and optimize the current methods of shuffle tracking in order to facilitate their use in casino play. Why should the “dummies” have all the fun? Us imbeciles wanna win besides! The following will summarize my findings on shuffle tracking – specifically what Mason Malmuth refers to as “card domination”, however I have mostly heard the term “cut-off tracking” used to describe it. This type of tracking is only effective against a single pass shuffle, but variations exist that can be implemented against various shuffles. I believe the approximations in this article will help to simplify these cases as well.

    Summary of Cut-off Tracking

    Cut-off tracking consists of retaining the count at the end of the shoe (after the final round has been played and the cards are about to be shuffled). Assuming a balanced count is employed, the remaining unseen cards (hereafter referred to as the “cut-off slug”) must therefore have a value that is equal to the running count but with the sign reversed. For example, if the running count is -7 at the end of the shoe, then the cut-off slug contains cards that will sum to +7 in order to assure a zero final count. That means the cut-off slug is made up of mostly low cards which are bad for the player.

    The next step in tracking the shuffle is calculating the “average count density” of the used cards in the discard tray (hereafter “discards”). In the above example, assuming a six-deck game with five dealt, you would figure that the discarded 5 decks with a count of -7 would average a count of -7 / 5 = -1.4 per deck. If we then shuffle our cut-off slug with one of the discard decks, we would estimate a count of 7 – 1.4 = 5.6 for the new two-deck shuffled slug. We could then cut these cards to the bottom of the shoe, adjust our starting running count, and play with a significant advantage in a four-deck game. We are essentially using the cut card to “short the deck” of cards we don’t want. Similarly, this method can also be used to cut good cards do the top of the shoe.

    As we can see, this can be an incredibly powerful tool to use in actual casino play. Unfortunately, the computations can be a bit too clumsy for some of us to have ready when the cut card lands in front of us. Hence the need for a system that can be employed by the average imbecile.

    The Approximation Formula

    So isn’t there an easier way to get from point A to point B? Happily, yes! Let’s take a look at the formula we have already:

    Shuffled slug = cut-off slug + average count density (per slug)

    Average count density = discards / (number of slugs in shoe – 1)

    To break this formula down, we will see that the shuffled slug (the value of the cut-off part that we are tracking AFTER the shuffle) equals the original value of the cut-off slug plus the value of the estimated average count of each slug from the discards. The average count is found by dividing the known count (the running count before the shuffle) by the number of slugs it is comprised of (number of slugs – 1). We subtract 1 because we don’t want to include the cut-off slug in our division because it has it’s own value already.

    This is the standard formula which most of you have probably wrestled with while the dealer is shuffling and stacking away. Although it is very straightforward, the division to find the average count density can be difficult when awkward numbers are used. How many of you would have come up with +1.4 in the above example? After a few hours of casino practice, I decided that I couldn’t get it. I was having problems with switching the signs as well. I would get confused with the “negative slugs are GOOD now” concept and was afraid that I would cut a bad slug to the front by accident. So I did what anyone with the mentality of a thirteen-year-old boy would do: I whined about it being “too hard” and gave up.

    A few months later I sat down with Excel and used the above formula to make a spreadsheet showing different running counts for the cut-off slug and their final outcomes. I thought that having the formula with various solutions in front of me would help me to understand the concepts and perhaps memorize some of the tricky division problems. I figured that memorizing +1.4 is easier than finding 7 / 5. However, after staring at the numbers for a while, something occurred to me. Why am I going through all of this trouble? Why am I swapping signs, subtracting slugs, and dividing “average count Densities?” If I have to figure out how many 1.5 deck slugs are in a six-deck game I’ll scream! Yes, I know the answer is 4 and it’s easy to remember – but when you’re starting out and the dealers are using different penetration levels, it can become maddening. That’s when I saw the shortcut.
    "The dogs bark but the caravan moves on."
    .....................The Zengrifter Interview (PDF) |
    The Zengrifter / James Grosjean Reputation Debate
    -----------------------------------------
    “Truth, like gold, is obtained not by growth, but by washing away all that is not gold.” — Leo Tolstoy........
    "Is everything a conspiracy? No, just the important stuff." ZG

  2. #2

    Default

    Originally posted by 'Sonny' at Ken Smith's BJINFO HERE

    Shuffle Tracking For Imbeciles – Part 2

    The Track-Factor

    If only there was a way to get the final answer without going through all of the dividing and swapping and slug-number nonsense. Well, there is. Once I saw all the numbers in front of me I saw the shortcut. In this case it was a matter of working backwards from the final answer. Once we know the value of the shuffled slug (our final answer from Part 1), we simply divide it by the value of the original cut-off slug to get a simple conversion factor.

    Conversion factor = shuffled slug / cut-off slug (before shuffle)

    In the example from part 1, we used 7 – 1.4 = 5.6 as the value for our shuffled slug. We now get 5.6 / 7 = 0.8 as the conversion factor. We can now use this number to MULTIPLY by our original cut-off slug to get our final answer. Instead of fumbling with the “average count density” and adding it to the cut-off slug, we can have our answer with one simple multiplication! This new Track-factor (A.K.A.-the “Sonny is a brilliant imbecile” factor, although I have a feeling the former will probably stick) gives you all the power of shuffle tracking without all the messy “thinking.” Now, to us imbeciles at least, multiplying by 0.8 isn’t much easier than dividing 7 / 5, but there are more shortcuts to come.

    I ran the same calculations for more running counts (-20 to +20) and found that the Track-factor was constant for all. This meant that no matter what the cut-off slug value was I could multiply it by 0.8 and get the value of the slug after the shuffle!

    After a moment of euphoria, reality kicked in. This would ONLY work for six-deck games where five decks were dealt. I doubted if many people would find this information helpful, so I ran the numbers for six-decks with 4.5 dealt and again with 4 dealt. I figured that these would encompass most situations. What I found was fantastic!

    In the 4.5/6 game, the Track-factor was a constant 0.67 (actually 0.6 repeating, but who multiplies to the 3rd decimal place in their head? Not us imbeciles! We’re not giving up much accuracy anyway), and the Track-factor for 4/6 was an even 0.5. This meant that if you were “lucky” enough to find a game that cut-off two full decks (a game where most counters would point and laugh at all the ploppies) you could take HALF the value of the cut-off slug as the value of the shuffled slug. You are now playing in a game where the conversion is EASY and you know the average count of four of the six decks. Imagine cutting the last two decks to the bottom and playing in a four-deck game with a positive running count off the top! Gee, maybe the “brilliant imbecile” title WILL stick. This is a fantastic compromise: The casinos get to keep their lousy games and we get to make a profit on their backs! Yaaaay!

    Not quite. There are limitations to this. Although it does become easier to calculate in games with close to four-deck penetration, it is completely useless with anything worse. As Malmuth points out, if only three decks are dealt, they will most likely closely resemble the undealt portion the majority of the time. Also, the reduction in EV due to the poor penetration level, even at the four-deck level, can be somewhat costly. Conversely, the more cards that are dealt, the less cards there are to track. In this case, however, even knowing that a few extra fours and fives are behind the cut card can give you a good starting advantage in most shoe games.

    Although I am certainly not encouraging players to seek out tables with two decks cut-off (I’m not a TOTAL imbecile), I am pointing out that if you are stuck playing in a poor game (due to location or bankroll issues) this technique becomes simplified and may help you to get your edge back.

    So the next time you see someone playing at a six-deck shoe with lousy penetration, he may not be a ploppy – he may be an imbecile!
    "The dogs bark but the caravan moves on."
    .....................The Zengrifter Interview (PDF) |
    The Zengrifter / James Grosjean Reputation Debate
    -----------------------------------------
    “Truth, like gold, is obtained not by growth, but by washing away all that is not gold.” — Leo Tolstoy........
    "Is everything a conspiracy? No, just the important stuff." ZG

  3. #3

    Default Interesting topic

    This was an interesting article to read since there is very little that gets talked about when it comes to shuffle tracking. Too bad I can't do a sit down with Sonny so he could better explain his method, his theory. The techniques he is describing is only beneficial to a hand shuffled blackjack game. If a player is playing a 6D game and lets just say that 1-1.5 decks get cut off, the dealer under today's procedures are going to break up that 1-1.5 decks into at least 3 groupings to be placed into the remainder of the decks that were played at different locations, then they shuffle them.
    Last edited by Blitzkrieg; August 31st, 2016 at 03:38 AM.

  4. #4

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    "Summary of Cut-off Tracking


    Cut-off tracking consists of retaining the count at the end of the shoe (after the final round has been played and the cards are about to be shuffled). Assuming a balanced count is employed, the remaining unseen cards (hereafter referred to as the “cut-off slug”) must therefore have a value that is equal to the running count but with the sign reversed. For example, if the running count is -7 at the end of the shoe, then the cut-off slug contains cards that will sum to +7 in order to assure a zero final count. That means the cut-off slug is made up of mostly low cards which are bad for the player.


    The next step in tracking the shuffle is calculating the “average count density” of the used cards in the discard tray (hereafter “discards”). In the above example, assuming a six-deck game with five dealt, you would figure that the discarded 5 decks with a count of -7 would average a count of -7 / 5 = -1.4 per deck. If we then shuffle our cut-off slug with one of the discard decks, we would estimate a count of 7 – 1.4 = 5.6 for the new two-deck shuffled slug. We could then cut these cards to the bottom of the shoe, adjust our starting running count, and play with a significant advantage in a four-deck game. We are essentially using the cut card to “short the deck” of cards we don’t want. Similarly, this method can also be used to cut good cards do the top of the shoe."

    "If we then." We, meaning I or you (the dealer). That sounds nice but in the casino environment the dealer is going to follow house procedure and they are going to break up the cut-off slug.
    Last edited by Blitzkrieg; August 31st, 2016 at 02:41 PM.

  5. #5
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    Default

    Quote Originally Posted by Blitzkrieg View Post
    This was an interesting article to read since there is very little that gets talked about when it comes to shuffle tracking. Too bad I can't do a sit down with Sonny so he could better explain his method, his theory. The techniques he is describing is only beneficial to a hand shuffled blackjack game. If a player is playing a 6D game and lets just say that 1-1.5 decks get cut off, the dealer under today's procedures are going to break up that 1-1.5 decks into at least 3 groupings to be placed into the remainder of the decks that were played at different locations, then they shuffle them.
    I have only seen a dealer NOT do this a couple of times. I think you can find it if you look for it as hand shuffles are not standard procedure at any place except maybe on a couple tables without ASMs.

  6. #6

    Default

    Quote Originally Posted by Villiam View Post
    I have only seen a dealer NOT do this a couple of times. I think you can find it if you look for it as hand shuffles are not standard procedure at any place except maybe on a couple tables without ASMs.
    I'm not so optimistic. The cut-off slug at many casinos multi deck BJ games gets plugged back into the decks at multiple locations and many use ASM. Under favorable conditions in casino poker or private poker games a player or players could glance into a deck before the flop hits to the tune of 15.38%, how would one value such information vs. your opponents 2 cards (3.84%), before you or they even see the flop? What about an 11.53% view into a single deck?
    Last edited by Blitzkrieg; August 31st, 2016 at 02:31 PM.

  7. #7
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    Default Thank you!

    Thanks so much for the repost, zg!

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