By Clarke Cant
Chapter 7, Shuffletracking to the Limits, how to use the blackjack formula for ST too.
Imagine if you will going in your favorite casino where you find a 4 deck shoe game and the dealer is shuffling an orange deck and has a red, blue and green decks stacked already to load into the shoe. She tells you, “hold on a second while I finish this deck. The pitboss is not in a good mood so I will have to shuffle on the last round where a card appears from the green deck. Otherwise I would deal them all out.”
You quickly salivate and try to come up with all of the ways you could borrow money if you needed to in that you are playing 3 single decks stacked together, but with a shuffle point, C=1, all the cards of each deck are dealt out and even part of the green deck. The estimate of your edge using this book, or BJF, is sky high.
As the chips go back and forth and your pile of chips eventually rises higher and higher (and turns ever more disgusting colors, but higher denominations) the pit boss suddenly appears with 4 red back decks and says, “enough of this crap.”
The shoe is now loaded once again but now the dealer shuffles each new deck and you notice that she is grabbing precisely 26 cards for each riffle. She deals. You notice that she has just gone through 51 cards, and of course the burn card, when on the next round she turns the discards 90 degrees and lo and behold, the discard rack is wide enough to fit the cards edgewise. She keeps all of the decks still separate.
You are every bit as good as she is, in eyeballing the cards, and are still able to tell when you are going from one deck to another during a round. Suddenly the pitboss appears and growls, “hey let me show you how I want you to shuffle these damn cards.” With that he takes the cards, it was time to shuffle anyway, and washes (moving the cards about face down as if shuffling a dominoes set) all 4 decks. He picks up precisely 52 cards and counts them out, saying, “just checking to make sure there are 52. Hey what count are you using there buddy?”
You meekly respond, “hi-lo,” as you try to reach your cell phone in case you have to face another rough session with the guards and want to have your lawyer on the line.
“Well bud, I usually use hi-lo myself. I am not as good at the Uston +/- or the Zen these days. Everybody seems to be using hi-lo.” With that he counts the 52 cards and keeps tossing and adding cards until he shows you the deck and asks, “could you count them sir? Hey I want you to wash all the cards and deal them,” he says to the dealer.
She responds, “oh he is not in a very good mood,” but she keeps on making sure each deck totals to 0 hi-lo points.
You don’t know what the hell to do now. But you go ahead and play as the dealer still grabs 26 cards in each hand, while doing each riffle, and still stacks the discards into separate deck size piles…..
The estimate is now your BJFT=BJF*CFS; using the BJF for C=1, still dealing each subdeck, here with a size of 1 deck, to the last card, and CFS=BE^2. For counts that don’t equate the ace value and tens value, you have to adjust the count for aces.
You adjust a count for aces the same way that you would adjust count values from an unbalanced count to obtain an equivalent balanced count.
The K-O count uses the hi-lo numbers plus counts the 7 as +1, or:
A 2 3 4 5 6 7 8 9 X
-1 +1 +1 +1 +1 +1 +1 0 0 -1
To evaluate the BE and PE, using the Blackjack Formula we must adjust out the imbalance, which we do by subtracting 1/13 from each of the above. The K-O count becomes:
-14/13 +12/13………._ to counting the 8s and 9s as –1/13, and the tens as –14/13.
(since Ken Fuchs said such nasty things about me and a prior draft of this book I am going to act childish, pout and leave it to the reader to figure out the PE and BE for the K-O system)
If you use the K-O in true count mode you have the full power for your BA and PA calculations. If you use the running count mode your effective PE is cut in half. For the K-O system Ken Fuchs has good betting tables (good for this count…) that let you use the full BE figure. For some systems this should be cut down as well.
When you adjust an ace zero count for the aces you do the same calculations except the count initially now has a minus imbalance. If you were ace adjusting the Hi Opt I count, used in chapter 3, you would have a minus 1 imbalance. Zen counts would initially use –2 for the ace. You would add +1/13 to the count values (or tags if you spend a lot of time on bjmath.com) and evaluate the same way.
In both converting unbalanced counts to equivalent balanced counts, and ace adjusting a count that has aces counted at a lower value integer than the tens, you adjust during play by keeping count of the number of ¼ decks seen, the aces as a side count. For typical unbalanced count adjustments you substract one point for each ¼ deck seen, from your running count; for typical ace adjustments you add the difference between counting ¼ decks as +1, and aces, as –1, to your running count. The true count is found by dividing by the number of decks in the initial pack unseen. Ace adjustment of this sort goes back to the first edition of Beat the Dealer, by Edward Oakely Thorp. Converting unbalanced counts occurred to many, many people, but the first to publish, and the first to write a formal proof of the validity of this, was Brett Harris. Brett Harris has also comeup with an unusual series of counts that use the additional information that subtracting that –1/13 gives, to have a count only have one or two levels of integers involved in its card values (tags), but give the same playing information as a much more complex count. Now back to our strange casino….
On every shuffle she checks each deck to make sure each subdeck totals 0 hi-lo points. But pretty soon the pitboss shows up and again and yells, “we are going to show him we know countermeasures. Shuffle them and deal them out just like the joint next door does.”
Magically as you play a screen flashes in your head, and reads, “the next subdeck has +3 points more than zero. The next subdeck has –2 points than normal. The last subdeck in play has –2 points more than normal, the discard subdeck has +1 more point then normal.” But you keep on playing and play the first subdeck as if the running count through it were 3 less than your actual count. You play the next as if the running count were +2 higher than normal.
If you were to magically know that a deck had additional points in it than zero, you should play as if the running count differed by the negative of that addition. For the first subdeck we have SD1=+3; play through as if the running count were 3 lower. SD2=-2, play as though the running count was 2 higher. SD3=-2; play as if the running count were higher. You still play as if each subdeck was separate, but your win rate goes up.
The reason is that each deck now has volatility within it – which is how profits from counting come about, and an added measure of volatility from being mixed in with the other subdecks. Your overall edge is: BJFS (your total edge playing this shoe game with this magic). BJFS=SQR (BJFT^2+BJFO^2).. BJFO is the BJF for the game if your were playing without this magic.
You win even more money than ever. The dealer starts hinting at romance, and the pitboss suddenly reapears and says, “don’t grab so many cards each time.”
Your profits skyrocket as she grabs only 13 cards in each hand. Your subdeck size is ½ deck now. This is why the V tables were left in interpolation form and didn’t have entries for the hundreds of possible subdeck sizes. This imaginary casino uses a one pass shuffle, leading to the following relationship:
Subdeck size (which you use for the BJFT) =Grab size (the fraction of a deck that the dealer uses for each riffle)*2 (since there are two grabs in each riffle) *passes (the number of times the entire pack of decks is broken down and shuffled)
This is how you estimate the BJFS for when you use the magic of shuffle tracking.
I appologize to people like George C. and others who may have covered this territory before and would like to give credit to him, and Arnold Snyder for some of the information that follows, but mostly I am going to use the above terms, as opposed to others like slugs, plugs etc., and follow the general description of shuffle tracking given by Michael R. Hall, who posted early on about shuffle tracking (ST hereafter). What we will add are my own labels , some tips on using the built-in error checksums that I believe are left out in most works to date, and some opinions (of course).
Approaching a fresh table you should first of all observed the shuffle used and the mapping of the shuffle. Cards as they are used are placed in the discard rack such that you should look at the rack as having sections you label, having counted them:
G1 is the first group of cards of G size number of cards. Most casinos deal using lay and pay these days, mainly for survelience reasons. The dealer may pickup the cards that complete the first grab size as she picks up the cards from the player, 2 spots to your right. You must keep that count in one register, whether it is in your head, using some memory trick (as in, The Memory Book, by Jerry Lucas and Harry Lorayne) or with some device (rotating your chips is suggested almost to death, but it works). You must then start the count for G2 on the hand one spot to your right. Unlike handheld games it is not recommended that you adjust your count too often during play unless the game is faceup or you can keep another spare register available in your head. You should count each card for each G section as it goes into the discard rack.
When the dealer reaches the shuffle card she will take out the remaining cards – called plugs, or sometimes the procedure of handling them is called plugging – and will either stack the discards on top or place them on top of the discards. It is slightly better that the dealer stacks the remainder, on top of the discards, than the other way around. If the last round is not finished on a G boundary, some of the remainders can be associated with the last incomplete G, or Gn, using the labels given here.
There are a variety of tactics to use to map the shuffle, that other works can cover, and where Arnold Snyder has developed mapping labels, where shuffle maps can be read too by paid users of his rge21.com, and where similar can be found to paid users of bj21.com and to registered shuffle tracking project workers on bjmath.com (I tend to avoid these paid or registered sites simply because I know how personal information could be hacked by the misfortune of teaching an otherwise dense ex-wife how to hack). For one pass shuffles the finished pack of cards should now be viewable as a stack of subdecks:
Take careful note of two or more of those SDs, and, well all of them of course. The highest value of SD of course, which for shuffle tracking, see above, is the SD with the most MINUS count total, and at least one or more of the SDs that are drawn from the discards ONLY, and not the remainders (or plugs if you still insist).
Now comes the cutting ritual. Long term your profits are enhanced if the cuts are made as close to the SD borders as possible. About everyone, except Bob Fisher (who I respect on everything else it seems except one prank that I still laugh at), recomends that you try to cut the most profitable subdeck to immediate play first, if you are cutting. I agree, in that you can then possibly be requested to cut by the other players—they feel you are a “lucky cutter,” as everyone will have a better chance with the best subdeck played first. You don’t really need the best subdeck to be played first, and knowledgeable pitbosses will often see this and suspect you are shuffle tracking from it, but your goal is to simply try to see that the cut is on a SD boundary (by the way SD is also a usual abreviation for single deck and this label should help keep in mind what ST can do). Whether or not the cut is, you begin counting for your playing decisions and G counting immediately (at least the SD you saw split up is now at the back of the pack and won’t “bother” you anymore, and you still have approximate information, that at least is good enough to raise or lower your betting on, about that fraction of SD section you are starting on—maybe it wasn’t ruined.
The last step is your error checksums. This involves the count in your selected SD, coming to the predicted count from your tracking information. Once again it helps if the cut fell on a SD boundary.
I know that this is a lot of work: counting G sections at minimum, and keeping separate registers, while counting as well through each already mapped SD section. The best way to handle it is to concentrate on the new G sections. Begin keeping a second count, called the temp, but thankfully with the same cards as you count them for the new G sections, everytime you are definitely in a new SD. Play that SD as its own subdeck, and with the negative of the offset from previously tracking and assembling G sections for that SD, added to your temp. You can even bet and play by the true count of the temp count, but be prepared to have to switch if completion of your hand takes you into another SD. If that happens, start the temp over, but keep on with the counting for the new Gs. Think of say seeing a hand bust that has a 4,X and X. For level one counts this hand is –1. Think of one minus thrown in the G and one in the temp.
Finally we are near the end—but you are correct ST is very hard work. It is at least 3 times as hard as regular counting. But few other books and posting have ever dared to put down what it takes to take ST to the absolute limits.
The last step to discuss is your checksum SD, when you come to it. These guidelines tend to match several trials runs on one of the popular tracking practice programs.
If your checksum SDs match predictions, you are ready and are likely getting the full advantage that this section predicts.
If you are off by +/-1 you should depend on getting 80% of the BJFT added to your edge and move your fraction of bankroll down accordingly.
Off by +/- 2 lower the BJFT for betting estimates to 60%
Off by +/-3 lower the BJFT to 40%
Off by +/-4 drop the BJFT.
You are not expected to have to work out these levels during play, but each session should have unit sizes already worked out to drop down to. Suppose you are betting in a game that has a fully mapable 2 pass shuffle, where the grab sizes are about 18 cards. Your suddeck size is about 1.4, (go ahead and round to 1.5) and 6 decks are in the pack. You might still have a huge edge overall but your unit size might go from $100, down to $15, depending upon the other variables. If your error is at the final level your betting should drop down to a normal betting spread for the game overall.
That is all the steps to take ST to the absolute limits but there are several pointers as well. Your mapping gets detailed, not having to estimate G sections averaged through the remainders, faster with deeper shuffle points. You don’t just gain from a higher BJFO component. Don’t be afraid to leave if a new dealer changes the shuffle (map-wise) or has different grab sizes. Grab sizes, and errors, can be compensated by adjusting your SD size upward by playing 2 SD sizes together, but you still should base your tracking on the grab size. Have as many estimates prefigured as possible after your initial scouting. You can use the BJF in a coffee shop, but believe me, this book is not going to be welcome in any casino, which you should be able to see after reading the prior chapters (maybe after casinos settle down and realize few people – as usual – are not going to apply themselves?, but only the future knows.). Many people may decide that the other tactics, such as bangers, are more than enough to add to their shoe playing. I don’t recommend that ANYONE (except maybe….naw too cheap a shot) use ANY unbalanced count for ST. You may or not want to take ST to these limits but I have yet to find any valid way to handle the numerous pivot adjustment that would be necessary to these limits, or any way whatsoever you could adjust your pivots to any unusual SD sizes. If you cannot take a system all out, why bother?