Card Counting Math Question ?
  • I have this lingering question about card counting strategy and the math used to calculate the odds of hitting any particular hand for all you experts out there. Do these formulas work for perfect decks or do they take into account that when playing an 8 deck shoe 2 decks are blocked? How can one know what the cards are if we are not playing with a full deck? LOL :D I'm just trying to be realistic. The blocked off decks can contain almost anything. Sometimes I have played through a shoe and wondered to myself and the other players...gee there were not many aces in play that round..or gee there seemed to be a shortage of face cards.....So is the wizards math based on perfect decks?
  • The quick answer, I think, is that it doesn't matter and of course there is no way to tell what is left in the deck.

    What is important is what the proportion of high cards to low cards is left in the deck (or A's), so that you know that the rest of the deck is loaded with high cards or loaded with low cards and then bet/play appropriately.

    You do know more and more about the deck, though, the further you make it through the deck. Thus, if there are 5 10's left and you only have six cards left, the chances are really good you are going to hit a 10. If there are 5 10's left and you have 100 cards left, not so great. Thus, "penetration" -- or how far into the deck the cards are dealt is important.
  • The cards behind the cut card are assumed to be in play because we don't
    know what they are. If for example, there are two decks behind the cut card
    and we have one deck remaining to play, the distribution accross all three
    decks is what we are interested in. If the count tells us that the three decks
    contain 10 extra 10's , that would be extra 10's accross all three decks.

    Yes, there will always be a level of uncertainty regarding distribution that
    would place most of the extra 10's out of play. More often than not the
    distribution is close to even accross all three decks and that is why we
    must true count using all the remaining decks.
  • I would add to Ray's comments that what you are talking about is called "penetration", generally specified as either number of decks cut off out of play, or number of decks actually dealt. For example, at the MGM, a typical game with a 6D shoe might be one deck cut off. I call that 83% penetration, since 83% (five of six) decks are actually dealt before the next shuffle. Others might say one deck cut off (same thing obviously).

    Penetration is really the most important "rule" a counter is concerned with. An 8D shoe with 3 decks cut off is not much of a game, compared to a DD game with 50% cut off (also not so good but far better than the 8D game). This is true because of the number of unknown cards you have. That means that the true count might be applied to a larger number of cards that won't be played, and who knows whether those 10's are at the front part of the remaining shoe (and will be dealt) or are they at the back part where they won't be in play. I personally consider a DD game with 60% penetration, meaning that out of the 104 cards used, about 62 cards are dealt in play, to be the minimum game I will play. I have no trouble finding DD games that have 67% to 75% penetration, and a few that reach 80% and beyond. The deeper the game is dealt, the lower the variance, and the better your hourly win rate...
  • stainless steel rat said:
    ....I have no trouble finding DD games that have 67% to 75% penetration, and a few that reach 80% and beyond. ... ...

    SSR - Where in the world do you have "no trouble finding" those DD games??.....Certainly not in LV, Laughlin, AC, or Connecticut..........Grifter
  • Grifter- In the Midwest and Tunica, you are lucky to get 75 on six deck and
    some are very close to two decks. DD 60% and many timesa 50%. You may
    find that on the off-days with few tables open and fast dealers some slight
    improvement. Zero single deck and no surrender anywhere that I know about.
  • Ray - Yep, same out here .....Grifter
  • From what I can get from Nickel's post, CT may have some of the best shoe
    games anywhere. Don't know about DD. The CT shoe games must be in the
    mid 30's HA.
  • Grifter:

    One of the places was the MS coast, although that is currently not an option. The now defunct Copa had a very good DD game, and a good SD game as well..

    I found two different dealers at the Plaza that would place the cut card about 75% back, and then deal another round (sometimes two if heads-up) after the card came out... The slot in the discard tray used to position the shuffle card is pretty wide and the dealer has some discretion. One older dealer I played with nearly every day didn't use the slot, just put it in where he wanted, which was usually at the 75% mark. I have heard that shortly after I was there, they were smoked by a hole-carding team and the DD game went to a DD shoe to stop the hole-carders. Haven't personally confirmed that however.


    played some good SD games, both at Binion's downtown, and in Laughlin. All that I played were 3:2 real BJ games, dealt to RO6 (and I found one dealer that would go RO7 heads-up, because I could play so quickly he got tired of shuffling. :)

    I think the trick here is that you have to put your eyes on every table, and watch the dealers. I spent my first day in Vegas scouting dealers downtown and nothing more. All the downtown casinos that I visited had some form of SD, most were RO6. The Copa on the MS coast often used a shuffle card but a couple of dealers would give very good penetration under the right circumstances, so long as we didn't "burn the game down"...
  • In other words, "no trouble finding DD games with 67%-75% penetration" is essentially "horse pucky".

    So let's clear the air for everyone.......DD games with penetration of over 65% are very difficult, if not impossible, to find. Those went away in the late '80's, early 90's.

  • Great info guys. I did find some DD games at the Riverside Casino in Laughlin and the Gold Coast in Las Vegas but that was 2 years ago. I had no idea they were the best to play as I was a relative newbee to the game. So are you guys saying that an 8 deck shoe with 2 decks blocked is a good game? Will the wizards odds be accurate and consider the variance of the blocked cards or does it assume the decks are equal? I would think the odds change based on the amount of 10's and aces in play and that is something you never have an accurate read on seeing as not all the cards are in play.
  • Moosehead- Hard to understand ain't it? Suppose that we have your 8 deck
    game with one deck of play remaining and two decks cut off (75% pen).
    Further, suppose the count is plus two and you bet 8 units. That works out
    to be a running count of 6/3= +2 true. What do you expect to happen?

    First, we know that there are 6 extra large cards somewhere in the three
    decks and this favors the player. Second, we don't know that our next hand
    will contain a BJ, 20, 2,6 10,6 or whatever. We simply know that the more
    large cards favor the player. In actual practice, we could lose every hand,
    but over the long run we will win more money as a result of this favorability.

    All our strategy variations and those of the wizard regard all cards as being
    available for the simple reason that we can't identify those specific cards
    that are behind the cut card. The card removal that we know about is our
    only method for decision making other than basic strategy.
  • As Ray points out... as one gets closer to the burn card the LESS likely the count will rectify to a neutral count.

    However it will correct to neutral by the last card in the shoe.
  • Let me note the "true count theorem":

    as cards are dealt and hands are played, the true count tends to remain the same, while the running count tends toward zero.

    This means that when you pop up to a TC of +4, it will tend to stay there rather than change, although the running count will tend to drop as cards are dealt. But since the remaining cards are decreasing, the true count tends to remain constant.

    A quick question: Ignore the case where the TC remains unchanged, so that we now assume that the TC is going to climb or fall as the game progresses. Which way is it more likely to change? Answer in the next post...
  • Here is the possibilities:

    For the TC to fall, big cards must come out. 5 of every 13 cards is a big card on average, so the probability of the TC calling is 5/13.

    For the TC to rise, either small cards come out, or neutral cards come out. First, it is obvious that if small cards come out, the TC rises, correct? But what about neutral cards? That's the tricky part. When a neutral card falls, the running count remains unchanged, but the cards remaining drops. SInce TC = RC / remaining_cards, the TC rises here as well.

    So, there is a 5/13 chance the TC will fall, an 8/13 chance the TC will rise. Of course, as the T/C theorem states, the most _likely_ thing is for the TC to remain constant, but if it is going to change, it will most likely rise rather than fall.

    Not very intuitive, until you understand the idea that neutral cards hitting the table makes the RC remain the same, but the TC rises because the cards left drops...

    Todays mental puzzler brought to you by SSR.

  • All very interesting and highlights just how thin things are in BJ. It makes me
    think of something seldom discussed in our post. You win or lose in chunks.
    last year about this time, I won 8-9 hands in a row playing two hands.
    It amounted to 1075 bucks without losing a single hand. How is that for a
    chunk? Ridiculous, but true and with flat bets of $35 thru-out.
  • I did that at the BC (vegas) two years ago. Got booted, never varied my bet, never used a departure index, just won. It is interesting that this is a "chunky" game more often than not. That is, large gains, large losses, ever moving upward over time. When someone thinks of an EV of $20 per hour, they rarely think of it is as +1040 the first hour, -1000 the second. :)
  • Where is the BC?
    Twice now you have mentioned it,but I'm not sure which casino you are referring to.
  • He's talking about the Barbary Coast.....Down by the Flamingo and Bally's... They have zero tolerance for counters and winners.
  • Thanks.
    I've walked thru it on my way to the now defunct
    Bourbon Street.never cared for the way it looked.
    Is Gold Coast the same way?
  • according to Max Rubin they are both (barbery coast and gold coast) anal about losing even a buck.
  • NYB...

    Never been in the gold coast myself. Was in the "El Kotex" and they seemed to be more than a bit paranoid about counters as well, but this was two years ago. I've since heard from other counters that things have gotten better there, except that it is down on the end of the casino row on Fremont and puts you off in the boondocks. Saw some very strange looking people gathering around in that area of town, wife didn't like it at all...

    And Grifer was correct. BC == Barbary Coast, Or Bar Counters. Either way. :)

    I have been "permanently" kicked out only twice in my counting days, once at the BC, once at a midwest casino where someone walked up behind me and bet big and won a couple of grand off my hand. Security ran both of us off saying "we don't appreaciate team play here, etc..." I had never seen my "team member" before in my life. :) We had a good laugh as we left, but it was pretty stupid...

    I did get "burned" on the MS coast the week before Katrina. I'll find out how good their records are if this particular casino opens back up next year. :) But I got burned there for stupidity, using my normal spread but a much bigger "unit" due to someone with me wanting to be the "bankroll"... Next time I went back, they were waiting. :)
  • stainless steel rat said:
    It is interesting that this is a "chunky" game more often than not. That is, large gains, large losses, ever moving upward over time. When someone thinks of an EV of $20 per hour, they rarely think of it is as +1040 the first hour, -1000 the second. :)

    Ya or in my case last weekend was -900 the first hour and +1000 the next 7 hours over 2 days :( .. :) I played the GC in LV but I guess I did not win enough to get a warning! :)

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