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The GameMaster's Secrets:
Card Counting at BJ Tournaments

Most of us who write about playing in Blackjack tournaments are card counters, but we all pretty much agree that counting has little value in tournament play, because other factors - such as proper bet sizing and luck - have a much bigger impact on your results, so counting might be trying to do too much, which can lead to expensive errors. And yet, counting cards at Blackjack is the primary way we beat the casinos at their own game, although it's admittedly an activity that may pay off only in the long-term scheme of things. As you undoubtedly know, Blackjack tournaments typically consist of only 25 or 30 hands, hardly a long-term event. (Hey, there's a "reality TV" idea for you: Get a bunch of pros together and play Blackjack 8 hours a day for a year. Could anything be more boring?) Nope, no one is going to hit the "long run" in your average BJ tourney. But does that mean counting is completely useless? I think not.

As you may or may not know, every month we co-sponsor an online Blackjack tournament with Global Player Casino, which has been a long-term advertiser here. The basic object is to end up in a head-to-head match with me, where if you win, you get $1000; but if I win, the prize rolls forward to the next month. Well, I'm hardly invincible in these matches, but of the 35 or 36 held up to this point, I've won my fair share, although I've never really kept track. But I do know that there have been at least two times when the prize for beating me was $4000 because I had won the previous three matches. Gee, I hope those $4000 winners think of me fondly, now and then. Sorry, getting a little side-tracked here, so let's get back to counting the cards in Blackjack tournaments. But before I get too deeply into it, let me remind you that there are two reasons to count the cards. The first is to determine your edge over the casino (if any) in order to determine how much to bet and the second is to alter the play of a hand, according to the count. For example, the Insurance bet is a waste of $$$ for the player who uses only Basic Strategy, but if the count is high enough, it's actually a very good bet. So, while what we bet will more likely be determined by what our opponents are betting, the way we should play a hand can be greatly affected by the count and I'm all for using any advantage available.

I'm sure there are some successful Blackjack tournament players who always count the cards, but as one who's done it, I can tell you it's not easy, especially when you get down to the last few hands where calculating the proper bet size and trying to also determine the chip counts of your opponents is crucial. The "multi-tasking" involved makes it real easy to discard the count at this point, so I often use the count for the first 20 or 25 hands of a 30-hand match, then let it go as things get busy. But as we near the end of a match, we're also usually getting more deeply into the decks in play. Much like a tournament run by a brick-and-mortar, the nice people at Global Player Casino deal into the decks before shuffling. (In case you don't know, most - but not all - Internet casinos shuffle the cards after every round of play, regardless of the number of decks in use). At Global Player Casino, they set the penetration to about 75% for the Blackjack tournaments, whereas it's normally 50-60%, which still is pretty good for an Internet casino. The deeper the penetration, the more valuable card counting becomes, if it can be done at no cost to the other important aspects of tournament play, namely bet sizing and chip counting. Fortunately at an Internet casino, you don't have to "eyeball" your opponents' chip stacks, because their chip total is always displayed by their name. And bet sizing is critical only for the last three or four hands, so there's really no reason to not count.

Well, maybe one. The count I use in multi-deck games, the Hi/Lo, requires a True Count adjustment, which basically means I have to divide the running count by the number of decks remaining to be played, which then "standardizes" the running count to a count per remaining deck. In order to determine just how many decks remain to be played in a brick-and-mortar casino, I first look in the discard tray, which is where the dealer stacks the cards that have been used up to that point. Then, with a little bit of subtraction, I can easily determine the number of decks yet unseen and use that number as the divisor of the running count, which then gives me the True Count. As realistic as the game at Global Player casino is, it's still pretty difficult to determine how many decks remain to be played (yep, they even have a discard tray that fills up as play progresses), which makes calculating the True Count an "iffy" proposition.

The best answer to this would be for me to switch over to an unbalanced count like the "KO", which does not require a True Count conversion. But, at least for me, there are a few problems with that approach. First and foremost, I've been using the Hi/Lo count since 1978 and I'd hate to have to learn a new count that I'd be using only once a month. Secondly, unbalanced counts are really good at determining bet size, but not so good at telling us when to vary from Basic Strategy and I've already pointed out that we're more concerned with using the count to help us play the hand, rather than determine how much to bet. That's not to say the KO Count won't help you in a Blackjack tournament; in fact, I highly recommend it, if you play 6-deck games and participate in a lot of tournaments; it'll give you a decided edge, in my not-so-humble opinion.

But, naturally, I wanted to have my cake and eat it too, so I came up with a way to simplify using the Hi/Lo count, specifically at the matches held each month by Global Player Casino. While what I'm going to share with you here (for the first time anywhere, by the way) could work in brick-and-mortar casinos, it won't be as easy to implement, although it's possible. You'll see what I mean as we go through it. You may be wondering if this will help my opponents in the monthly tournaments and I have to answer, "maybe". But you need to remember that I usually share my secrets only when I've found something to replace them, so plan accordingly if you're going to be my opponent some day.

Basically, what I did was simplify the True Count conversion process by recognizing that several important components of my head-to-head matches remain pretty much unchanged as the match progresses. The first is that my number of opponents (one) does not change; if my opponent loses all of his or her $$$, I win and the match is over. Vice-versa, of course. Second, an interesting statistic of Blackjack is that each hand will, on average, use 2.7 cards and that's fairly accurate over a relatively small sample of hands of, say, 5 or 6. If you combine those two components, it's easy to see that one can determine - with reasonable accuracy - just how many cards remain to be played by simply knowing which hand is being played. For example, if we're about to play hand #10, then 9 hands have been played. Well, 9 hands with three players (don't forget the dealer) will use 9 x 3 x 2.7 = 73 cards, which is 1.4 decks. If the game uses 6 decks (as it does at Global Player Casino), then it means 4.6 decks remain to be played. So, to get a True Count for hand #10, all I have to do is divide the running count by 4.6 and I'll have a pretty accurate number.

You'll quickly see the problem with this shortcut in a tournament with more than one opponent: If the number of players changes, the system breaks down, because with fewer players, fewer cards will be used and the number of remaining decks will be somewhat inaccurate. For example, if you were playing against 5 others, there would be 7 hands (six players and the dealer) dealt each round. If you were about to play hand #10, a total of 9 x 7 x 2.7 = 170 cards or 3.25 decks have been used, which tells us 2.75 decks remain to be played. But if someone got eliminated on that hand, from that point on instead of 7 x 2.7 = 19 cards being used in each round, it would drop to 6 x 2.7 = 16 cards per round. The net effect of that would be to make you think there are fewer cards left than what's actually there, although that will make the True Count more conservative, which isn't all that bad. That said, it hasn't been my experience that players will drop out very quickly, so perhaps my concerns in that regard are somewhat over-stated.

Be that as it may, what I did was set up a worksheet on MS Excel, which calculates the number of remaining decks for various rounds of play, given a certain number of players. It ranges from 3 (2 players and a dealer) up to 8 (7 players and a dealer), because I'm not aware of any tournaments where there are more than 7 players at the table. Rather than go into a lengthy explanation of the chart, take a look at it and I'll meet you down below with some comments.

Across the top, I've placed the number of players, which includes the dealer and down the left-hand column, I've placed the hand number, which runs from 1 to 30. (If you want to create your own version, here's the basic formula for hand #1 with 3 players: =SUM(6-(((B2*A5)*2.7)/52)). You must copy this exactly, including all of the parens, or it won't work.) Anyway, if you'll look down at hand #28 for 3 players, you'll see the number 1.6 in red. I did that to "prove" my formula. If 3 players have finished 28 hands, then they've used 3 x 28 x 2.7 = 227 cards, which is about 4.4 decks, so 1.6 decks remain to be played. I highlighted the number below it, because that's the approximate shuffle point for a 6-deck game with 75% penetration and I'll talk about that in a bit. In the columns that cover other numbers of players, I did some more proving, like hand #17 for 4 players. Just to show the math one more time, if four have played 17 hands, then they've used 4 x 17 x 2.7 = 184 cards or 3.5 decks, which leaves 2.5 decks to be played. See how that works? You'll notice that I rounded all of the numbers to 0.10 of a deck, which is really more accurate than we need to be, but if you can divide a running count of 12 by 4.7 quickly and accurately, be my guest. The other notation you'll see is that some numbers are marked in bold print. Those indicate the approximate shuffle point, assuming 75% penetration. Of course, the cards won't always be shuffled at exactly the 75% level, because the software will complete all hands before shuffling the cards. But when the cards are shuffled doesn't really matter. All you need to do is make a mental note of the hand on which the shuffle occurred and then start at the beginning again. Obviously, once the cards are shuffled, six decks remain to be played, so that's the divisor to use for the next hand. Let's say we were playing at a table with four hands (3 players plus the dealer) and the shuffle happens at hand #23. As you were playing hand #24, the divisor would be 6, but at the end of hand #24, it would be 5.8, as is shown on the worksheet. That would be the divisor to use for calculating the True Count for hand #25.

Rounding to the nearest half deck saves a lot of this hassle, so that's how I do it. For my purposes, using a half-deck accuracy is just fine. What this means is, I divide the running count only by full- or half-deck amounts, like 6 decks, 5.5 decks, 5 decks, etc. So what I did was take the worksheet and create a more practical and easy-to-use version for my matches. I just set the little rascal next to my computer, keep the running count in my head and convert to True Count when necessary, by mentally dividing the running count by the indicated number. Again, I'll explain this after you look at it.

The first thing you'll notice is that I use the same divisor (6) for the first three hands, then switch to one that's half a deck smaller for hands 5-7, which reflects rounding more than anything else. But if you make a chart like this, remember that it's more accurate to determine the actual number of decks remaining at the end of, say, hand #7 and then use that to calculate the True Count for hand #8. At the end of hand #7, with three players (2 plus the dealer), a total of 3 x 7 x 2.7 = 57 cards or 1.1 decks have been used. So, there are 4.9 decks remaining when the cards for hand #8 are dealt. I round that to 5, but my point is that you need to move the divisor as shown on the worksheet "forward" one hand in order to get the best accuracy under this system. Beyond that, once you get the chart set up, it's very simple to use. I just look at what hand number we're on and then divide the current running count by the appropriate number in order to get the True Count. The only other thing I need to do is (mentally) make the first hand after a shuffle #1 and start the process over until the match finishes. If you're at a table of 6 (5 players plus the dealer) or more, you'll likely see two shuffles in a 30-hand match, but it shouldn't be a problem keeping track.

Big question: Could one use a chart like this at a tournament held at a brick-and-mortar casino? At some, yes. That's because some tournament rules allow players to have charts and other such items at the table, so long as they don't write anything down. The only way to know for sure is to ask prior to playing. You wouldn't want to get disqualified, so be sure to ask, first.

I'll see you here next time.