The GameMaster’s Blackjack School
Lesson 20: A Field Trip with the GameMaster
On February 1, 1997 the Station Casino St. Charles which is located on the banks of the Missouri River in a western suburb of St. Louis began offering a handful of tables of double deck Blackjack. The rules are the same as their six-deck game: dealer hits A-6, double on any first two cards, resplit pairs up to 4 times (and, effective March 3, resplit Aces as well) and double after split. Most of the tables are $25-$500, but there are usually one or two with a $10 minimum. The casino has an edge of .35% over the basic strategy player and the game is cut at the 75% penetration point and it’s dealt from a shoe (a Missouri Gaming Commission rule) with all cards face up.
Basic Strategy Variations
I have never played double deck before for any length of time, so I knew I’d have to do some homework to get ready. The basic strategy for double deck is the same for 4 or 6 decks, so there was not a lot there which I needed to work on. However, unlike the 6-deck games where I get up when the true count is -1 or lower, I knew I’d have to play through all the double deck shoes, so I’d need to learn more of the ‘minus’ indexes in the basic strategy variations. For example, in a six-deck game, I’d be long gone before I’d have to play a 13 against a dealer’s 5 in a highly negative count. But, one should hit a 13 vs. 5 at -4 and I needed to learn that. I added all the plays from -3 to -6 to my pack of flashcards which covers -2 to +10 and began to learn all the basic strategy variations from -6 to +10.
Next I had to work out a betting schedule. I always like to use an example of a betting schedule based on a $3000 bankroll so, even though I actually use a multiple of that, I’ll break everything down to that size so you can see how it will work with a minimum bankroll. The casino has a starting edge of .35% now that resplit of Aces is allowed; it was .40% and since each increase of 1 in the true count is worth .5%, at a true count of 1 I’d have a small edge over the casino. Since I’d be playing at a $10 table, I’d be over betting somewhat until the true hit 2, but there was no choice in the matter. Because double after split is allowed, my optimum bet would be 76% of my advantage. If this is confusing to you, reread the section on money management which begins at Lesson 7. Here’s a table I use to calculate the optimum bet:
|True Count||Advantage||Optimum Bet|
|0 or lower||(.35+)||0|
|1||.15% X .76||.00114|
|2||.65% X .76||.00494|
|3||1.15% X .76||.00874|
|4||1.65% X .76||.01254|
|5||2.15% X .76||.01634|
|6||2.65% X .76||.02014|
|7||3.15% X .76||.02394|
|8||3.65% X .76||.02774<|
Following me on this? At the beginning of a shoe, the casino has an advantage of .35% because of the rules of their game and the fact that they’re dealing from 2 decks. If the count goes minus, their edge will increase and the OPTIMUM bet in that situation is $0. That’s not the PRACTICAL bet, however, since it’s a $10 minimum table, so I have to bet that amount. As the count goes up, I can bet the prescribed percentage of my bankroll as indicated. For example, with a $3000 bankroll, my optimum bet at a true count of 3 is .00874 X $3000 = $26.22. Here’s how the chart looks for a $3000 bankroll:
|True Count||% Optimum Bet||Optimum Bet|
|0 or lower||0||$ 0|
|1||.00114 X $3000||$ 3.42|
|2||.00494 X $3000||$ 14.82|
|3||.00874 X $3000||$ 26.22|
|4||.01254 X $3000||$ 37.62|
|5||.01634 X $3000||$ 49.02|
|6||.02014 X $3000||$ 60.42|
|7||.02394 X $3000||$ 71.82|
|8||.02774 X $3000||$ 83.22|
That’s the theoretical, not the practical. As I stated before, I must bet at least $10 and I really feel strongly about the fact that the top bet should not exceed 2% of the total bankroll, so I end up with a $10-60 spread until the bankroll gets bigger. A 1 to 6 spread can beat this game, but there’s a nice little trick I can use to get more money on the table without increasing my risk too much: play 2 hands in positive situations. Here we go with more math, but stick with me; it’s important.
Since I would, whenever appropriate, play 2 hands, I’d need a table for the optimum bets for those situations. The rule here is that 56% of the advantage times the bankroll is the optimum bet for each of two hands. In other words, if it’s correct for me to bet $25 on one hand, I would be over betting if I bet $25 on each of two hands at the same true count. Because of covariance (the relationship of two hands to one another), the optimum bet must be reduced. Since I must bet at least $10 on each hand (Casino Station St. Charles doesn’t have that silly rule that a player must bet twice the minimum on each hand when playing more than one; many do, so check), it’s practical for me to spread to two hands of play only when the true count is at 2 or more. Here’s how that chart looks:
|True Count||% Advantage||Optimum Bet for Two Hands|
|2||0.65% X .56||.00364|
|3||1.15% X .56||.00644|
|4||1.65% X .56||.00924|
|5||2.65% X .56||.01484|
|6||3.15% X .56||.01764|
|7||3.65% X .56||.02044|
|8||4.15% X .56||.02324|
Factoring this with a $3000 bankroll gives us the optimum bet for each of two simultaneous hands at different positive counts:
|True Count||% Optimum Bet||Optimum Bet for Two Hands|
|2||.00364 X $3000||$ 10.92|
|3||.00644 X $3000||$ 19.32|
|4||.00924 X $3000||$ 27.72|
|5||.01484 X $3000||$ 44.52|
|6||.01764 X $3000||$ 52.92|
|7||.02044 X $3000||$ 61.32|
|8||.02324 X $3000||$ 69.72|
At Last! The Betting Schedule
Obviously I cannot place a bet of $10.92 so I’ll have to round things off in order to arrive at a practical betting schedule. In doing that, I keep several things in mind. First, I want a schedule which will allow me to ‘parlay’ winning bets as the count goes up. For example, if the bet for a true count of 2 is $20, it would be great if the bet for a true count of 3 was twice that; it makes me look like a ‘gambler’ to just add my winnings to the original bet. Of course I’d only be doing it because the count has gone up, but it’s something to keep in mind as I design the schedule. Another ‘nice-to-have’ thing is a schedule which allows me to bet some multiple of the true count. For example, “$10 times the true” would mean that at a true of 2 my bet would be $20, at a true of 4 it’d be $40, etc. Another point to keep in mind is that we have a bit of a ‘fudge’ factor built into counts above 2.4 in a double deck game. Why 2.4? Well, that’s the true count at which one should take insurance in a double deck game and that option is so valuable that it adds to our advantage. While the advantage goes up about .5% with each increase of 1 in the true count, above 2.4 the advantage increase is more like .58%. So our ‘real’ advantage at a true of 7 is more like 4% than the 3.65% which I show on the charts above. This gives us a cushion for rounding up a bit.
So, here’s the betting schedule I worked out for a $3000 bankroll. Bear in mind that as the bankroll increases (or decreases), the schedule must be changed in order to keep the risk of ‘gambler’s ruin’ about the same. I will modify the schedule at $1000 increments; that is, if I win $1000, I’ll refigure the betting schedule by remultiplying all the percentages by $4000. On the other hand, if I choose to spend my profits, I’ll just continue to operate with the original schedule. In the unlikely event that I hit a big losing streak (how’s that for positive thinking?) I really couldn’t downsize the bets very much. As long as the bank remains above $2000, I’ll stick with this schedule. If it should go below $2000, I’d quit until I could build the bank up again.
|Betting Schedule $3000 Bank – Double Deck |
(DOA; DAS; RSA; Dlr hits A-6)
|True Count||Bet: One hand||Two Hands|
|0 or lower||$10||N.A.|
|6 or higher||$60||$50|
Notice that I top out at one hand of $60 or 2 hands of $50, regardless of how high the count gets. I’ll stick with that until the bankroll increases and I get a ‘feel’ for just how the floor supervisors at the casino react to such a spread. The ‘pit critters’ know that counters vary their bets widely, so I’m going to be conservative for a while since this is my ‘home’. If I was playing this game somewhere else — where they wouldn’t see me for months at a time — I’d be more aggressive. The single-hand schedule is not an easy to memorize; it’s not a straight parlay and it’s not a simple multiple of the true count. I’m going to be screwing around a lot with $5 and $25 chips and precise betting is another indicator of a card counter, so I may find myself ‘pushing’ the count; that is, over betting a bit on a true of 2 or 3. I’ll have to watch that, since my reaction will be to bet $20 on a true of 2 and $30 on a true of 3. With that, the schedule is $10 times the true, but a bank of $4000 is required to justify those bets. I’ll just have to see how it goes.
Playing Two Hands
Whether or not one should play one or two hands is more a factor of opportunity than strategy. If there is no space available at the table for a second hand, I obviously must play only one. Neither am I going to play two hands when the true count is below 2, nor am I going to play two hands if I’m alone with the dealer. The reason for that last rule is twofold: First, by playing a second hand, more cards are used and — since I only go to two hands on positive counts — I’ll be ‘eating’ good cards. That’s okay, but when head-to-head with the dealer, my two hands represent an increase in the total bet of about 150% but I’m also using up 150% more of the cards. Second, the game has a high maximum bet, well above my maximum so I don’t need to spread to two hands in order to get more money on the table. So, whenever I’m alone and the table limit is above my top bet, I’ll always play one hand.
If there is at least one other player besides me at the table, I’ll then spread to two hands whenever possible. In that case I do want to ‘eat’ the good cards; why give the opportunities to others when I can get them for myself? Mercenary, perhaps but this IS about money, you know.
Lots of gamblers play two hands, so the maneuver won’t draw a lot of attention to you unless you make a big deal about it. First, most casinos allow two hands only if they are located in two adjacent betting circles. If you’re sitting at ‘first base’, don’t try to place a second bet at the empty spot on third base. Also, I don’t ask people to move to the next spot over in order to accommodate my second hand and I never refuse to allow someone else to sit down and play in the spot I was using for my second hand. You have to look indifferent about the idea of a second hand — just like a gambler would. One neat trick is to spread to two hands when a new player joins the table (assuming of course that the count justifies it); gamblers seem to think that doing so ‘keeps the cards in proper order’ when someone is jumping in and out. Naturally it’s BS, but anything that makes me look more like a gambler is welcomed.
Practice Makes Perfect
Next I had to set up a regimen of practice to get used to playing a double-deck game. I already own several decks of cards from the casino, so I can use them to ‘calibrate’ my eyes for estimating the number of decks left to be played. I did this to a half-deck accuracy and can consistently cut 26 cards from two decks shuffled together. I accomplished this simply by breaking the pack into four parts over and over again and counting the segments when I was done. Just looking at a half-deck, a full deck and a deck and a half gets you used to estimating the number of cards remaining to be played. It’s hard to describe until you try it for yourself, but I think you know what I mean. I also did some mental calculations of dividing various running counts by 1.5 and .5, etc. to get used to figuring the true count.
I further practiced by counting down two decks to check my accuracy; I can do it in 22 seconds which is more than ample for casino conditions.
But the practice I did most was with a program called “Blackjack Professor” which I set up to reproduce the conditions and rules for the game at Station Casino St. Charles. Whenever I had a spare hour or so I played the game, which is dealt on a head-to-head basis with no other players, utilizing my betting schedule and the other techniques which I use in the casino. For example, if I had $10 bet and the count jumped up considerably, as it will near the end of a shoe, I would not come out with a $40 bet on the next hand, since I wouldn’t likely do that at the casino. I’d bet $20 instead and then go to $40 on the next hand, if there was a next hand. Conversely, if I ‘pushed’ a hand and the count had dropped dramatically, I’d leave the bet out there, just as I would do in the casino. By doing all that, I felt my results from practice would be similar to what I could expect in the casino. Here are the results of 6 different sessions on the computer. Remember, I played each hand according to the basic strategy variations and I bet according to the schedule above, though I never spread to 2 hands because I was always alone at the table. The earnings per hour are based on a rate of 60 hands an hour, a much more realistic figure than the 300 hands an hour I was able to play on my computer.
# of hands
|% won||$ won||$/hour||% adv|
This totals to 4603 hands which represents about 76 hours of casino time and a profit of $490 or $6.44 an hour. From the program, I was able to extrapolate that my average bet size is about $14, so my overall advantage for these 6 sessions works out to be about .76% which is about half of what I would expect in a bigger sample size. My big losing session saw me reach a low of about $1050 which is not surprising. The lesson to learn from these simulations is that “the money in Blackjack comes in chunks.” To anticipate a steady income from this game is a big mistake; you can easily see how wild the swings are.
All the above is theoretical; what matters are real results from actual casino play. To date I’ve played 7 sessions and here are the results, based on a $10 to $60 spread:
|Session 1||2.5 hours||($110)|
|Session 2||1.5 hours||($410)|
|Session 3||2.0 hours||$240|
|Session 4||2.0 hours||$250|
|Session 5||3.0 hours||$355|
|Session 6||3.0 hours||$205|
|Session 7||2.5 hours||($260)|
These actual playing sessions total 16.5 hours of play and a profit of $270 for an hourly income of $16.36. I must add that the first two sessions were played before I had fully developed my betting schedule and before I had put in a lot of practice time. I will freely admit that those two loses were a ‘wake-up’ call that I needed to spend some time practicing the double-deck game, even though double deck is MUCH more closely related to 6 decks than it is to single deck. Once I got ‘in the groove’, my results are about as I expected. If we ignore those first two sessions, I’ve won $790 in 12.5 hours for an hourly rate of $63.20. That number cannot be sustained, but it’s very typical of how this whole thing works. Over the coming months, I’ll probably win about 65% of my sessions and lose or break even in the rest. The hourly income will drop to a more realistic $20 or so, assuming I don’t increase the bank size. That’s not enough to retire on, but it is a nice part time job.
I hope the thought processes which I’ve tried to show in this lesson give you an insight into how to structure a plan for your own play. I guess the only ‘sage’ advice I have at this point is that you must practice a lot more than you play to be successful at this game.
As always, if you have any questions, e-mail me at [email protected] and Ill get back to you ASAP.
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