This free course on blackjack and card counting was created by the GameMaster, publisher of the GameMaster Online website. It is reproduced here in its entirety with permission of the author. His 24-lesson course is an excellent introduction to winning blackjack.
To start at the beginning, visit the Welcome page.
In Part 1 (lesson 21), I tried to demonstrate that the real key to winning at this game is finding one where the casino deals more than 50% into the decks before shuffling. Admittedly, you can make a few $$$ in a game where only one deck of the two is dealt, but it’s certainly not easy and your earnings really are limited. Shallow penetration can be overcome, somewhat, by using a bigger bet spread (like $5-$60 instead of $5-$40, for example) but please notice that I said “somewhat”.
A bigger (or wider, if you prefer) bet spread – the ratio between your minimum and maximum bets – creates its own set of problems that you have to consider. First of all, many DD games have higher minimum bets, so you may find yourself at a $10 table and the 1-12 spread will require you to make a $120 “top” bet. That will require a pretty hefty bankroll, far more than the $3000 minimum I recommend in my Blackjack School lessons for the $5 minimum bet, six-deck game. The second and probably the biggest problem is that the casinos aren’t stupid. They know their games can be beaten by card counters who use big bet spreads and I think it’s fair to say that most aren’t going to allow you to spread $10-$120 for long periods of time, unless they are just totally convinced you’re some sort of wild-assed gambler. Hey, some people can pull that off; I know, because I’ve done it and I’ve seen it done by others.
But, surprisingly, there isn’t that much to gain in overall advantage by going from a 1-8 spread to a 1-12 spread in our “core” game, which is 2 decks, the dealer hits A-6, you may double on any first two cards, including after splitting pairs and no surrender is allowed. Even if you can find a game where 60 cards of the 104 are dealt (57% penetration) a 1-8 bet spread that consists of betting one unit at a True Count (TC) of 1 or less, two units at 2, four units at 3, six units at 4 and eight units at a TC of 5 or more will yield an overall “initial bet” advantage of only 0.58%. (See Part 1 for how this is calculated.) A 1-12 spread where a TC of four has us betting 8 units, ten units at 5 and twelve units of 6 or more under the same conditions has an initial bet advantage of 0.81%. That tiny extra edge is hardly worth the cost of the added risk of ruin and the extra scrutiny you’ll get from the “pit critters” while using it.
The reason for the small gain is simple: The penetration is just so shallow that you’ll seldom be making a 10- or 12-unit bet, but you need them to make up for all the minimum bets you’ll be making at counts where the casino has the edge over you. We lessen the impact of that quite a bit in the six-deck games by leaving the table when the TC drops to -1 or lower, but we pretty much agree that tactic isn’t as feasible in a double-deck game and you’ll generally have to play through all the counts, negative and positive. It’s costly. Sure, you could “ramp” your bets more quickly so the top bet is out at a TC of, say, 4, but that’ll have you bouncing bets all over the place and it’s sure to draw a lot of attention, if not “heat”. I think I can show you a better way to go and, a little later on, I’ll show you a tactic that can really make you some $$$ at even this mediocre game.
Betting With the True Count
For each increase of 1 in the true count as figured by the Hi/Lo counting method, the player’s advantage increases by about .5% in the average Blackjack game. If the casino has an edge over the basic strategy player of .41% (2 decks, double on any first two cards, double after splitting pairs, dealer hits on A-6 and surrender is not available), it takes a True Count (TC) of just about 1 in order to get “even” with the house. Being even means that the player who utilizes proper basic strategy will win as much as s/he loses – in the long run – at a True Count of one. A TC of 2 gives the counter an edge of .5% over the house; a TC 3 gives the player an edge of 1% and so forth. These are conservative numbers because beyond a TC of about 2.4 (the point at which you should make the insurance bet) in a double-deck game, the value of each increase of 1 in TC is actually worth a little more than 0.5%.
It is the edge that a player has on the upcoming hand that determines their bet. Counters bet only a small portion of their capital on any one hand, because while they will win in the long run, they could lose any given hand. By betting an amount that is in proportion to their advantage (called the “Kelly Criterion”), they are maximizing their potential. A lot of people misinterpret the Kelly Criterion by assuming that the amount bet is in direct proportion to the advantage. They think that if you have a 1% edge, you should bet 1% of your “bankroll” and that is incorrect. What they are forgetting is the doubling and pair splitting that goes on in the course of a game, which increases the risk or “variance” of a hand. For a game with rules like those listed above, the optimum bet is 76% of the player’s advantage. Here’s a table of optimum bets that will work well for a game where the casino has a 0.41% advantage over the Basic Strategy player:
|True Count||Advantage||% Optimum Bet|
|-1 or lower||-0.91% or more||0%|
|1||0.09% x 76%||0.07%|
|2||0.59% x 76%||0.45%|
|3||1.09% x 76%||0.83%|
|4||1.59% x 76%||1.21%|
|5||2.09% x 76%||1.59%|
|6||2.59% x 76%||1.97%|
|7||3.09% x 76%||2.35%|
|8||3.59% x 76%||2.73%|
|9||4.09% x 76%||3.10%|
|10||4.59% x 76%||3.49%|
By using this table, you can determine the optimal bet for any bankroll; just multiply the figure in the last column by the amount of the bankroll. Thus, for a bankroll of $5000, the optimal bet for a true count of 2 is .0045 X $5000 = $22.50.
Some Practical Considerations
First and foremost, it isn’t practical to bet in units of less than $1, so a betting schedule must be rounded off. Secondly, it is more appropriate to bet in units of $5 or $10 so that you’ll look like the average gambler, plus it cuts down on the calculations you need to make. Further, it is impossible to refigure your optimal bet while seated at the table, even though it should be recalculated as the bankroll varies up and down. Finally, it just isn’t possible to play only at games where the true count is 2 or higher so you will have to make a lot of bets when the house has an edge. All of this rounding and negative-deck play cuts into your win rate, but by knowing the conditions that can cost you money, steps can be taken to minimize their impact on your earnings.
The Betting Spread
The most effective 1-8 betting spread would be to bet one unit whenever the casino has the edge and 8 units when the counter has the edge. That concept, however, presents two problems. First and foremost, the “pit critters” are going to know you’re a counter after about ten minutes of play and they’ll likely ask you to leave. An even bigger problem is that you’d be making your maximum bet when you had a tiny advantage of only 0.09%. Such a small edge virtually guarantees that you’ll lose many of those hands so you could hit a losing streak that would wipe you out if your top bet were, say, one-fiftieth of your bankroll. But, if you can get away with it (as I know some players in Europe can), you have to make sure your bankroll is much bigger than just 50 times your maximum bet. A bankroll of 200-300 max bets would be more appropriate in that case.
A more practical answer to both of the problems presented above is to “ramp” your bets, which is another way of saying gradually increase them. If your minimum bet is $10, then a 1-8 spread will make your top bet $80, no matter how high the count gets. Depending upon when you’d like to get your top bet on the table, that is, at which True Count, it’s then a simple matter to calculate just what size your total bankroll should be. Let’s say you wanted to bet $80 at a TC of 5 or more. The optimum bet for that count is 1.59% of your total bankroll, so if you divide $80 by 0.0159, you get $5031 as the proper bankroll. Now remember, you won’t be making every $80 bet at that count because it’s your “top” bet and some will be made at a higher advantage, but $5000 is a good number and one that I’ll recommend.
Just a quick note here: That $5000 represents the total amount you should be willing to commit to this adventure, but it’s not what you’ll carry with you on a trip to the casino. For most trips, a “session” bankroll of 20 top bets or $1600 should suffice, but there will be a time when even that’s not enough. We’ll talk about that later. With a $5000 bankroll, the betting schedule could look like this:
|True Count||Player’s Bet||Optimum Bet|
|0 or lower||$10||$0|
Please notice that “Optimum Bet” means the best bet for that count, were you able to make it. Because our top bet is purposely capped $80, this schedule uses it at a count of 5 or more. But, if you’re able to get away with a higher bet, the $5000 bankroll supports the bets shown: $100 at a TC of 6 and so on. If you do that, though, your “session” bankroll should be bigger than the $1600 previously recommended.
The Bet Schedule Examined
First of all, I hate this schedule for a lot of reasons. The main one is that it’s a dead giveaway to any “pit critters” (PCs) that know the generally accepted bet spread needed to beat a double-deck game is 1-8. And here you are, playing away, hour after hour with a minimum bet of $10 and you never bet over… what? $80! Well, duh. Gosh, is 80 eight times 10? Even the thickest PC knows that. Don’t forget that they’re “hawking” these games anyway, so we don’t want to make it easy for them. I’m firmly convinced that a lot of counters are getting 86’d at good DD games because they’re betting $25 at a minimum and $200 at a maximum; 8 to 1, the magic number for a DD game. We need to change that for our game.
The other reason I hate this betting schedule is, it’s “clunky”. By that I mean it requires some fairly precise bet levels and precision betting is another sign of a counter. This one goes from $10 to $25, which is fine if you’re playing at a $10 table. I don’t have a problem with that. But then it goes to $40, which is three red chips on a green chip. It actually makes you look like you’re betting more than if you were to just go to two greens ($50). After the $40, you go to $60, which isn’t too bad, because it’s a 50% “parlay” if you won the previous hand and the dealer didn’t color you up to all green when s/he paid you on the last hand. But the dealer will constantly be taking away reds and giving you greens in an attempt to make you bet more per hand, not to mention trying to eliminate the difficulties s/he’s having in continually breaking down your bet if you’re at a casino where they have to separate the colors before paying you. Clunky! Precise, to be sure, but it will definitely slow down your game and actually help the casino to toss you out. You don’t need that. But what’s the alternative? Let’s look at some possibilities.
The Betting Schedule Simulated
To test this betting schedule and to find some alternatives to it, I ran a series of simulations on Statistical Blackjack Analyzer (SBA) using the rules of our “core” game: 2 decks, double on any first two cards, double after splitting pairs, dealer hits on A-6 and surrender is not available. What got changed from simulation to simulation will be shown in the explanation for each.
The SBA software is no longer available. For simulations, I use the newer, faster, and more powerful CVData.
Simulation #1 – Basic Strategy for the play of the hands, Player’s Bet as shown in the schedule above according to the Hi/Lo count, never left the table regardless of how low the count got (“play all”). Penetration was 60/104.
|Simulation #1: Results|
|Initial Bet Advantage:||0.59%|
|Estim. Payoff per 100,000 rounds played is $10,325.65,
with an estimated standard deviation of $8950.40.
|Average st. dev. per round:||$28.30|
|Av. std. per round per unit:||1.13153|
|Average bet per round:||$17.42|
Comments on Simulation #1 –
This will serve as our “baseline” game and it’s easy to see you’d really be wasting your time at it. The primary reason is the shallow penetration, just as I showed you in Part 1. The SCORE is a measurement called “Standardized Comparison Of Risk and Expectation” that was developed by Don Schlesinger and others and is thoroughly explained in his book, “Blackjack Attack”, which every serious card counter should own. For our purposes here, it’s an effective way of comparing the value of each game or bet schedule or whatever that we will be examining: the higher the SCORE, the more $$$ you’ll make. As a side note, a SCORE of 40-50 ought to be the minimum one should look for in the games they’ll be playing.
The other numbers are pretty much self-explanatory (yeah, right!) and are calculated by the SBA software. I’m basically tossing them in for the “math boyz and girlz” out there, but the 100,000 rounds of play number is one you need to understand. This number has caused more card counters to quit the game, convinced that it cannot be beat, than any other factor out there. What it says is this: Were you to play 100,000 hands of this game (at 100 hands per hour that’s 1000 hours of play!) your expectation is to win roughly $10,000. However, that $10,000 result can fall within one, two or even three standard deviations from a reality point of view, so if you experienced a one standard deviation event to the loss side of the ledger, your result would be a profit of $10,000 minus $8950 or $1050! That’s about a buck an hour. Should you be really unlucky (about a 1 in 50 shot), you’d actually end the 100,000 hands of play with a loss of your entire $5000 bankroll, plus a couple of grand extra, should you care to toss it into the pot. And this could happen even if you play each hand perfectly, never over-bet, don’t lose count at the table, etc. Some people use stats like this to justify their idea, “It’s all luck, not skill” and they couldn’t be more wrong. But don’t get me started. We have some way to go before we rest this night and, as “The Duke” would say: “We’re burnin’ daylight, Pilgrim.” Plus, I’ll talk about “risk of ruin” later.
Simulation #2 – Everything is the same, except the most important Basic Strategy variations are used to play the hands (These are the “Illustrious 18″ that are explained in “Blackjack Attack”, the most important being taking insurance at a TC of 2.4).
|Simulation #2: Results|
|Initial Bet Advantage:||0.92%|
|Estim. Payoff per 100,000 rounds played is $16,048.10,
with an estimated standard deviation of $9187.70.
|Average st. dev. per round:||$29.05|
|Av. std. per round per unit:||1.13153|
|Average bet per round:||$17.42|
Comments on Simulation #2 –
You can quickly see that the average bet remains the same, but the potential profit has increased by nearly 60% and that’s due to making better plays with the cards you’re dealt. It should point out that you cannot expect to get a big advantage at this game playing only Basic Strategy and by just varying your bets according to the count, like you can in a six-deck game. While the “Illustrious 18″ will get most of the $$$ for you, it’s a series of variations that are based upon “high” counts and it ignores low-count plays such as hitting 12 against a dealer’s 4 and others like that. I agree with the concept because you’ll be betting minimums in those situations, consequently the potential gains aren’t all that big, but later on I’ll show you what you can do with variations in the -6 to +10 range and then you can learn what you’d like.
Simulation #3 – In this one, I want to “de-clunk” the original betting schedule presented above by making it less precise and by using as few $5 chips as possible. We can’t get around using “reds” if we’re at a $10 table because nothing will kill you quicker than betting $25 in negative counts and then spreading only to $80 or so in positive counts, so the minimum bet has really got to be the minimum: $10, period. But what will happen if we ramp-up a little faster by betting $50 at 3, $75 at 4 and topping out somewhere between $80 and $100 at 5? This will require a bigger bankroll if our average bet is $90 at a TC of 5, about $6000. What I’m suggesting here is that you not bet the same amount each time the count’s at 5 or more. In some places, the dealer will call out, “checks play” if you bet $100 or more and that will attract some attention, but in a lot of places that won’t happen and, in fact at $100 per hand, you may be the small bettor at the table! Only you know your local game, but keep it in mind and check what they do the next time you go. Another approach is to play two hands as the count goes up, but so many casinos now have a “no mid-shoe entry” rule that precludes it, I’m reluctant to add it into what is already a very long lesson. Plus, I’ve already covered that in the series, “Playing Multiple Hands”, which is archived at The GameMaster Online if you think that’s how you’d like to proceed.
Here’s the schedule I used for this simulation, otherwise everything is like #2:
|True Count||Player’s Bet||Optimum Bet|
|0 or lower||$10||$0|
I made the top bet $90, but remember that it’s an average; sometimes you’ll bet $80 and other times you’ll bet $100. Our “risk of ruin” has gone up, no doubt, but let’s see if it’s justified.
|Simulation #3: Results|
|Initial Bet Advantage:||1.02%|
|Estim. Payoff per 100,000 rounds played is $19,845.70,
with an estimated standard deviation of $10,557.60.
|Average st. dev. per round:||$33.39|
|Av. std. per round per unit:||1.15907|
|Average bet per round:||$19.40|
Comments on Simulation #3 –
Hey, not bad! We’ve just about doubled the estimated profit and it would take a two standard deviation event to put us at a loss, but even then it would be only (!!) $2000 or so. It’s obvious that this is a better betting schedule, but can you pull it off? You’re now using a 1-10 spread at least part of the time and that’ll require either a good “act” or short playing sessions. Basically, we’re dragging a $20/hour profit out of the game (assuming 100 hands per hour) and to some people that’s a nice return on a $6000 investment. To others it’s a pittance and I understand that; we all want different things.
Before I let you go, I want to show you what this simulation looks like if you are able to avoid playing when the TC drops to -3. It’s tough to do, I know, but definitely worthwhile, if at all possible. Develop an overactive bladder or any other trick to avoid playing the negative decks and you can make some nice $$$ at this game!
Simulation #4 – Everything is the same as # 3, except you leave when the count drops to -3 or lower.
|Simulation #4: Results|
|Initial Bet Advantage:||1.40%|
|Estim. Payoff per 100,000 rounds played is $29,929.60,
with an estimated standard deviation of $11,527.45.
|Average st. dev. per round:||$36.45|
|Av. std. per round per unit:||1.1583|
|Average bet per round:||$21.43|
Comments on Simulation #4 –
Wow! This puppy makes you want to run out and find a game, doesn’t it? But hold on, pardner. First of all, you need to remember that it’s going to take you longer to play 100,000 hands because you’ll be away from the table quite a bit. How often? Well, SBA can tell us that because it keeps track of the “dropouts” and they are considerable. This simulation played 10,946,376 “shoes” and it left 4,912,246 when the count dropped. That’s just about 45% of the time, which is a big number. So, it’ll likely take you twice as long to play the 100,000 hands and that’ll cut the hourly win to $15, if you consider an “hour” to be time in the casino. If you consider it to be time on the table, it’s another matter. But who’s going to figure it that way?
You actually make more per hour under the conditions of Simulation #3 because you’re “on the green” almost all the time but you make more per hand played when you use the tactics of Simulation #4. Like so many other things in life, you pays yer money and you takes yer choice.
Here’s some homework. Decide on a betting “schedule” you’d like to use, then make up a set of flashcards to help you memorize it. Just put the various True Counts on the front (1 or lower, 2, etc.) and then put the proper bet on the back. Go through them until you know what you should be betting for each count.
In the next (and last lesson on Double Deck) we’ll wrap up with basic strategy variations.