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The Blackjack Page Archive

Beating the 8-deck Game


 

Thanks to the opening of Atlantic City's newest casino, The Borgata, those of you who play Blackjack there have seen a considerable improvement in playing conditions, which obviously leads to increased opportunities for making $$$. I've always said that there's nothing like competition to give the player a better deal and the amazing change that has occurred in A.C. is proof of that. Prior to the opening of the Borgata, the Atlantic City Blackjack scene was pretty bleak. Dominated by the fact that card counters cannot be barred from the casinos there, the industry had fallen into a basic "take it or leave it" attitude of poor penetration on mega-deck games and, sad to say, they were getting away with it. But not without some cost. Casino income from Blackjack was flat or exhibited very little growth for several years; that is, until Borgata opened. What management did there was actually very simple: they offered a decent game to Blackjack players. Not a great game, mind you, but a good game, especially when compared to what their competition was doing. As this is being written (May, 2004), Borgata is all 6-deck games with the usual A.C. rules: the dealer stands on soft 17, you may double on any first two cards, including after splitting pairs; all pairs, except Aces, may be split to form three hands and split Aces receive only one card. Surrender is not allowed. Not long after Borgata began offering 6-deck games, the Sands went that way, too. But because 6-deck games are adequately covered in the other lessons of my Blackjack School, I'm going to address just the 8-deck game here. This article will eventually become lesson #25 of the Blackjack School.

Is an 8-deck game much different than a 6-deck game? Not really, but the penetration you get at an 8-deck game is very important, as you'll see when I discuss the simulations I did for this. But before we get into those, let me make a few general comments about playing Blackjack in Atlantic City. First of all, A.C. is always busy in the summer, so finding $5 minimum bet tables is tough, if not impossible. Mostly, the minimums are $10 or $25 and that's a real trap for the under-funded player. You cannot operate with a $60 top bet as I recommend in my lessons if the minimum bet is $10. That's only a 1-6 bet spread and you'll never get a long-term edge with such a narrow spread. So, if you're going to play BJ in A.C., bring money. Or go there in non-busy times, like Sunday night and during the week. But whatever you do, don't expect to win if you're using a bet spread of less than 1-12. You'll see why when we get to the simulations. For those of you that don't play in A.C., but find yourself confronting 8-deck games, this will all apply to you as well. What I hope to do here is develop a sound betting strategy for the 8-deck game, based upon the True Count, much as I did in my series, "Beating the Double Deck Game", which is now lessons 21-23 of my Blackjack School.

Just as I did in that series, I'll begin with some comparisons based only on penetration. In other words, for the sims I did to develop the chart below, the only thing that changed was the penetration; the rules, the bet spread (which I'll cover later) and all other aspects of the game remained the same. If you've read my other lessons, you'll recall that I say you're wasting your time if you play at any 6-deck game that has penetration of less than 65%. For an 8-deck game, the minimum penetration needs to be 75%, but that's usually available in Atlantic City, which is another improvement you'll find in the games there. Here's some data to consider:

Impact of Penetration on an 8-deck Game
Percent Penetration Theoretical Player Edge
65% -0.028%
75% +0.186%
80% +0.312%

Pretty sad, isn't it? Even with a 1-12 bet spread (I used the spread I show for 6-deck games in my lessons) and good penetration, the long-term edge one can get is only about 0.30%. But don't worry, I'll show you how to get a bigger edge, because we really need an absolute minimum of 1% to make it all worthwhile. The first way is to leave the table when the True Count drops to -1 or lower. With the A.C casinos being such big places, it's really not a problem to leave a table when the count drops. As I teach in lesson 8, you should leave only after losing a hand, because "gamblers" seldom leave after winning a hand and we want to look like gamblers. The next simulation will show you the impact of leaving.

Simulation # 1: 8-decks, standard A.C. rules, 80% penetration; leave when count drops to -1 or lower.

Theoretical player edge: 0.828%
Expected return for 100,000 hands of play: 1440 units
Standard Deviation for 100,000 hands of play: 981 units

Comment: When I say "Theoretical Edge", that's the overall advantage as determined by the software I use for my sims, which is Statistical Blackjack Analyzer" (SBA), a program I've written about many times before. The problem here is that SBA plays each hand perfectly, plus it "leaves" the table religiously when the count drops. You and I probably won't play every hand perfectly and if we want to look like gamblers, we won't always leave the table immediately when the count drops. So, to put a realistic spin on these numbers, my advice is to reduce them by 10% or so. That being the case, an overall edge of about 0.66% can be expected with this method of play. Just so you know, SBA calculates your expected profit for 100,000 hands, which in this case would be 1440 units, or $7200 if your unit is $5. The Standard Deviation figure is 1 SD, which will cover about two-thirds of all your playing results. What this means is, if you play a series of 100,000 "trials", two-thirds of them will show a result of 1440 units won, plus or minus 981 units. In other words, two-thirds of the time your result will fall somewhere between a profit of 1440 + 991 = 2431 units and a profit of 1440 - 981 = 459 units. Remember, that's for a series of 100,000 hand trials or maybe 1-2 million hands of play. Well, darn few of us are ever going to play a million hands in our lifetime, so does that make these figures meaningless? Not really. The value of these figures is that they show you whether or not a game is worth playing in the long-term. If the SD were, say, 3000 units instead of 981, that would mean you could play 100,000 hands and still have a high probability of being in a losing position. A game with a high SD is a high-variance game, which requires either a large bankroll or a very big player edge to make it viable. We obviously do not have a big edge in this game, but it is an edge and, with the relatively conservative betting schedule I used, the SD is kept fairly low. If we go to a more "aggressive" bet schedule, we can increase our long-term edge, but at a cost of increasing the variance, which increases the SD, because SD is the square root of variance. But that's what we have to do.

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 .44% (8 decks, double on any first two cards, double after splitting pairs, dealer stands 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 3 (the point at which you should make the insurance bet) in an 8-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 likely 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're 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 0.44% advantage over the Basic Strategy player:

True Count Advantage % Optimum Bet
-1 or lower -0.94% or more 0
Zero -0.44% 0
1 +0.06% x 76% 0.05%
2 +0.56% x 76% 0.43%
3 +1.06% x 76% 0.81%
4 +1.56% x 76% 1.19%
5 +2.06% x 76% 1.57%
6 +2.56% x 76% 1.95%
7 +3.06% x 76% 2.33%
8 +3.56% x 76% 2.71%
9 +4.06% x 76% 3.09%
10 +4.56% x 76% 3.47%

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 $3000, the optimal bet for a true count of 2 is .0043 X $3000 = $12.90.

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 above zero, so you'll have to make some bets when the house has an edge. All of this roundinl 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 1-12 betting spread would be to bet one unit whenever the casino has the edge and 12 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 take counter-measures (no pun intended) against you because they cannot ask you to leave in Atlantic City. Such measures might be to reduce the penetration to 50% or "cap" your bet spread at 1-4. Obviously, if you're playing in Vegas or in many other jurisdictions, they may just toss your butt out. However, 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 the problems presented above is to "ramp" your bets, which is another way of saying gradually increase them. If your minimum bet is $5, then a 1-12 spread will make your top bet $60, 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 $60 at a TC of 5 or more. The optimum bet for that count is 1.57% of your total bankroll, so if you divide $60 by 0.0157, you get $3821 as the proper bankroll. Now remember, you won't be making every $60 bet at that count because it's your "top" bet and some will be made at a higher advantage, but $4000 is a good number and one that I'll recommend.

Just a quick note here: That $4000 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 $1200 should suffice, but there will be a time when even that's not enough. We'll talk about that later. With a $4000 bankroll, the betting schedule could look like this:

True Count Player's Bet Optimum Bet
0 or lower $5 $0
1 $5 $2
2 $15 $17.20
3 $30 $32.40
4 $50 $47.60
5 $60 $62.80
6 $60 $78.00
7 $60 $93.20
8 $60 $108.40
9 $60 $123.60
10 $60 $138.80

You can see that I topped the bet out at $60 when the True Count is at 5 or more. That's just an artificial limit, based upon what kind of a spread one can usually expect to get away with in actual casino play at a $5 minimum bet table. Remember, even though they can't bar you for counting in A.C., you'll still want to disguise your skill so they don't "half-shoe" you or take other steps against you. However, if your "act" will allow you to get away with using a bigger spread , the optimum bets shown will apply to the same $4000 bankroll, which will give you a 13.5% risk of ruin factor. By capping the top bet at $60, your risk of ruin is below 10%. To help clarify the impact of the bet spreads, I first ran a sim using the $5-$60 bet schedule, then did one using the optimum schedule (rounded to the nearest $5) and for those who want to play at a $10 minimum bet table and can spread $10-$120, a look at how that would work. The problem with the $10-$120 spread is that you're seriously over-betting when the count is at 1 or lower, so the risk of ruin factor will be higher; in the area of 25% for the recommended $4000 bankroll. Anyway, here are the sims:

Simulation # 2: 8-decks, standard A.C. rules, 80% penetration; leave when count drops to -1 or lower, $5-60 bet spread.

Theoretical player edge: 0.889%
Expected return for 100,000 hands of play: 1780 units
Standard Deviation for 100,000 hands of play: 1160 units

Simulation # 3: 8-decks, standard A.C. rules, 80% penetration; leave when count drops to -1 or lower, $5-140 bet spread

Theoretical player edge: 1.01%
Expected return for 100,000 hands of play: 2128 units
Standard Deviation for 100,000 hands of play: 1338 units

Simulation # 4: 8-decks, standard A.C. rules, 80% penetration; leave when count drops to -1 or lower, $10-120 bet spread

Theoretical player edge: 0.889%
Expected return for 100,000 hands of play: 3559 units
Standard Deviation for 100,000 hands of play: 2319 units

Comment: As you can see, it's darned difficult to get a 1% edge at this game. We barely cleared that mark with a 1-28 bet spread, plus you need to remember that these sims are based upon leaving the table when the count drops to -1 or lower! The last sim, which uses a $10-$120 bet spread, shows no increase in the edge but both the income and SD are doubled, which is no surprise since the bet sizes are doubled. But, as I mentioned earlier, the risk of ruin is nearly doubled as well. It's all a matter of how much risk you're willing to take. When playing a $10 table, your good days will be very good, but your bad days will be terrible.

A Few Refinements

All of the simulations I've shown you up to this point have used the count for betting purposes only, because a big bet spread is the primary way to beat multi-deck games. But if we add Basic Strategy variations to our arsenal, some small gain will be realized. The variations I teach for the 6-deck game apply here, so let's see what happens when we use them, along with a 1-12 bet spread that tops out at a True Count of 6.

Simulation # 5: 8-decks, standard A.C. rules, 80% penetration; leave when count drops to -1 or lower, $5-60 bet spread, risk-averse variations.

Theoretical player edge: 1.03%
Expected return for 100,000 hands of play: 2114 units
Standard Deviation for 100,000 hands of play: 1173 units

Comment: Well, it's not much beyond the 1% mark, but every little bit helps. What if we "tweak" this some more by revising the bet schedule a bit? The only way to go is to get the top bet out a little earlier, but you need to remember that doing so really calls for a bigger bankroll. Remember how we determined the bankroll requirement? If we get the top bet out at a True Count of 4 instead of 5, we really need a bankroll of $60 divided by 0.0119 or about $5000. Sure, you can play this bet spread with a $4000 BR, but at a cost of increased risk; about 18% or so. Here's a sim with a faster-ramping bet spread, plus the Basic Strategy variations.

Simulation # 6: 8-decks, standard A.C. rules, 80% penetration; leave when count drops to -1 or lower, $5-60 bet spread that tops out at a TC of 4, risk-averse variations.

Theoretical player edge: 1.07%
Expected return for 100,000 hands of play: 2213 units
Standard Deviation for 100,000 hands of play: 1234 units

Comment: I'm beginning to feel like we're beating a dead horse here. The more aggressive bet schedule gives us a small increase in overall advantage, but not much, especially when you factor in the increased BR requirement, plus the increase in variance.

One More Trick

Although it's difficult to do in Atlantic City, the only sure way to get an edge of more than 1% at an 8-deck game is to "backcount" the tables and not place a bet until the True Count is 2 or more. The reason it's difficult to do is that most A.C. casinos use the "no mid-shoe entry" rule, which basically prevents you from placing a bet once the first hand has been dealt from the shoe if you weren't betting from the beginning. But, because I'm also addressing 8-deck games in areas other than A.C., perhaps this technique will work for you. Here's a simulation where the amount bet was $0 whenever the count was 2 or lower. At counts above 2, I used a flat bet of $50, which will definitely lower any suspicions about your play if you use this strategy.

Simulation # 7: 8-decks, standard A.C. rules, 80% penetration, $50 bet at TC2 or more; $0 otherwise; risk-averse variations.

Theoretical player edge: 1.46%
Expected return for 100,000 hands of play: 14,647 units
Standard Deviation for 100,000 hands of play: 3617 units

Comment: Now we're getting somewhere! But, while this method of play looks good on paper, in reality it's a tough way to go. First of all, you'll spend a lot of time just watching the game, so your hands per hour rate will be low. Secondly, the casinos aren't stupid; they know this technique works very well, so you'll undoubtedly attract more than your fair share of attention. On the plus side, it gets the $$$, so if you can limit your playing sessions to one hour in very large casinos, it's a viable strategy.

Conclusions

I think it's fair to say that playing an 8-deck game is a grind, at best. But some of you haven't much choice in the matter, so please use the discussion above to help your game. As for me, when I'm in A.C., I'll be at the Borgata hammering away at their 6-deck game.

 

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