The Blackjack Page

Evaluating Double Deck Games - A New Idea

There are a lot of money-making opportunities for the individual card-counting Blackjack player in double-deck (DD) games, but there are also a lot of bad DD games out there, so before you waste your time and $$$, let’s discuss the differences.

Casinos and their average patron know that the fewer decks used, the better it is for the player, which is why the 6 to 5 single-deck game of BJ can succeed, at least among “average” players. But you and I are not average, so we avoid those lousy single-deck games, but can we avoid a lousy DD game as well? Unfortunately, it’s not as simple as just looking for a 3 to 2 payoff on a “blackjack” because all the DD games I know of do indeed pay the correct amount for a natural – at least they’re not messing with that for the moment. (Although I now hear some Downtown Vegas casinos have put in 6:5 DD games...sigh.)

Many casinos do, however, alter the DD game in such a way as to negate its advantages, yet still treat it as what I call a “premium” game. Such games typically have a higher minimum bet, are few in number and are usually watched very closely by the casino supervisors as though somebody may get rich by playing them. A good example is the DD game that Harrah’s here in St. Louis offers. First of all, there are only 2 tables (of a total 40) that offer DD games and the rules on them actually give the casino an edge “off the top” that’s higher than the edge they have in their 6-deck games! Plus, the minimum bet is $25 with a $500 maximum, as opposed to the $5-$1000 for the six-deckers and then they deal out just a smidgen over half the cards. For all intents and purposes, the game is unbeatable in the long run by most card counters. Even a team cannot beat those games because they have the “nms” – no mid-shoe entry – rule there.

I have always preached that a counter must be able to realize a long-term advantage of at least one percent in order to make the effort worthwhile; otherwise, you might get stuck early on and spend the rest of your life trying to dig out. And that 1% really is the minimum, which leads us to a discussion of what’s called N0 (the letter N and the number 0). The logic here is that it’s possible to calculate how many hands you must play in order to overcome a one Standard Deviation downswing, given a specific overall playing advantage. For the math geeks, the formula is N0 = Var/EV^2, with VAR being variance and EV being expected value, but you don’t need to know that in order to find a good DD game. However, you do need to take N0 into consideration, especially if you’re a part time counter, so let me explain. Whatever number of hands N0 is, it’s the number of hands you could play – and play perfectly – but still show no profit, just due to bad “luck” alone. The bigger your overall advantage, the lower N0 will be; that is, you’ll have to play fewer hands to overcome the 1 SD loss due to bad luck.

For the calculation of N0 for a game, go to: http://www.bjmath.com/bjmath/refer/N0.htm You’ll need a copy of Don Schlesinger’s book “Blackjack Attack” to make it work, but I’ll cover some representative games here.

One of the better DD games in Las Vegas is available at Bellagio; that’s no secret. The dealer stands on soft 17, you may double on any first two cards, including after splitting pairs but surrender is not available, although penetration is pretty good; about 62 cards of 104 are used before the shuffle. The casino has an edge of 0.19% over the Basic Strategy player, but here too, it’s treated as a premium game. There are only 8 tables, the minimum bet is $50 and the games are watched closely. Nonetheless, it’s still pretty good and yields a long-term edge of about 1.2% when using a $50-$400 bet spread.

If you were to play the Bellagio DD game while faithfully adhering to a $50-$400 bet spread and playing through all counts, positive and negative – something you typically have to do in DD games – the N0 works out to be 19,144 hands. If you were to play 60 hands per hour, you could play for over 319 hours; a full month of 10 hour days and still not show a profit, simply because of variance (or “bad luck”, if you prefer.) And that’s at one of the best DD games out there!

Now let’s look at a more typical DD game where the dealer hits soft 17, you may double on any first two cards, but not after splitting pairs and penetration is 52 cards of 104. The casino’s edge is 0.53%, which is not better than many six-deck games, but let’s play it anyway. With a 1-8 bet spread, a long-term edge of about 0.60% is attainable; well below my recommended 1%, but I want to make make a point here. The N0 for this game is a whopping 86,501 hands. This means you could play 60 hands per hour for 1441 hours – 6 months of eight hour days – and still be just even due to luck alone. Yes, in both of these examples you could also get lucky to the upside and actually make a profit, but since when do we, the card counters of the world, depend upon luck?

So what kind of DD game is worth our trouble if we’re a part time counter who can play, say, 300 hours a year or about 18,000 hands? What we really need is a game that has a N0 of fewer than 18,000. At least that way our year of play will not have been spent in vain; we have a fighting chance to overcome a one SD move to the downside. Remember, in the long run you’ll win if you have an edge – it’s just when will you collect the $$$ that’s the issue here. In my series "Beating the DD Game", the absolute minimums I espouse are a game where the dealer hits soft 17; you may double on any first two cards and double after splitting pairs. This gives the casino an edge of 0.40%. Penetration is the key here: with 52 cards of 104 used, this game yields a long-term edge of only about 0.71% if a 1-8 bet spread is used, so it’s on my “do not play” list.

However, if you can find such a game with 62 of 104 cards used before the shuffle, it just makes my minimum; a 1-8 bet spread yields a 1.02% long-term advantage. As we expect, the N0 drops to 27,552 but it’s not the 18,000 we’d like. If the penetration is 70 of 104, the N0 is 18,464 – at last, the Promised Land. Of course we got there because the overall edge is now in the 1.25% area, which demonstrates how important penetration is in DD games, especially if you don’t play them very often.

The lesson here is to not play DD games just because it seems like they’re worthwhile due to using fewer decks. The “premium” game some casinos are dealing simply aren’t worth your valuable time and $$$ - stick with the 6-deckers if your local DD isn’t dealt beyond the 50% point. If you’re in a situation where the penetration is better than that, then it’s probably worth a shot because it only takes a few extra cards to turn an “okay” DD game into a “great” DD game. Hey, bribe the dealers with generous tips; it works for me.

I'll see you here next time.

The Blackjack Page

Risk-Averse Betting

In Lesson 14 of my Blackjack School, I make this reference to the index numbers I use in the Basic Strategy variations presented therein: "...a few have been modified based upon the theory of 'risk averse' play which was developed about 15 years ago. These numbers work well; they have been proven in thousands of hours of actual casino play by me and my students."

Basic Strategy variations cause us to modify the play of a hand according to the count. For example, Basic Strategy for my "school" game (6-decks, S17, DA2, DAS) tells us to always hit a hand of 9-7 or 10-6 (sixteen) against a dealer's 9. But the variation is to stand if the True Count (TC) is 5 or more. That makes sense; as the count increases on the plus side, the probability of receiving a 10 as the hit card increases proportionately. On the other hand, Basic Strategy says to hit a hand of 9 versus a dealer's up card of 7, but the variation is to double 9 vs. 7 when the TC is 6 or higher. As the count increases in our favor, we will not only bet more, but will also stand more, surrender more often (if possible), double more and split pairs more often. All of those variations are primarily a function of the mathematics involved - if you will make X $$$ hitting 9 vs.7 when the count is 0 (the count a Basic Strategy player effectively uses), when the TC is 6 or higher you will make X+ if you double. My index number for 9 vs.7 is 6, but most counting systems show an index of 3 for that play. My index is a "risk-averse" number, whereas the 3 is an "expected value" (EV) number. Why the difference?

Hopefully you understand that expected value for each hand is the means by which we determine the Basic Strategy. For example, if you hit a hand of 9 versus a dealer's up card of 7, the EV is +17.61%; if you double, the EV is +11.60%, so the proper play - if you're not counting the cards - is to hit. But if the TC is 3 or more, the EV for doubling is +17.95%, which is a higher return than just hitting. But you can also see that the EV gained is very small; 17.95 versus 17.61. However, to get that additional 0.34%, you must risk an extra bet (remember that the EV for doubling is based upon the original bet, but the play requires you to place another bet that typically matches the original.) To further clarify this, let's say you've bet $1000 on a hand because the True Count's up to 3 (you're a high roller) and you receive a 9 against the dealer's 7. You double your bet to $2000 and take just one card. Now your risk is $2000, but your expected gain is 0.0034 x $1000 = $3.40. That's fine, it's what we do in this business, take every opportunity and exploit it to the max. It's an extra $3.40, which is good. But it's only good, if...

Making Basic Strategy variations based solely upon the EV assumes that a loss will not affect how you will play the next hand. I'm not talking psychology here - none of us like losing $2000 doubles - but what impact will that have on your bankroll? Obviously, your bankroll will be smaller. (All together now: $2000 smaller.) But will that loss require you to change your bet size? If you're truly rich and such a loss will have no impact, then the EV play is the way to go. But, if you're like most of us, your bankroll is finite, so 2, 3 or 4 such losses might require us to change the bet schedule from, say. $350 times the TC - a $1000 bet at TC 3 - to $250 times the TC or $750 at TC 3. The idea that we should bet in proportion to our advantage (the Kelly Criterion) is what creates the need for risk-averse indices for those plays where extra bets are risked, namely splitting and doubling. If your bet-to-bankroll size is just a small fraction of "Kelly", as opposed to the 75% of Kelly that I always recommend, risk-averse indices aren't as important. But, if you - like most beginners - are basically funding your play from current income, then you should use the numbers I show in lessons 14-16, which are available here: http://www.gamemasteronline.com/BlackjackContent.shtml

In those lessons, there are several numbers that I omitted on purpose, like doubling your hand of 10 versus a dealer's up card of 10 and splitting 10-10 vs. a dealer's 5 and 6. In the case of 10 vs. 10, the EV number is 4, but the risk-averse number is much higher, so I just left it out because you'll likely never see that high a count in a 6-deck game. In the case of splitting 10s, I left that out not so much because of the risk of losing, but more because of the risk of getting barred from the casino. For those of you who want to do it, the risk-averse number for splitting 10-10 vs. 5 is 6 and for 10-10 vs 6, it's 5. Easy to remember, but don't say I didn't warn you.

I'll see you here next time.

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