Just Another “Overdue” System

By Arnold Snyder
(From Casino Player, September 1995)
© 1995 Arnold Snyder

Question from a Reader:  What do you think of the “Triplet” system that I recently purchased by mail order? The system is made for playing craps, but I think the theory behind it would be useful for blackjack also, or any other games of chance. The author even says you can use it for roulette, and describes how on the last page.

The system costs $100, but I only had to send $25 to get it. I’m supposed to send the other $75 after I win it from the casinos. It seems to me the publisher is pretty confident that I’ll win, since he sent me the complete system “below wholesale.”

Answer:  You purchased four photocopied pages for $25. The total cost to “manufacture” this system to the author/publisher/seller was realistically about 25¢. Add to this the cost of an envelope and a 32¢ postage stamp, and the seller’s overhead expenses on this sale come to about 60¢.

So, even though you were shrewd enough to buy this system “below wholesale,” I don’t think the seller is sweating that $75 you still owe him. I suspect most “shrewd” purchasers of this system never send the remaining $75 owed for one simple reason: This system isn’t worth the paper it’s printed on. My heart goes out to the tree that died for this nonsense.

I agree with you that the “theory” behind this craps system would apply equally to all even money bets in any game of chance, assuming the theory was valid for the game of craps in the first place. But it’s not. Ironically, it’s slightly more valid for blackjack than it is for other casino games — but not valid enough to be profitable.

To simplify the author’s brainstorm, he is proposing that because it is unlikely to have three consecutive same results, you will make money if you wait until two consecutive same results have already occurred, then bet against the third occurrence. For example, if the pass line wins twice in a row, bet don’t pass. At roulette, if red comes up twice in a row, bet black, etc. The system combines this ploy with a martingale double-up betting strategy to be applied when you are losing.

At any given time in the past twenty years, you would have been able to find dozens of craps, roulette and blackjack systems on the mail order market espousing this same faulty theory. When I read your letter, and examined the “Triplet” system you enclosed, I almost tossed it in the circular file as just more garbage. I wanted to write you a short personal note telling you the system was worthless, but you failed to include your address on your letter.

Then, it struck me that this type of system is one of the most common types of phony baloney systems on the market, that seems to be based on “logic.” So, let’s debunk this theory once and for all.

It makes sense to many people that it is unlikely (or, at least, less than a 50/50 chance) that three consecutive same results would occur. If the crap table had an even money payout bet on the layout that three consecutive pass or don’t pass results would occur, and you could take either side of this wager — call it “triplet” or “don’t triplet” — we could all get rich by betting “don’t triplet.” This, in fact, is the analogy the author of the Triplet system uses in describing the “logic” behind his method.

The error the author makes is in assuming that the “don’t triplet” bet is just as strong after two of the three “don’t” results have already occurred, when all you’re betting against is the occurrence of the third result.

WRONG!

The reason the “don’t triplet” bet would be so profitable if it were on the layout with an even money payout is precisely because there are three chances for the triplet to fail. Using a simple coin flip example, we all know that with an honest coin there is a 50/50 (even money) chance that heads will come up. For two consecutive heads results, however, the odds are 3-to-1 against it. This is easy to see if we consider all possible results of two flips: (1) H,H; (2) H,T; (3) T,H; or (4) T,T. We only win once, but lose three times, with the four possible outcomes.

For three consecutive heads to come up, the odds are 7-to-1 against it: (1) H,H,H; (2) H,H,T; (3) H,T,H; (4) T,H,H; (5) H,T,T; (6) T,H,T; (7) T,T,H; or (8) T,T,T. Out of these eight possible outcomes of three consecutive flips, there are seven losses and one win, if we’re betting on three consecutive heads.

But, as soon as I stipulate that two consecutive heads have already occurred, the odds against the third occurrence are no longer 7-to-1. What I’m looking at is “H,H,?” where only that third result figures in to the bet, and we’re back to a 50/50 chance of it being either heads or tails.

If I pulled out an honest quarter, and offered you an even money bet that I could flip three heads in a row, you’d be very smart to take the bet, since the odds against me doing it are 7-to-1. In fact, you could give me 6-to-1 odds and still make money on this bet in the long run.

But if I said, “Wait until I flip two consecutive heads, then I’ll bet you that I can flip a third head,” you’d be foolish to give me anything other than even money, because it’s back to being a 50/50 proposition. At a crap table, or roulette table, you are giving the house odds on that third bet, because unlike our coin flip example, the house has a 1.41% advantage over you on the pass line, and a 5.26% advantage over you on the even money bets with a double-0 wheel. The Triplet system does nothing to change the house edge.

Any time you see a system which tells you to consider the likelihood or unlikelihood of occurrence of some result, based on results which have already occurred, don’t waste your time or money with it. I call these “overdue” systems, because the sellers often claim that when there has been a preponderance of reds, black is “overdue,” etc.

The reason I said that this “Triplet” system is slightly more valid if applied to blackjack than to other casino games is that computer simulations have shown that in blackjack, wins are slightly more likely to follow losses, and losses to follow wins. Unlike dice or roulette, the cards do have “memory.” I.e., cards which have already been played are out of the game until the next shuffle.

But don’t expect to get rich applying the “Triplet” system to blackjack. The total amount of the change in your win/loss expectation based on previous wins or losses at a blackjack table is measurable in thousandths of a percent — not enough to overcome the house advantage.  ♠

The Best Blackjack Betting System for Finishing a Trip with a Win

by Arnold Snyder
(From Player Magazine, November/December 1995)
© 1995 Arnold Snyder

Blackjack Betting Systems: The Long Run Vs. The Short Run

Players ask me more questions about betting systems for blackjack than just about any other topic. Not betting systems for card counters—just betting systems.

I always start by going into my spiel that pure betting systems don’t win in the long run. They can make you more likely to win in the short run (in the case of Oscar’s System, a lot more likely). But not in the long run. And the usual response I get is, “I don’t care about the long run. I’m going to Vegas this weekend. I just want to win on this one short run.” (Continued below)https://www.888casino.com/blackjack/free

As a matter of fact, there are betting systems that provide a player a much bigger chance of finishing a trip with a win than a loss. If you use this type of betting system, and you look over your records after years of play, you’ll see a whole lot of small wins—and one (or a few) big losses, big enough to wipe out the profits from all of your small wins, and then some. (Mustn’t forget that house edge!)

But, you don’t care about the long run. You just want a win this weekend. So, let’s look at what betting system works best in the short run. We can’t guarantee a win, but there is a logic to betting systems that can greatly increase your chances of success.

Types of Blackjack Betting Systems

There are two main types of betting systems for blackjack or any casino game—positive progressions and negative progressions. With a positive progression, the general theory is that you raise your bets after wins, which means that your bigger bets are primarily funded by money won. This is a conservative betting system insofar as a long string of losses will not wipe out your bankroll as quickly as with a negative progression.

With a negative progression, you raise your bets after your losses. This is more dangerous, since a bad run of losses can wipe you out quickly. In its favor, however, it allows you to win on a session in which you’ve lost many more hands than you’ve won. Since your bets after losses are bigger bets, you don’t have to win so many of them to come back, assuming you can avoid a truly disastrous series of losses that empties your pockets.

There are dozens of variations on betting systems that incorporate features of both the positive and negative progressions, in an attempt to create the “perfect” betting system that wins the most often with the least chance of busting out.

But the best system of this type I’ve seen for accomplishing this end was first published 40 years ago by mathematician Allan N. Wilson, in his Casino Gambler’s Guide (Harper & Row, 1965). Dr. Wilson called it “Oscar’s system,” named after the dice player who’d invented it.

How to Use Oscar’s Blackjack Betting System

Here’s how Oscar’s System works:

The goal for any series of bets is to win just one unit, then start a new series. Each series starts with a one-unit bet. After any win, the next bet is one unit more than the previous bet. After any loss, the next bet is identical to the previous bet. That is, if you lose a two-unit bet, your next bet is a two-unit bet until you have a win, at which point you raise your bet one unit to a three-unit bet.

That is the whole system, except for one stipulation—Never place any bet that would result in a win for the series of more than one unit. In other words, if you win a 4-unit bet, and you are now down only 2 units for the series, you would not raise your next bet to 5 units because of the 4-unit win; you’d only to 3 units, which would be all you’d need—if successful—to achieve a one-unit win for the series.

Oscar’s betting system combines the best features of both the positive and negative progressions. You can suffer much longer runs of losses without busting out than you can with a negative progression, since you don’t raise your bets after losses. Yet, a much shorter run of wins can get back your previous losses on a series, since you raise your bets following wins. It’s kind of brilliant, actually. Strings of losses hurt less, yet strings of wins pay more.

When Oscar told Dr. Wilson that he had been using this system for many years and had never had a losing weekend in Las Vegas, Dr. Wilson did some mathematical and computer simulation analysis on it. Was this possible? His findings were amazing. Using a $1 betting unit on an even money payout game, the betting progression is so slow that the player would bump up against the house’s $500 maximum bet (at that time) on only one series of every 5,000 played. On 4,999 of those series, the player would expect to achieve his $1 win target.

Since Oscar was shooting for a weekend win of only $100 (back in 1965, this was a very healthy win!), Dr. Wilson concluded that it was quite likely that Oscar had played on many weekends over a period of years with never a loss.

So, should we all start using Oscar’s system? One word of caution: Watch out for that one losing series. How much does Oscar lose when his system fails on that one unlucky series out of 5,000?

About $13,000.

You see, even though he’s just bumped into the house’s table maximum of $500, he’s gotten to this point by losing lots of bets in the $100+, $200+, $300+, and $400+ range during this horrendously long series. So, if you try Oscar’s system, you still have to be prepared to lose in the long run.

Oscar’s System: Sample Betting Sequences

Conclusion

No betting system will ever overcome the house edge in the long run. But they’re not worthless. Professional gamblers do find opportunities for profiting from various types of betting systems in gambling tournaments, as “camouflage” to disguise an advantage play that is not based on the betting system itself, and especially in online casinos where betting systems can be used to milk the casino “bonuses.”

To actually win at normal casino blackjack in the long run, however, you have to start by counting cards–not because card counting is the best or most profitable way to win at blackjack, but because the principles behind card counting are the same principles that are behind every type of professional gambling system at blackjack, even methods that don’t require counting. ♠

The Martingale: Progression to Depression

by Arnold Snyder
(From Card Player, April 1995)
© 1995 Arnold Snyder

(Note from Arnold Snyder: To learn how to win at blackjack over the long run, with or without card counting, start with our Intro to Winning Blackjack.)

Question from a Reader regarding the Martingale Betting System: I lost a substantial amount of my savings playing blackjack at [casino name deleted] in Atlantic City — almost $30,000. I admit that I was using a progressive betting system — a straight martingale, and I know that won’t give me any advantage — but even so, I feel pretty certain that I was cheated.

I was winning steadily for quite a few hours using this betting system (a simple double-up after a loss), then in a short series of hands that lasted only about 30 minutes — they totally cleaned me out. I was playing perfect basic strategy.

I have enclosed a chart which shows the series of bets I made, and the win/loss results that eventually bankrupted me. I would like to know your expert opinion on whether or not this could have happened in an honest game.

Can I take any kind of legal action against the casino if this series of hands is indicative of cheating? I have a friend who witnessed the debacle who can attest to the truth of what happened.

Answer: I have studied your results, and although anyone would acknowledge that you suffered an unusually unlucky series of hands — and an especially devastatingly unlucky series for any martingale player — the series of hands in and of itself would not be indicative of cheating. I highly doubt you were cheated.

The straight martingale is one of the riskiest betting systems any gambler could use. Any gambler who ever has used it with any regularity could tell you his own hair-raising “impossibly unlucky” tale of why he gave it up for more conservative betting methods.

Here is what happened to you:

1) You bet $10, and lost.

2) You bet $20, and lost.

3) You bet $40, and lost.

4) You bet $80, and lost.

5) You bet $160, and doubled down on your 11 vs. the dealer 8, and you lost.

6) This double loss required you to place a next bet of $480, which you then lost.

7) You placed a bet of $960, and split your 8s vs. a dealer 10, and you lost both hands.

8) This double loss required you to place a bet of $2880, which was higher than the $2000 table max. So you bet the max, and lost.

9) On your next hand, you bet the max again, and insured your 20 vs. the dealer ace. You lost both the insurance bet, and your hand when the dealer hit to 21. This put you behind by a total of $7880.

10) You then bet the max, and pushed.

11) You then bet the max and won!

You say that the above series of results took about 10 minutes, and that you do not recall the exact series of wins and losses in the approximately two dozen hands that you played over the next 20 minutes. You note there were a few wins interspersed with the mostly losses, but you had to have had 12 more max bet losses than wins (perhaps 18 losses and 6 wins?), as you left the table a $29,980 loser.

How “impossible” is this?

Unfortunately, not very.

You must realize that you were required to start placing max bets after only 7 consecutive losses. Once you are actually placing $2000 bets, a loss of $30,000 is not at all unusual. This would be equivalent to a $5 bettor losing $75 — which any experienced $5 bettor could tell you would not be uncommon. If you count your double loss on your split pair as two hands, you actually began your unfortunate series of losses by losing 10 hands in a row. How unusual is this?

If I were flipping a coin, with heads being a win, and tails a loss, the odds against me coming up tails 10 times in a row would be about 1000-to-1. That’s pretty unlikely, though far from impossible.

Blackjack, however, is less advantageous than a coin flip. In 100 hands, a basic strategy player will experience, on average, 43 wins, 48 losses and 9 pushes. Since a martingale bettor ignores pushes and lets his bet ride, we can ignore them in our analysis. For every 100 win/loss decisions, a basic strategy player will see about 53 losses and 47 wins.

With these win/loss proportions, the odds against losing 10 consecutive decisions are only about 500-to-1. Now 500-to-1 may seem nearly impossible to many people, but realistically, at any given time, a series of losses equivalent to yours is happening to dozens of players in Atlantic City, and to hundreds of people every day of the year in U.S. casinos. It’s happening right now to one out of every 500 people who are playing. How many tens of thousands of people are playing blackjack right now in U.S. casinos?

You must realize that if you had been flat-betting $10, instead of “doubling-up” to try to recapture your previous losses, you would only have lost $110 (and this includes both your pair split and your double down loss!), instead of being behind by $7,880 at the end of that first unfortunate string of losses. And your total loss at the end of the debacle would only have been $230, not $29,980.

The martingale is a systematic method of chasing your losses. There’s no other way to describe it. This is about the most foolish way to gamble. You violated the single most important rule for gamblers: If you can’t afford to lose it, don’t bet it. ♠

Battle of the Babies: A Comparison of the Red 7, Hi-Lo, and KO Card Counting Systems

By Arnold Snyder
(From Blackjack Forum Volume XIX #3, Fall 1999)
© Blackjack Forum 1999

[Editor’s note: This is a technical article on how to best evaluate card counting systems. It addresses how system sellers sometimes fudge results to make their systems look better.

The Search for the “Best” Card Counting System

New players typically search anxiously for the “best card counting system” before learning their first count. This article will provide simulation data on the Red Seven Count for comparison to the Hi-Lo and KO counts. It will also discuss important issues in the comparison of different blackjack card counting systems.

John Auston used the approach that has recently become commonly known as “score” to compare the Red Seven (Red 7), Hi-Lo, and KO count systems. For those unfamiliar with this approach, I would describe it very briefly as an attempt to compare systems and games on an even playing field, assuming we define “even” as an equal and constant risk of ruin, assuming the same starting bankroll and the same betting limits for each system in identical games.

In order to accomplish this in the sim, unrealistic bets are forced. For example, if the optimal bet is $137 with one system, but $138 with another, and $134 with a third system, then these are the bets that are placed. In practice, if these were human players and even if they had very accurately devised their count betting strategies to reflect a similar risk of ruin for identical $10,000 bankrolls, all would likely have bets of either $125 or $150—some slightly underbetting their banks, some slightly overbetting.

I can already see a barrage of letters from players asking me to explain why anyone would want an analysis based on such an impractical, nay impossible, betting methodology. Briefly, the purpose of this type of analysis is not to tell us our win rate to the exact penny per hour, nor is it to suggest that we should attempt to mimic the impractical betting strategies in the real world so that we may obtain optimal results.

The purpose is simply to evaluate the potential profitability of applying a system to a game assuming a given level of risk—one way of dealing with the “best card counting system” comparisons. Let me provide one practical example.

It is not difficult for me to set up a computer simulation where the Hi-Lo Count will outperform the Advanced Omega II (a much stronger and more difficult count), even when both counts are being played accurately and employing the same betting spread. All I have to do is play around with the betting strategies so that Omega II is waiting too long to put its big bets on the table. If I simply raise the true count by one or two numbers where these bigger bets are placed, then Hi-Lo will appear to be a stronger system. But in fact, the Hi-Lo is simply being played more aggressively and with a higher risk of ruin.

I first learned about this aggression factor back in the early 1980s, when I was working with Dr. John Gwynn, Jr. In order to compare different count systems using the same betting spread in the same game, I asked Gwynn to produce data showing the full range of possible betting schemes for each system based on the various true counts. For example, with the Hi-Lo Count, spreading from 1-2-4 units in a single-deck game, he would produce data showing the bet raises to 2 and then 4 units at +1 and +2, then +1 and +3, then +2 and +3, then +2 and +4, etc.

The data Gwynn and I came up with showed nothing about risk of ruin, but it did show that a player who wanted to optimize his percent advantage over the house could do so by raising his bets at precisely the right counts. A player who wanted to optimize his dollar return, on the other hand, could do so by betting more aggressively (placing high bets earlier), even though this tactic would lower his percentage return.

Whenever I published Gwynn’s system comparison data, I always chose the betting scheme that would provide the highest percent advantage to the player. I did this because it was more realistic. A player with an unlimited bankroll, in fact, will show the highest dollar return if he places his high bet as soon as he has even the slightest fraction of a percent advantage over the house. Players with unlimited bankrolls, however, do not exist. Such hypothetical players have no risk of ruin because they can always dig out more money.

In the real world, it is more meaningful to optimize the percent advantage than the maximum potential dollar win. In optimizing the percent advantage from Gwynn’s data for many systems in various games back in the early to mid-80s, and then up into the mid-90s using John Imming’s RWC software, I discovered that the optimal betting spreads were never intuitive. If I was spreading from 1-2-4-8 units in a 6-deck game, one system might perform best by raising bets at +1, +2, +4, and +5; while another’s optimal betting scheme would raise at +2, +4, +5 and +6; while yet another might perform best at +1, +3, +4 and +6.

When I didn’t examine every possible betting scheme for each system, I would often see data that would seem illogical. A system with a lower betting correlation and playing efficiency would appear to outperform a technically superior system. In almost all cases, as soon as I would look at the results of the optimal betting scheme for that system, defining optimal as the scheme that would produce the greatest percent advantage, the greater profit potential of a technically superior system would exhibit itself.

Optimizing system performance to obtain the highest percent advantage for each system does not ensure that all systems being so compared are playing with the same level of risk. This was simply the best way I knew to compare the various systems’ ultimate levels of performance.

Misleading Simulation Data for the KO Count

One of the worst examples of misleading simulation data from ill-chosen betting schemes can be found in Knock-Out Blackjack by Olaf Vancura and Ken Fuchs. They designed a unique method of attempting to simulate equivalent levels of risk in their system comparisons that produced data that computer programmers used to refer to as GIGO—garbage in, garbage out. The system comparison charts in Chapter Five of the 1996 edition and again in the Appendix of the 1998 edition would lead one to believe that the KO Count was superior to or equal to just about every other counting system on the planet, and especially powerful in one-deck games.

For example, the chart below reproduces the simulation data provided by Knock-Out Blackjack comparing the win rates for KO vs. Red 7, Hi-Lo, and Omega II, assuming 1-5 spreads in the one and two-deck games, 1-8 in the 6-deck games, and 1-10 in the 8-deck games, with all systems using the 16 most important strategy indices.

The Simulation Data Provided by Knock-Out Blackjack

When I first looked at this data back in 1996, my initial thought was, “Impossible! KO beating Omega II in a single-deck game? And beating Hi-Lo in all games?” I did not know whether or not it might beat Red Seven, but it was illogical to me that it would perform so powerfully, so consistently, in comparison with the balanced counts. I knew that Red Seven performed close to Hi-Lo in shoe games, and did occasionally outperform it, but never in single deck.

I ran some single-deck simulations myself using John Imming’s software, setting up the game and system conditions as described by Vancura and Fuchs, and quickly confirmed what I already knew—that KO was similar to Red Seven in performance, but notably less profitable than Hi-Lo and Omega II. In fact, it also slightly under-performed Red Seven throughout all the tests I ran.

I called Anthony Curtis, who was distributing the KO book through Huntington Press (now publisher of the second edition) and told Curtis that I thought the authors may have jerry-rigged the sims to make KO appear stronger than it actually was. I told him that in the one-deck sims I was running, Red Seven outperformed KO, not by much, but slightly.

Curtis assured me that he felt the authors were honest and that their simulation data was real, with no intention to skew the system comparison data. At this point, I had never met Olaf Vancura or Ken Fuchs, so I did not know if these guys were legitimate experts or big phonies. I have met and corresponded with both of them since, and I now know that, in fact, they are both gentlemen and scholars with no intent to deceive.

Here’s where Vancura and Fuchs went wrong. KO’s imbalance makes it strongest and most accurate when the running count is at its pivot. So, the authors, very logically, set up their sims so that KO was placing its high bets precisely at this point. The other systems, however, were then forced in their simulations to play with the same “average bet” that KO used.

The KO counting system is actually very easy to use and very strong. It is similar in strength to the Red Seven, which itself is close to the Hi-Lo in strength within certain confines. In fact, Hi-Lo is notably superior to both Red Seven and KO in one and two-deck games, and from many professional players’ perspectives, where accurate bet-sizing according to Kelly principles is important, Hi-Lo is also far superior in shoe games.

For most casual players, however, I still believe the unbalanced counting systems are the best choice because they’re simpler, can be played longer without costly errors, and allow the player to focus more on heat, getting away with a big bet spread, and other factors that matter more to your win rate than the count system you use.

I have been hesitant to publicly criticize Vancura’s and Fuch’s less than brilliant system comparisons in Knock Out Blackjack because the book really is one of the better ones on the market. The system is good. The explanations of blackjack and card counting are clear. There’s no get-rich-quick b.s., and I believe there was no intent to deceive.

I certainly don’t want to push new players away from Knock Out Blackjack and into the arms of one of the con-man books out there. Also, many serious players are already aware of why the KO system looks so strong in the sims Vancura and Fuchs provide in their book. There has been a lot of sim data posted on the various Internet blackjack sites that refute the findings in the KO book.

Also, anyone who looks at John Auston’s “World’s Greatest Blackjack Simulation” reports can see that KO’s strength is about what one would expect of a level one unbalanced counting system.

John Auston’s Comparison of the Red 7, KO, Hi Lo and Omega II Card Counting Systems

In the chart below, I am reproducing John Auston’s “World’s Greatest Blackjack Simulation” data for comparing KO with Red Seven, Hi-Lo, and Omega II in the same games that Vancura and Fuchs used in their book. The single-deck penetration was 65% and all other games were 75%. Note that in the single and double deck games, Auston did not provide sim data for a 1-5 spread, so I used his data for 1-4 in single deck, and 1-6 in double.

Auston’s Data on KO, Red Seven, Hi-Lo, and Omega II

Since the World’s Greatest Blackjack Simulation reports were published in 1997, many players have asked me why the KO data does not show any indication of the consistent superiority to other systems that KO is purported to exhibit in Knock Out Blackjack. The answer is simply that John Auston did not set up his WGBJS sims so that all systems had to conform to the “average bet” specs of the optimal KO betting strategy.

A few interesting points on Auston’s WGBJS data. Note that Omega II is in a class by itself, solidly trouncing the level one systems’ results in all games, as expected. Hi-Lo, KO and Red Seven go back and forth in their exhibitions of strength relative to each other.

Hi-Lo is slightly superior in single deck, while Red Seven and KO are about the same. Red Seven is slightly weaker in the double deck, where Hi-Lo and KO are about the same. Red Seven is stronger in both the six deck and eight deck, where Hi-Lo and KO are slightly weaker. If you actually look at all of the data in the WGBJS reports, you find that all three of these counts continually go back and forth, depending on the number of decks, penetration, and betting spreads. But none of them are a match for Advanced Omega II.

I would also point out that even these independently run sims—done with no attempt to bias the data towards any system—are inadvertently set up with conditions that are more favorable to the unbalanced counts, at least in comparison with the Hi-Lo. This is because John Auston used the “Illustrious 18” shoe strategy indices for all systems other than Advanced Omega II. These indices—which are the ideal indices for shoe games—are not the best 18 indices for one and two deck games. Since all but two of these indices call for Hi-Lo strategy changes at neutral to slightly positive counts (0 to +5), this is precisely the range of counts where both KO and Red Seven will perform best.

A Hi-Lo player who is using more indices for the common playing variations that occur both at negative counts and at higher positive counts would actually expect a performance level closer to the Advanced Omega II system (which Auston simmed with a full set of indices) in the one and two deck games. Red Seven and KO simply do not have a playing accuracy level comparable to Hi-Lo outside the limited Illustrious 18 range.

Also, Red Seven’s dominating performance in the six deck and eight deck games, where it solidly trounces both Hi-Lo and KO, is due to the way the system is designed, where it performs with maximum strength when the advantage has risen by about 1%. Because it is strongest at this point, this is where it will be placing most high bets.

In these shoe games with only 75% penetration, higher advantages only rarely occur. So, Red Seven is optimized to play in precisely these types of games.

I can assure you, however, that it is playing with more risk than Hi-Lo, so in reality it would require a larger bankroll to play Red Seven to its optimum performance in these games. Auston’s six deck WGBJS data shows Red Seven’s average bet to be 1.63 units, while KO and Hi-Lo are making average bets of only 1.42 and 1.47 units respectively.

If we were to force average bets of 1.63 units on Hi-Lo and KO, they would perform even worse in comparison with Red Seven. KO’s playing and betting accuracy do not optimize until a 2% raise in the player advantage has occurred, and Hi-Lo suffers from not counting the sevens, which raises the Red Seven’s betting correlation (BC) and playing efficiency (PE) enough at its pivot point to justify the more frequent higher bets.

John Auston’s risk-adjusted analysis, which we have yet to look at in this article, solves the problem of equalizing the risk factors for the various systems tested, but it is still unfairly skewed toward the unbalanced systems in hand-held games, because it again uses only the Illustrious 18 range of indices, with which the unbalanced systems perform best.

One other problem with the Red Seven data is that in all of these sims—WGBJS and risk-adjusted—the advanced version of the Red Seven system cannot be simulated as published in the 1998 edition of Blackbelt in Blackjack [editor’s note: the Advanced Red Seven can now be simulated using CVDATA, which was not available at the time this article was written].

In shoe games, for example, I provide index numbers for the Advanced Red Seven that are to be used only in the second half of the shoe. The player is advised to use only the six “simple Red 7” indices in the first half of the shoe, then switch to the advanced indices for the second half. The ability to “step up” to the much more powerful Advanced Red Seven when ready is something not available to players with the KO Count.

Also, although both the simple and advanced Red Seven indices are employed by running count, the Advanced Red Seven advises the use of the “true edge” method of estimating advantage for bet sizing, which is actually a simplified method of adjusting to the true count. In other words, the Advanced Red Seven player would be making strategy plays by running count, but some of these plays would not be made until after the 50% level of penetration was reached, while bet sizing is done by true count.

The performance of Red Seven in these simulations will be hurt by not employing these techniques. The sims will simply not show accurate data for the Advanced Red Seven’s true power.

Also, the SBA software used for these simulations was incapable of counting sevens by color. John Auston adjusted for this deficiency by essentially counting all of the 7s as +1/2, instead of just the red sevens as +1. In both the 1983 and 1998 editions of Blackbelt in Blackjack, I wrote: “One may even count all sevens as +1/2, or simply count every other seven as +1” in order to maintain the same imbalance as is provided by counting just the red sevens—and over the years not a few players have told me that this is what they do at the tables.” This method of unbalancing the count has a slightly better betting and playing efficiency than the traditional Red Seven, however. In prior sim comparisons published in Blackjack Forum, I always used Imming’s RWC software (no longer commercially available), which does allow counting by suit.

Also, Auston chose to simulate the Red Seven for his risk-adjusted analysis with the indices he derived from SBA, and which I published in the Red Seven Count edition of his “World’s Greatest Blackjack Simulation” report. So, both the betting and playing strategies used in these risk-adjusted analyses are different from those you will find in the 1998 (and 2005) edition of Blackbelt in Blackjack, which I believe to be superior. Just bear in mind that these comparisons are specifically for the 1997 version of the simple Red Seven as published in Auston’s WGBJ Sim.

More Problems With Comparing Card Counting Systems

Finally, the risk-adjusted method of analysis will give an unbalanced system an ability to bet far more accurately in all games than would be possible in the real world. A Hi-Lo or Omega II player who is using a true count system will truly know when his advantage is approximately +1/2%, +1%, +1.5%, +2%, etc., and he will be able to size his bets accordingly. This would also be true of an Advanced Red Seven player who is using the true edge method of bet sizing.

For a KO player or a simple Red Seven player who is purely going by the running count, an accurate bet can only be made at the pivot. If a Red Seven or KO running count is +6 above the pivot, the actual player advantage will be quite different in a six deck game if only two decks have been dealt than if 4.5 decks have been dealt.

This is why most professional blackjack players steer clear of the unbalanced counts—and why I added the true edge methodology to the 1998 Advanced Red Seven. If you are betting multiple black chips for every ½% rise in your advantage, or calling in a big player who will be doing this, you do not want to be constantly overbetting and underbetting your optimal Kelly bet—or most likely, a fractional Kelly bet you’ve chosen to minimize your risk.

So, as you look at this risk-adjusted comparison data, bear in mind all of these factors. The validity of the data extends as far as the assumptions used in the sims for playing and betting. Ultimately, Red Seven and KO perform very well compared to Hi-Lo, and I still believe these simplified unbalanced systems should be used by most players for practical reasons, in particular the cost of errors associated with inaccurate true count adjustments.

Again, I want to emphasize that Hi-Lo is being severely penalized in the hand-held games in the charts below by using the Illustrious 18. If you use the Hi-Lo in one or two deck games and you are using the Illustrious 18 indices, then you could probably do almost as well with Red Seven or KO—better, if your true count adjustments aren’t perfect. Most single deck players I know use many more indices than this in single deck, especially some negative indices that are more important than some of the Illustrious 18 in these games, and unbalanced counts are incapable of using more indices with accuracy.

Risk-Adjusted, One Deck, H17, DAS, 75% Dealt

Risk-Adjusted, Two Deck, S17, DAS, 75% Dealt

Risk-Adjusted, Six Deck, S17, DAS, LS, 75% Dealt

Risk-Adjusted, Six Deck, S17, DAS, LS, 87.5% Dealt

Risk-Adjusted, Six Deck, S17, DAS, LS, 92% Dealt

In the six deck comparisons above, we have a perfect illustration of the power of the pivot. Note that with 4.5 decks dealt (75%), Red Seven is the strongest performer. With five decks dealt, Hi-Lo and Red Seven pretty much equalize, both slightly outperforming KO. But look what happens when we go to 5.5 decks dealt out (91.67% penetration). Red Seven is now the weakest performer, as KO is capitalizing on its strength when many more opportunities arise for playing and betting with a 2% advantage.

The Red Seven (that is, the simple running count version tested here) simply performs better in shoes at most common levels of penetration, whereas KO performs better in the rare games with an extremely deep level.

Also, in some games under specific conditions, KO does outperform Hi-Lo in a risk-adjusted sim. For example, look at this six deck game with a less favorable set of rules:

Risk-Adjusted, Six Deck, H17, DAS, 75% Dealt

Risk-Adjusted, Six Deck, H17, DAS, 87.5% Dealt

KO outperforms both Hi-Lo and Red Seven in these H17 games. Again, the explanation for these types of seemingly aberrant results is that at some levels of penetration, and with certain rule sets, the sevens (which Hi-Lo ignores) are important enough on some of the Illustrious 18 strategy decisions as to give these unbalanced counts, which count sevens, a slight edge. Also, the betting schemes are such that the optimal high bets happen to occur very near the unbalanced counts’ pivots, and counting the sevens also gives them a slightly higher betting correlation right at this crucial point.

Unless we are adjusting an unbalanced count to a true count, we cannot cite its betting correlation (BC) or playing efficiency (PE). For example, the Red Seven has a betting correlation of about 97% at the pivot, just slightly greater than the Hi-Lo. But the Hi-Lo has better than 96% betting correlation throughout the full range of counts that occur. It is simply incorrect to attempt to compare a balanced system with an unbalanced system based on BC and PE if you are using the unbalanced system as a running count system.

Now let’s look at some 8-deck back-counting risk-adjusted comparisons (below). We’ll look at the risk-adjusted results with six decks (75%), 6.5 decks (82%), and 7 decks (88%). Here again, we see that KO outperforms Red Seven at the very deepest level of penetration.

Risk-Adjusted, 8-Deck, Back Count S17, DAS, LS, 75% Dealt

Risk-Adjusted, 8-Deck, Back Count S17, DAS, LS, 82% Dealt

Risk-Adjusted, 8-Deck, Back Count S17, DAS, LS, 88% Dealt

Note that in most comparisons, regardless of the number of decks, Hi-Lo slightly outperforms both KO and Red Seven. I think in the real world, a good Hi-Lo player would outperform the unbalanced running count players more than these sim results indicate. In the hand-held games the Hi-Lo player would simply be able to use more strategy changes, and in the shoe games the Hi-Lo player would be betting more accurately according to his advantage throughout the full range of counts that occur.

Overall, as we would expect, the risk-adjusted comparisons do show Hi-Lo (accurately used) to be the stronger counting system.

For those of you who do not have John Auston’s “World’s Greatest Blackjack Simulation—Red Seven Edition,” I am reproducing below all of the running count indices that John used in that report as well as in his risk-adjusted analyses. Note that these indices assume that you begin your count at 0. The indices were specifically derived for the Red Seven Count that counts all sevens as +1/2 instead of counting just the red sevens as +1. This would not change any of the indices.

Some players who use the Red Seven in this way have told me that the easiest way to count by halves is to simply count every other seven as +1. I believe I actually first heard of this technique being used by players who did it with Wong’s Halves Count. I may even have read about the technique in one of Wong’s newsletters many years ago, or possibly in one of the earlier versions of Wong’s Professional Blackjack.

I was unable to find the reference in print but the technique has been used by some Red Seven and Halves players for many years. I do not believe my suggestion that Red Seven players might count in this way in the 1983 Blackbelt in Blackjack was the first reference to this technique in print. Those who use it swear it is the easiest and most accurate way to count with these systems.

I once ran some simulations using Imming’s RWC software to compare the difference between counting the red sevens as +1 and all sevens as +1/2, but the results were statistically insignificant. I suspect that I did not run a sufficient number of hands. (Computers were notably slower back then.) The simulations Auston used in his WGBG repots, his risk-adjusted analyses, and his truly amazing Blackjack Risk Manager software, are all based on sims of 400 million hands each, quite enough to obtain statistically significant data for practical comparisons.

Below, you will find all of the Red Seven risk-adjusted data that John Auston produced for this study. Some Red Seven players may regret that he did not run risk adjusted sims on the full range of rule sets that he did for Hi-Lo and KO.

John chose five different rule sets for his Red Seven single-deck analyses, and four different rule sets for each of the two deck, six deck and eight deck analyses. I don’t think a more exhaustive risk-adjusted analysis of this version of the Red Seven is called for at the present, as I believe that most Red Seven players probably use one of the versions (simple or advanced) from Blackbelt in Blackjack, rather than the version I published in the WGBJ sim report.

In summary, the “best” blackjack card counting system for you, whether the Red Seven, Advanced Red Seven, KO, Hi-Lo, Zen, or some other count, will depend partly on your current abilities as a card counter and partly on the games you actually play in. I hope this article will help you better understand some of the issues involved in blackjack system simulations and comparisons. ♠

Back Betting: Optimal Pair Splitting Strategy

By Arnold Snyder
(First published in Card Player, June 1999)
© 1999 Arnold Snyder

Many casinos outside the U.S., and a few inside, allow “back betting” by players who are not playing their own hands. Back betting is the practice of placing bets on the hands of other players at the table, whether or not you are seated at the table yourself.

Most casinos that allow back bets allow them only to the extent that the total amount bet on the hand does not exceed the table maximum. In other words, with a table maximum of $500, if the seated player is betting $100, back bets would be capped at $400.

Generally, most casinos that allow back bets also allow the seated player to make the strategy decisions on the hand. In practice, seated players will sometimes, but not always, defer this decision to a back bettor who has more money on the hand than the seated player.

Because pair splits and double downs require a player to put more money on the table, casinos that allow back betting usually must give back bettors the option of not placing more money on the table. This is due to practical considerations. If a seated player doubles or splits, and a back bettor on the hand doesn’t have the money, does the game stop? Does the casino tell the seated player he’s not allowed to double his bet since the back bettor can’t afford it?

With a pair split decision, if the back bettor does not put more money on the table, then the back bettor’s initial bet will all be played on one hand, and only the seated player’s money will be at risk on the second (and any third and fourth) split hands. This rule does allow back bettors to take advantage of some profitable opportunities not available to the seated player.

For example, when the seated player has a pair of eights versus a dealer high card, the back bettor can choose to play just one hand starting with a total of eight, instead of two. Obviously, an eight is not a great starting card when the dealer has a nine showing, so you don’t want to play two hands, but you’re also much better off starting with an eight than you are with a total of hard 16 (two eights unsplit).

The optimal back-betting split strategy will depend on whether the game is single-deck or multiple-deck, whether the dealer hits or stands on soft 17, whether or not doubling after splitting is allowed, and whether or not the European no-hole-card rule is in effect (i.e., dealer blackjack takes all on splits and doubles).

I’ll provide a down-and-dirty back betting pair-split strategy guide in this article, but if you are going to be playing extensively in back-betting games, then I’d advise you to get a copy of Stanford Wong’s Professional Blackjack. Wong never discusses back betting in his book, but his “Appendix E” charts show the expected value for every player hand versus every dealer upcard for most different rules and numbers of decks. With this information you can easily devise optimal back-betting strategy for any blackjack game you encounter.

These back-betting split strategies are often not intuitive, and they are quite different from regular pair splitting basic strategy. Let’s consider some of the back-betting strategies for pair splits in a shoe game, where the dealer stands on soft 17. Let’s also assume that the seated player is making all decisions and does not defer to you for advice. If the European no-hole-card rule is in effect, and if the seated player splits aces and tens against all dealer upcards, you should match his bet against all dealer upcards except the ten and ace.

If it seems crazy to you to split tens against sevens, eights and nines, you are right; you would win more money by keeping the hard 20 against every dealer up card. But if the seated player splits his tens, you too should put more money on the table. The reason is that, with the European no-hole-card rule, you’ve got a positive expectation on any hand that starts with a hard ten against every dealer up card except the ten and ace.

In other words, if you were controlling the hand, you would keep the twenty. But since you’re back betting, and the seated player has decided to split, you should go ahead and put more money on the table.

With a pair of nines, you would match his splits versus 2 through 8. With a pair of eights, you would match his splits versus 3 through 7 only. With sevens, match the splits only versus six. Never match the split when he splits a pair of sixes. If he’s stupid enough to split a pair of fours or fives, incredibly enough, you would match these splits versus a dealer six! If he splits twos or threes, match the splits only versus five and six.

A two-man team, consisting of a low-betting seated player and a high-betting back bettor, can use Wong’s charts to devise some very unique and advantageous split strategies. For example, consider the case of a pair of sevens versus a dealer nine. The best strategy for the seated player (hitting) has an expectation of -44%. This is a bad hand. If the seated player splits the sevens, however, and the back bettor doesn’t match the bet, the back bettor’s new starting total of hard 7 has an expectation of only -29%. So, if the seated player has a $10 bet, and the back bettor a $1000 bet, this is a very smart defensive play. ♠