Leonard Benson's Power Numbers Blackjack system is tested by mathematician and player John Leib in this article for Blackjack Forum. During 22 hours of testing the Power Numbers Blackjack system, Leib was guided in his play by Dr. Morton Jacobs and Leonard Benson themselves. Leib reports on the Power Numbers Blackjack system claims, training materials and results at the table.
Arnold Snyder's Blackjack Forum Online Home Arnold Snyder Contact Information About Arnold Snyder's Blackjack Forum Online How to Win at Blackjack Arnold Snyder's Blackjack Forum, Trade Journal for Professional Gamblers Since 1981, New Issue Blackjack and Gambling Forums Moderated by Professional Gamblers Leonard Bensen's phony Power Numbers Blackjack system From Blackjack Forum Gambling Library Best Internet Casinos and Smart Online Gaming Gambling Books Recommended by Professional Gamblers Links to Gambling Sites Recommended by Professional Gamblers  
 

Leonard Benson's Power Numbers Blackjack

 
Leonard Bensen's phony gambling system Power Numbers Blackjack
 
SCAMS, CONS, AND PHONY SYSTEMS : CONTENTS
Articles about Leonard Benson and the Power Numbers Blackjack System
Power Numbers Blackjack by Leonard Benson John Leib Challenges
    Leonard Benson
    By Arnold Snyder and John Leib
Power Numbers Blackjack by Leonard Benson Leonard Benson Takes the Challenge
    By John Leib
Articles about Jerry Patterson and the TARGET System
Jerry Patterson and TARGET blackjack system Patterson Bars Snyder from TARGET
    By Arnold Snyder (Coming soon)
TARGET gambling system and Jerry Patterson Off Target
    By Arnold Snyder
phony blackjack system and Jerry Patterson I Saw It With My Own Eyes
    By Arnold Snyder
<i>Break the Dealer</i> by Jerry Patterson Review of Break the Dealer, by Jerry L.
    Patterson and Eddie Olsen
    By Arnold Snyder
phony blackjack system by Jerry Patterson Response to Arnold Snyder's Review
    of Break the Dealer
    By Jerry Patterson
phony gambling system, Break the Dealer by Jerry Patterson Snyder's Response to Patterson's
    Response to Snyder's Review of
    Break the Dealer
    By Arnold Snyder
Other Gambling Cons and Scams
Gambling scams and cons Reach Out and Fleece Someone
    By Arnold Snyder
Gambling scams and cons Flipped
    By Dunbar
NBJ Blackjack System by E. Clifton Davis, phony gambling system New Blackjack, Same Old Baloney:
    Review of E. Clifton Davis' NBJ System
    By Arnold Snyder with commentary by
    Boardwalker
 
 
 




 

Leonard Benson's Power Numbers Blackjack System: A Report on the Claims, Training, and Results at the Tables

By John Leib
(From Blackjack Forum XVI #1, Spring 1996)
© 1996 Blackjack Forum

[Ed. note: In the September '95 issue of Blackjack Forum, we published a letter that mathematician John Leib wrote to Leonard Benson, in which Leib offered to test the POWER NUMBERS BLACKJACK™ system, which Benson was heavily promoting through newspaper advertisements all over the country. (Benson, by the way, continues to promote and sell the system.)

Leib told Benson he wanted to use Benson's money to test the non-card-counting system, and stated that he would publish his analysis and results in Blackjack Forum. This is Leib 's follow-up report on his experience learning and playing the POWER NUMBERS BLACKJACK™ system. — Arnold Snyder]

Leonard Benson Responds to the Challenge

Monday, September 11th, I returned from that ritual which humbles most of us: my 50th high school class reunion. When I got to the house, my wife had a telephone pink slip which I had not expected; I had gotten a call from Leonard Benson, purveyor of the Jacobs POWER NUMBERS BLACKJACK™ way to relieve the casinos of their money.

I had not expected the call because the claims made for POWER NUMBERS BLACKJACK™ did not seem possible to satisfy in actual casino play. I, as perhaps most of you, figured this was just another scam, designed to take money from the gambling public by use of the motivating feature shared by gamblers: greed. I was sure Leonard Benson knew it was a scam which could not withstand critical testing in actual casino play.

I had attempted to chide Leonard Benson into some response by my original letter (which was reprinted in the September issue of Blackjack Forum).

After that issue was distributed, I sent another letter, calling attention to my ability to deliver on getting ink in Blackjack Forum describing the results which I would experience by actually using POWER NUMBERS BLACKJACK™ with real money. If Leonard Benson knows the system does not work, he surely would not initiate further contact, and instead would hope that, by ignoring my challenge, it would pass.

But he had called! What could he possibly want to talk about? The next day I called him and found him receptive to my proposal! We talked about how ten trials might not be enough, what with one fluctuation or another, and agreed to go for 25 trials instead. Except for the time involved, I knew the more the merrier. Leonard said he wanted to talk it over with Dr. Jacobs, the inventor of POWER NUMBERS BLACKJACK™.

Later that same day, Leonard called to confirm agreement with my proposal. Dr. Jacobs thought it was a great idea, too. Leonard promised to send me the complete set of materials so that I could become proficient at utilizing POWER NUMBERS BLACKJACK™ before I got to Vegas and was certified as competent to put it to the test with their money.

I must say that this agreement to test POWER NUMBERS BLACKJACK™ in this unbiased way, agreeing to publication of the results, good or ill, told me that they were serious about the validity of POWER NUMBERS BLACKJACK™. This was not a scam! I was very skeptical about its value, even if they weren’t, but I was determined to give them a fair shake.

Leonard Benson Provides the Power Numbers Blackjack Training Materials

True to Leonard’s promise, the material was shipped September 13th and arrived three days later on the 16th. I decided to chronicle the pertinent events from that point forward in diary form.

As advertised, the package contained:

A 2 hour video tape that explains, illustrates and plays the POWER NUMBERS SYSTEM™. There is no guesswork.

An 83-page Home Study Manual and Workbook explaining the POWER NUMBERS BLACKJACK™ system in step-by-step detail.

A felt blackjack layout, chips and 6 decks of casino cards for practicing at home.

Free phone consultation on the Blackjack Hotline whenever you have questions.

Well, the free phone consultation wasn’t in the package, but everything else was.

I immediately dived into the Home Study Manual (HSM) and noticed rather soon that the claim of “no guesswork” did not quite apply to it. There were several inconsistencies, ambiguities and optional playing choices which would necessarily call for “guesswork” when one of these situations arose at the table.

Later, on viewing the 2 hour video (for which the claim was made), I found further areas requiring interpretation by the student (and, therefore, “guesswork”), as well as inconsistencies with the HSM.

On Sunday the 17th, and again on Monday the 18th, Dr. Morton Jacobs (the creator of POWER NUMBERS BLACKJACK™) called me to see how I was faring in my pursuit of truth. I told him that my plan was to catalog my questions and concerns, and review them with him in Las Vegas the following Monday (the 25th). I wanted to play like a computer in the fashion he though would show off POWER NUMBERS BLACKJACK™ in its best light.

In particular, I explained that I would be reviewing POWER NUMBERS BLACKJACK™ in casino play against the claims made for it in the pre-sale literature, as I thought this was the appropriate standard since this was the promise made to the potential customer to encourage him to buy. Dr. Jacobs agreed with this thinking.

My plan was to layout the claims I felt were substantive, and then gain agreement on the machine-like casino play which should produce results which would validate these claims. Dr. Jacobs was in agreement with this approach, so all seemed to be “go” and I began to catalog claims and casino play questions where there still seemed to be “guesswork.”

Over the next week I did a lot of reading, watching and dealing, so that I would be well versed in the areas which required no “guesswork,” and had uncovered and recorded the areas where there was “guesswork.”

Note: I cannot reveal any of the concepts or details of POWER NUMBERS BLACKJACK™, as that is part of my agreement with the Leonard Benson Company. Only the actual results of casino play and my evaluation of how well it supports the pre-sale claims may be reported.

Sunday, September 24th. Full of my newly acquired knowledge (and newly acquired questions), I headed for Las Vegas. Five hours of determined driving got me there. I called Dr. Jacobs, but we couldn’t get together that evening. It was imperative that I be in full agreement with him on how to play and how to bet before I engaged in any actual casino play. So we planned to do this the next day.

My Power Numbers Blackjack Competency Test

Monday, September 25th. I was invited to Leonard’s apartment to meet with him and Dr. Jacobs. The discussion was frank on both sides. I told them that the ideal situation would be for Dr. Jacobs to play and for me to observe, and this was seen as a good thing all around. All my preparation to actually use POWER NUMBERS BLACKJACK™ was not to be used in casino play, but this preparation did give me the ability to critically monitor Dr. Jacobs in action. We soon developed a good rapport and became at ease.

Dr. Jacobs was to play for a high roller that night at the MGM, and I was invited to come along.

Casino Play with Power Numbers Blackjack

Monday, September 25th. At the MGM I met the high roller, a Midwesterner named Al. Apparently Dr. Jacobs had played for him twice the day before, also at the MGM, and had won both times. Al was, of course, evaluating Dr. Jacobs, and was impressed. The first session had been using $100 units, the second was $200. (These earlier sessions are not included in my review because I did not witness them.)

So now it was time to move up to $300, and that was the level for the play on this night. The results were spectacular. In one hour Dr. Jacobs had won $2050. (After winning $1950 at the $300 level, he had dropped back to $50 units, and won another $100, two units. We stopped for the night and were comped to a fine dinner before we left the hotel. I had been accepted.


Tuesday, September 26th. Now it was time to move up again, to the next level: $400 units. This meant a bank of $8000, which didn’t seem to bother Al. We were still working out on the MGM, and they didn’t seem to mind. One thing that impressed me about POWER NUMBERS BLACKJACK™ was the level of camouflage, the difficulty of detection that it provides. There was never any heat regardless of the betting spread and the amount we were ahead. I say “we” because, emotionally and acceptance-wise, I had become a member of the team trying to make the system work.

For a few hours we hovered around even, up a few units, down a few units, but mostly up. There was a time on a two-unit bet that the dealer had a two-card 19 and we had a two-card 18. If we had won that bet, we probably would have ended the session and quit for the night, up seven units ($2800). But we didn’t win and we didn’t quit. Things went downhill from there.

About a quarter to five the next morning, after seven hours in pursuit of our goal, we broke for breakfast. We were down fifteen units ($6000) and needed a time away from the emotional roller coaster to evaluate the situation. Over bacon and eggs, we considered what to do now.

It’s the same old story we have all been through at least once in a casino: we come to win some set amount with a betting and playing system and a pre-selected bankroll. We are sure of the soundness of our approach and know, rationally, that even if it isn’t winning at the moment, there is no basis to change. And we are prepared to lose the entire bankroll if the specific cards we must confront just don’t like us up to now, whatever “now” is. And we know we may lose all of this session’s bankroll occasionally. Not to worry. The system is sound and will overcome transient negative behavior in the long run.

Then this significant downsizing actually happens and all of our cool pre-session analysis and thought escape us. The plan no longer is inviolate and we look for changes to implement which will, by themselves, turn the trend around.

And on this early morning, hunkered down over coffee and eggs, the process began. I was mostly listening. After all, I was just an observer, and I didn’t want to taint my reporting by influencing the outcome. So the money man (Al) and the expert (Dr. Jacobs) made all the decisions. I only answered direct questions, and never said, “If I were doing it, then I would…”

Then we did something Kellyesque [Editor’s note: the author is referring to the Kelly principle for bankroll management, which professional gamblers use. To Kelly bet is essentially to bet a fraction of your total, non-renewable bankroll proportionate to your edge.] Since we had only one quarter of the original bankroll left, we dropped the unit size from $400 to $100, a move I though was only valid if this was not a renewable bankroll (which was not the case, since this was only a “session” bankroll). I did not voice this concern.

Another concern was that Dr. Jacobs was asking advice from us on how to modify his system. This hardly showed a strong conviction (at that moment) in the long-run correctness of the system. The emotions were overcoming clear thought.

So now we were back to a 20-unit bankroll, and in my mind this terminated the original session and began a new session. I mentally made a note to score it this way. Perhaps Leonard will not agree with this determination of scoring practices, but it made sense to me. This change in the system [ed. Note: reducing the unit due to loss] was not in accordance with what was advocated in the POWER NUMBERS BLACKJACK™ manual or video, which was the system I was attempting to evaluate. So I decided to separate the data and deal with “units,” not dollars.

Dr. Jacobs played with the new bet sizing. His play didn’t always seem to agree with my understanding of POWER NUMBERS BLACKJACK™, but no mention was made that we were no longer getting data that was useful to my review. (If Dr. Jacobs had said that, I would have gone home and gotten some sleep.) Two hours later, we had lost the remaining $2000. Not a good night for showing off POWER NUMBERS BLACKJACK™. At 8:15 in the morning it was all over.

Later, both Leonard and Dr. Jacobs said I shouldn’t count that last portion of play since it wasn’t POWER NUMBERS BLACKJACK™. It isn’t clear how they would have wanted it viewed if we had made a remarkable recovery with this new approach. I am including it in my data as Session #3. You can adjust my conclusions as you like, removing this session if you feel so disposed.


Wednesday, September 27th. Much of this day’s activities were a continuation of the play started the night before, and are chronicled above. Then we all went home to rest.

Later that evening I was called home to San Diego for personal reasons. I called Dr. Jacobs and told him I was leaving, but would be back in November and would like to continue the data taking at that time. I told him that the best of all possible worlds for me (and, I presumed, for an objective review of POWER NUMBERS BLACKJACK™) would be to have him play at low stakes just to provide data for my review. This way we could treat it as a laboratory experiment, and not get emotionally involved with the size (in dollars) of the wins and losses.

Dr. Jacobs thought this was a great idea, and offered to put me up in his guest bedroom when I was in town. Through the trials of the previous two nights, we had become good friends.

Another Trial of Leonard Benson's Power Numbers Blackjack

COMDEX in November(the world’s largest computer trade show) presented the next opportunity to take data on the effectiveness of POWER NUMBERS BLACKJACK™. Dr. Jacobs was not feeling well and could not commit to playing at any specific time, so I called Leonard and he got one of his students, Mike, to play while I watched.

Mike’s approach to stopping a session was different from that advocated in the POWER NUMBERS BLACKJACK™ manual and video, so a “session” meant something different. But he was playing with his own money, so I could not object. Anyway, the most important thing was whether the basic play according to POWER NUMBERS BLACKJACK™ will win significant money, measured in units per hour, so this data could be incorporated that way. And I needed data.

We played at the MGM again. Mike’s “unit” was $25, so the pressure from the amount of money was not great. Mike played for about an hour and a half, lost 6 ½ units, and declared the session over. We set the next session for the next day, and went home for the night. [An aside: later that night I played at a single-deck game at Circus-Circus, flat betting $3 and playing basic strategy. In about 100 hands, I won 27 ½ units ($82.50). Had I been playing $25 units, this would have been $687.50. And I didn’t even have a system!]

Wednesday, November 15th. Mike and I met at the Mirage for a short session (because his son was in town), and he played there for 25 minutes. He was ahead one unit ($25) when we quit.

Thursday, November 16th. Back at the Mirage with Mike. After 35 minutes, Mike declared the session over, 5.5 units ($137.50) ahead. This brought Mike back to even in my score book. We decided on another session that day.

Later we returned to the Mirage and had phenomenal cards, winning 10 units ($250) in just 15 minutes. Now Mike was helping the recovery from the disaster I had witnessed with Dr. Jacobs and Al.

Friday, November 17th. Mike and I met under the balloon at the MGM in the morning and things went as badly as they had gone well in the previous session. In 20 minutes he lost 6 units and called it a session, but not a day.

As it turned out, it was a day for Mike, at least where I was concerned. My pages to him, which had been promptly returned before, went unanswered that afternoon. Since my time was running out, I called Leonard, and then I called Dr. Jacobs, who was to coach another player that evening and thought that acceptable data could be gathered at the same time, and invited me to come along.

The player, it turned out, was an entrepreneur from Minneapolis named Steve Renner. Steve’s interest in POWER NUMBERS BLACKJACK™ was in marketing it via multi-level marketing (MLM) though WIN (Winners; International Network, 612-349-5221), a company he owned. He wanted to master POWER NUMBERS BLACKJACK™ so he could teach it to his MLM recruits.

The plan was for Dr. Jacobs to watch as Steve played, advising and correcting him in both betting and playing. This was their second such session. They said they lost 10 units the first time, but those results are not included in this evaluation because I have limited myself to what I have actually seen.

Dr. Jacobs chose Bally’s for our session. Play was to be with units of $10. After about 45 minutes and with Steve down 7 units, Dr. Jacobs had to take his daughter to some kind of lessons. He (Jacobs) knew I knew how to play POWER NUMBERS BLACKJACK™, and he suggested I take over coaching Steve while he was gone. (NOTE: He was correct that I knew both how to bet and how to play POWER NUMBERS BLACKJACK™, but nonetheless, I was surprised he let me direct the action while taking data.)

Steve continued playing, with me keeping him strictly on course in both betting and play. The cards continued to show POWER NUMBERS BLACKJACK™ no mercy, and in another 30 minutes Steve had lost an additional 9 units. At this point he thought he should turn the task of digging out over to Dr. Jacobs when he returned.

It was about 9:00 pm when it became clear that Dr. Jacobs would not be back until after he had brought his daughter home (the plan had been for him to return during the four hours she was to be gone), and it would be about midnight when he would get there. Since I had to drive back to San Diego before morning, I called it a session and left. Down 16 units.

Third Trial of Power Numbers Blackjack

I drove all morning New Year’s Day to get back to Vegas and continue the data taking. Leonard knew this would be my last chance before submitting my results for the March issue of Blackjack Forum, and he accepted the task of finding someone to play the POWER NUMBERS BLACKJACK™ system for my observation.

This time it was Chuck, a local student of POWER NUMBERS BLACKJACK™ who said he had seldom lost in more than 100 hours of play up to that point. His unit size was $10. First we played at Bourbon Street and quickly won six units. Then we took on the Maxim, dropping 2 units and calling it a session. Finally we played at the Poker Palace in North Vegas, losing 3.5 units and stopping for the night. Up 0.5 units for the day.

Tuesday, January 2nd. The first stop was back to Bourbon Street and two more quick units, then to the MGM and a 5-unit win, and then to the Tropicana for six more. Ahead 11 units, we declared this a session.

The next session started at the Maxim with a 1-unit win, continued to Bourbon Street for another 2 units, then finished at Bally’s with another 5.5 units. Session over +8.5 units.

The final session for the day combined play at Bally’s and the MGM. +4.5 units at Bally’s, -9 units at the MGM. Net for the session: -4.5 units.

Wednesday, January 3rd. The first session included playing at the Maxim (broke even), Bally’s (-1 unit), and the MGM (+5.5 units). Net for session: +4.5 units.

The second session was conducted at the Tropicana. Results: -5 units.

The third session was downtown at the Golden Nugget. Results: -3 units. Net for the day: -3.5 units.

Thursday, January 4th. Our last day of testing started off with a -4 unit session at the Maxim, followed by a +9 session, split between the Maxim and Barbary Coast. Two other short sessions at Barbary Coast netted +2.5 units and +2 units. Chuck’s contribution to the study of POWER NUMBERS BLACKJACK was a healthy +21.5 units.

This ended my data taking, as I needed to get back to San Diego. We hadn’t quite gotten 25 sessions, but 22 would have to do.

Evaluation of Leonard Benson's Power Numbers Blackjack

My evaluation of the effectiveness of POWER NUMBERS BLACKJACK™, based only on mathematical considerations, is that the player risks money at a disadvantage of between 2.0% and 2.5%. [Editor's note: John Leib was an aerospace engineer for Lockheed with a Ph.D in math. I met him after the great gambling analyst, Allan Wilson, recommended him as a brilliant math mind.]

Since I am prohibited from divulging the specifics of POWER NUMBERS BLACKJACK™, I am not free to explain where this range comes from, but suffice it to say that I can back up this estimate by analysis, regardless of the actual data collected.

I analyzed the data, if sloppily, well enough to draw a conclusion of how well it supports the 2.0%-2.5% estimate of player disadvantage. It should be noted that, sloppiness and all, we don’t need to tie this down to the nearest 0.1% to be confident of the validity of the conclusions.

Since there was a loss of 18 units during Session #3 (which is disputed as being the result of improper application of POWER NUMBERS BLACKJACK™, I decided to analyze the data in two ways (you may choose the analysis that appeals to you):

1. Using all the data collected, and

2. Using all data except Session #3.

The argument for (1.) is that:

  1. No announcement was made before hand that this data was inappropriate for my analysis. It was not my job to validate the betting/play as being in conformance with POWER NUMBERS BLACKJACK™. And besides, we had Dr. Jacobs, the inventor of POWER NUMBERS BLACKJACK™, betting the money and playing the hands.
  2. If POWER NUMBERS BLACKJACK™ works, there would be no rationale for departing from it when things aren’t going well.
  3. I was asked to play a hand (at low stakes and with basic strategy) most of the time during Session #3 so we would have a better number of hands from which to know how to bet. This was in line with the precepts of POWER NUMBERS BLACKJACK™, so it looked like we were trying to follow, at least to some extent, POWER NUMBERS BLACKJACK™.
  4. It worried me that, perhaps, this session would not have been protested if it had been highly successful.

Analysis of the Power Numbers Blackjack Data



Win Rate: -0.67 Units/Hr.
Action: 580 Units
Return on Investment (ROI): -2.6%
ROI Sigma: 4.2%

The return on investment (ROI) of -2.6% is comfortably close to the -2.0% to -2.5% range predicted by rough analytical methods for POWER NUMBERS BLACKJACK™.

It should be noted that a change in the data of only 15 units (0.6 sigma) would have resulted in no loss at all.

Obviously, this limited data cannot adequately pin these numbers down from an experimental viewpoint. The only way to adequately approximate the true ROI figure with great precision is to perform an extensive simulation.

Data Analysis Excluding #3

Win Rate: +0.15 Units/Hr.
Action: 497 Units
Action Rate: 24.5 Units/Hr
ROI: +0.6%
ROI Sigma: 4.5%

The data excluding Session #3 showed a net win of 3 units. If one is inclined to throw out this session, then it is impressive that POWER NUMBERS BLACKJACK™ showed a profit; an impression which is limited by the fact that if 13 units (also 0.6 sigma) less were won, the data would match the -2.0% of the predicted range of -2.0% to -2.5%.

The primary conclusion to be made is whether or not POWER NUMBERS BLACKJACK™ is a winning system. From a mathematical analysis point of view, disregarding the actual collected data, the answer is “No.” This conclusion was tested by taking data, and including Session #3 shows the shows the experience was a losing one. Ignoring Session #3 results in a very modest win, a win with little statistical support because of the limited amount of data.

It is my opinion that POWER NUMBERS BLACKJACK™ is less desirable by 1.5% to 2.0% than is basic strategy, even though the situations it finds are better than average. The departures from basic strategy are quite costly. But, even with correct (basic) strategy, the player will be investing money at about -0.5%. In either case, POWER NUMBERS BLACKJACK™ is doomed to long term failure. As I say, this is my opinion.

Power Numbers Blackjack: Results Versus Promises

The time has come to review the promises made for POWER NUMBERS BLACKJACK™, and to compare them to actual casino experience and analytical predictions.

“$1,000 and more Profit Per Day Playing POWER NUMBERS BLACKJACK.”

This was the grabber in the ad, the thing that makes you read the rest of the ad and, perhaps, call the 800 number. But what does it mean? Does this mean that, given enough days, you can average $1,000 per day, or will you, on some good day, net the promised $1,000? The use of the expression, “Profit Per Day”, implies an average; otherwise it should have read, “Profit A Day,” and be qualified with “sometimes.”

Using the (perhaps optimistic) results excluding Session #3 of 0.6% ROI, $1,000 would require “investment” of about $160,000 in the “1 to 3” hours required for a session, or about $50,000 an hour. With an action rate of 25 units per hour, this would require the unit to be $2,000.

“Amazing new discovery gives you a mathematical advantage Without Counting!”

Also from the ad, and the real grabber for one who has some analytical skills at the game of blackjack, particularly when coupled with the expanded claim, “Consistently win 10 units in 1 to 3 hours. Even win against so called ‘bad playing conditions, including bad players, 6 to 8 decks, crowded tables and clumps’.”

The “Without Counting!” claim did not turn out to be as anticipated. While the counting system used is not one recognized by the blackjack press, it is, nonetheless, a form of card counting.

Now, I have always believed that the ultimate test of a gambling hypothesis is experiment (simulation or actual casino play) to compare results to prediction. A mathematical advantage will then show up as a net win if sufficient play is involved. Unfortunately, enough data was not collected to be sure, but averaging a 10 unit win in 1 to 3 hours seems out of reach, at least by rational reasoning.

“It can be learned in 5 to 10 hours.”

Again, from the ad. This seems to be an overly optimistic estimate. The 2 hour video recommends that you watch it at least twice (4 hours plus rewind time).

The HSM takes longer than that, perhaps 4 hours per reading if you follow through the examples, and you should expect to do this at least twice (8 hours).

And then there is the recommendation that you have enough home practice to master the system before you go to actual casino play. My estimate for me is at least another 8 hours. My absolute minimum estimate is, then 20 hours. Probably much more for most players.

My estimate seems to be in line with this quote from the forward in the HSM, signed by Leonard Benson:

“…With a couple of weeks of diligent study and practice you’ll be able to be a consistent winner at blackjack, enabling you to make money the rest of your life.”

“Everyone is winning!”

From promotional material signed by Leonard Benson. This was brought into question by Leonard, himself, in our first telephone conversation when he said, “… We’ve had a couple people that the first time they started they got discouraged ‘cause they lost three times in a row.”

If the probability of winning any given session is .9 (“9 out of 10”, see the next claim), the chance of starting off with three losses is .001, one in a thousand. “A couple of people” experiencing this would suggest a population in the neighborhood of 2,000. In any event, the “Everybody is winning!” claim seems to be factually flawed.

“You’ll win 9 out of 10 sessions.”

From promotional material signed by Leonard Benson. It should be noted here that, given the amount you are prepared to lose and the amount you wish to win in a session of POWER NUMBERS BLACKJACK™, and if you were betting on tosses of a “fair” coin, then you would expect to win 2/3 of the time. This (2/3), then, would seem to be an optimistic number to use.

The argument might be made that many times you will “lock up” a small win and are prepared to risk your entire bankroll to do it. In a fair game, you would need to be prepared to lose nine times your “small” win to enjoy “9 out of 10” success.

“I have restructured the game of blackjack from the laws of probability to those of certainty. Structuring my betting on percentages, instead of luck or random chance betting, bringing it into the realm of reversing the edge of the House to the player.”

From “Comments from Dr. Jacobs.” This claim does not seem to be supported by the facts of POWER NUMBERS BLACKJACK™. While POWER NUMBERS BLACKJACK™ does find situations with better-than-average potential, it does not improve enough above the off-the-top expectation to overcome the disadvantage of shoe games. Making it worse, POWER NUMBERS BLACKJACK™ calls for disastrous departures from basic strategy, compensating (negatively) much more than this improvement gives.

“You will not lose your bankroll if you play POWER NUMBERS BLACKJACK.”

From “Typical questions and answers about Dr. Morton Jacobs and POWER NUMBERS BLACKJACK™.” This is not the sure thing suggested by this statement.

“Q: Will everyone who uses the POWER NUMBERS BLACKJACK system make money?

“A: Yes. You just have to follow the rules.”


From “Typical questions and answers about Dr. Morton Jacobs and POWER NUMBERS BLACKJACK™. This does not seem to be correct.

“Q: Will I have a mathematical edge over the casinos?

“A: Yes. POWER NUMBERS BLACKJACK players have an advantage ranging from 5% to an incredible 20% and more! It’s absolutely amazing. You’ll be winning 10 units for every 50 to 150 units in action.”


From “Typical questions and answers about Dr. Morton Jacobs and POWER NUMBERS BLACKJACK™.” Surely, this is the most “amazing” claim of all. No one can take seriously a claim of an advantage of 20% “and more!” (It is, after all, “incredible.”) 5% might be credible, except that expert card counters would not seriously claim near that level of success.

My rough analysis suggests a negative player’s edge of at least 2.0%.

Observations of Leonard Benson and Dr. Morton Jacobs

There is no doubt in my mind that Leonard Benson and Dr. Morton Jacobs believe POWER NUMBERS BLACKJACK™ is everything they claim. There was no defensiveness. There was no attempt to keep me from seeing everything that was going on at the table, and keeping score for myself (which I did, and my score agreed with Dr. Jacobs’ and the other players’ scores). This was not the behavior pattern of people who are running a scam…

Since the last four days of data showed a strong positive surge for POWER NUMBERS BLACKJACK™, it might be argued that only then was its true potential being revealed. But one must remember that, in cases like this, the data could have come in any order. (This is also true for the individual hands.) So “trends” must include all the data. The last four days could have as easily been the first four days. Would different conclusions then be appropriate? ♠

For information on the winning blackjack systems that professional gamblers use, including winning without card counting, see Winning Without Counting by Stanford Wong and The Big Book of Blackjack by Arnold Snyder.

Return to the Blackjack Forum Professonal Gambling Library

Return to Blackjack Forum Online Home

 
© 2004-2005 Blackjack Forum Online, All Rights Reserved
 
 
 
  Leonard Benson's Power Numbers Blackjack
Mathematician and blackjack player John Leib performs a mathematical analysis of Leonard Benson's Power Numbers Blackjack system. He also reports on 22 hours' experience at the tables playing the Power Numbers Blackjack system with Leonard Benson and the system's inventor, Dr. Morton Jacobs. Included in this report is information on Leonard Benson's training materials and practices for the Power Numbers Blackjack System.