Back in 1967 I was talking calculus at a small Junior College in Mississippi (no names to protect the guilty). I was always very good in math, any my calculus teacher was a rare type of mathematician. The first day of our calc class, he walked into class and asked the following question:
"I am going to stand 4 feet from the wall. I am going to step 1/2 of the way toward the wall, and repeat this over and over. Question: Will I ever get to the wall?"
He went down the class roll, name by name. When he got to me, and asked "what is your answer" I responded "yes" which was different from everyone in front of me that had said "no". He looked at me carefully, a few giggled, and he went through the rest of the roll. Near the end of the roll was a high-school classmate of mine and when he was asked, he responded "yes" too. He looked carefully, then continued and finished up the roll. Two yes, about 25 no. He started at the back of the roll going forward and asked each student "why did you choose that answer" and the usual reply was "if you step 1/2 way there each time, you will never get there, there will always be some distance left to step since at any step you halve the previous distance..." When he got to my classmate, he asked and he replied "because The reason for the above is to explain that we sort of "connected" and he took an interest in me from that point forward.
A couple of things about this teacher nearly blew my mind over the first few weeks I had him in class. First day, he said "ok, everyone turn to page 30 in the book, and let's look at what we are going to be doing in the first half of this course, which is differential calculus." He was reading along word-for-word, when someone beside punched me and said "look". I looked up, and the teacher was sitting in his chair, feet propped up on his desk, eyes closed, quoting the book word for word, including equations, explanations for simple derivatives, etc. He also told us to "turn to page 280 and look at these special cases" and he then read from there, without the book. Turns out he had a photographic memory that was beyond belief.
The other thing that caught my attention was that as we got into integral calculas the next semester, those involve some hairy math to get numeric solutions after the integration is complete. You end up with lots of fractions, sines, cosines, things raised to powers, and so forth. We found that getting the integration part right was easier than solving all the complicated fractional expressions. And in every case, our teacher came up with the answers very quickly. I originally assumed that he had just memorized the answers which were in the back of the book. But one day I had a problem from physics and I asked him about it. He showed me how to integrate the thing to get the answer, and when I started solving the actual fractions to get a number, he said "2 pi over e" which is ... (you can divide 3.141592 * 2 by 2.71828 if you want the answer) but he did it in his head, as well as find some difficult common denominators, etc. All in his head with no paper. After I asked "where did that come from" he said "I have always been able to do basic arithmetic operations in my head very quickly."
Now fast-forward a few months, after dozens of classes, dozens of oddball problems he cooked up especially for me, etc. He says " He said sit down and let me tell you a few things about me. The next bit is sort of a quote, so take it as words coming from him for a bit:
"What would you think if I told you I only teach for a hobby?"
I said "wouldn't surprise me, you seem to enjoy doing this tremendously and spend a lot of time working with students."
"No. You didn't understand. I don't teach for the money at all, I don't need the money. I have found a way to make an incredibly good living outside of my teaching."
I asked "what does this have to do with blackjack?"
"I learned quite a few years ago how to beat the game of blackjack and make a lot of money playing in the casinos."
(he specialized in probability by the way) He went on
"First, using probability theory, it is possible to accurately predict the best strategy for the different combinations of cards you can get vs the dealer. I have done this and have a table that I have memorized (I snickered at that and said I'm sure memorizing that wasn't much of a challenge). Playing with this chart reduces the house advantage to under 1%."
At this point I interrupted "OK. If the house still has a 1% advantage, how on earth can you beat that, if the best you can do with your chart is to narrow the edge to 1%?"
"Hold on and listen to the rest of this.
"I noticed that if you remove a certain card from the deck, you improve the player's odds. For example, if I remove a 5, that hurts the dealer more than removing any other card. I have calculated this for every card. The way I win is to play the game, and after the deck is shuffled, each time a card is dealt, I adjust the "advantage" by what removing that one card does. removing some cards is bad for the dealer, removing some cards is bad for me."
At this point I interrupted again and asked "what do these numbers look like and how can you do that much adding and subtracting while the game is playing?"
He continued
"By now you should know that I can add 3 digit numbers instantly. You've seen me do this in class. But most people can't do this and I had not imagined that anyone would come across this system I am using because it is too difficult for most people to do.
At this point he showed me his table that had 3 digit numbers that indicated how much removing each individual card (from a deck of 52 cards) hurt or helped the player. Some were +, some were -, and while I don't remember the numbers almost 40 years later, I am sure they match the numbers we see for this today in several of the counting books that are around. The thing that was unique about his "counting" system was that it used the actual probabilities, not 1/0/-1 or even "Wong Halves" either of which is trivial compared to what he was doing. we took to playing blackjack in his office, and sure enough, he could keep up with that ugly math without any apparent difficulty, and at any point could tell me "the deck favors the dealer by XX.XX or it favors the player by YY.YY."
I asked "how much have you won doing this?"
"I have no idea. I own my house. I own my car. I have a nice retirement fund saved up. I go to Vegas as often as I can 'to visit my sister' (that was apparently what he told everyone at the JC). That's why I said I was teaching for a hobby. I make more in one night at the BJ tables than I make in 3 months here."
Now to the meat. I asked "OK, what does this have to do with me, with this book, and with your down mood?"
"A friend of mine that is a publisher sent me a copy of this book. When I first saw it, I thought 'probably won't work' and so forth. But after reading it, what I found is that this guy Thorp has come up with a simpler version of what I am doing that is not nearly as accurate, but unfortunately, it appears to be accurate enough"
"OK" I said, "so it will work, who cares? You can continue to do what you are doing, so what if others use something that is inferior to your system, and make a few bucks?"
He replied
"You don't see the problem. The casinos are really big money operations. You would not believe how much money they make in a week out there. They see me as a very lucky high-roller, they watch me, they study me, they ask me 'how do you consistently win?' and so forth. But one person is just an enigma to them. Now there will be an army of "enigmas" but the casinos will have access to this book as well, and something bad is going to happen. Either blackjack will go away, and that is the only game in a casino that can be beaten, or the rules will be changed in some way to stop what I am doing, or I won't be allowed to play or whatever. The casinos have overlooked me (and probably others) but now that there is a book out, they are not going to sit idly by while droves of system players come in and take their money home."
So far as I know, he is probably still happily counting cards and winning lots of money, although he is probably long-dead as he was beyond 50 when he was teaching me, putting him at 80+ now. I've tried to look him up, but never had any luck at all.
END OF STORY
I thought the idea was interesting. His counting system was impossible for me, and believe me I tried it. But no way I was going to add/subtract oddball 3 digit numbers with a decimal point and remember his "basic strategy" (he didn't call it that then, but the ideas he mentioned match pretty well the way we play BS today although I can't say he had all the plays correct by today's standards as I just don't remember any details).
He did have a basic strategy chart based on his calculations, and he also modified this strategy based on the "advantage" he had or the house had, again very similar to what we do today.
I thought his ability was absolutely amazing. He told no one what he was doing. I suppose this would be a 10-level counting system as I recall that each card had a completely different "value". He also said "I can actually count the 10 types of cards perfectly" and he demonstrated this by doing what we would call a "deck count-down" where I pulled a few cards out. He then told me _exactly_ which cards I was holding, except that he did lump 10-J-K-Q into one count. He said "I can't count 13 types, I seem to lose a few here and there. But when I have only 10 counts I can keep up easily." But his next comment was "but I can't really use that information very well, which is why I collapsed this into one "advantage/disadvantage" value that when positive says I have the advantage and when negative says the house has the advantage."
He then explained his betting strategy which is no surprise at all. I don't recall any discussion about risk of ruin, but he understood variance, and small/big bets and the like obviously. He said that he was betting at a minimum of $100, and the maximum was whatever he could get away with, as apparently max bets were more restricted back in the middle 60's when this was going on...
So there you have it. I left the JC shortly after that and went on to a university. The year I finished at the JC, he retired and moved "out west to be close to his sister" I was told although I never encountered him again, as I went on to a 4-year university, graduated, and moved on myself.
I would not be surprised if he was possibly the best card counter there ever was, but then I suspect that his very unique ability was not completely unique. I'd bet there were a very few others that could pull that off.
But wouldn't it be nice to have a counting system with a BC of 100%, and a PE that is as good as it is possible to be since the remaining deck can't actually be seen, with regards to order.
This idea of "card counting" stayed dormant until about 10 years ago. My wife wanted to take an occasional trip to the MS Gulf coast, and I learned basic strategy and played BJ and did about as expected. But as she got more interested in playing, I decided that I was going to see what could be done with the old counting idea. Of course I didn't know about all that had happened since 1966 or so, and was amazed at all the different counting systems. I decided to go with Thorp/Wong and give HiLo a chance as it looked managable and seemed to work.
Anyone else know of someone or something similar?
I believe I still have my old calc book where he wrote some of his numbers down, particularly the numbers about "advantage for removing a card" numbers that he actually counted. I'm going to try to find it and compare the numbers to what has been published more recently on the same topic, just to see how good he really was. :)
