Two blocks of diamonds and a calculator
My studies in Freiburg consisted of pursuing my passions. And for the attentive reader, my passions have already shone through here and there: Playing, playing, playing. Not only that there was playing day and night, and that is absolutely no exaggeration. A few hours a day were reluctantly sacrificed to sleep. Otherwise, there was “rolling”. And the cafés and pubs in Freiburg are not open all the time, so the game was shifted to private rooms at night. At the same time, C. and I initially lived in a shared house, a student digs, so to speak, in Lehener Strasse 29 (always this 29, somehow it haunts me; I will dedicate an extra chapter to this part of my superstition).
The house was inhabited by students through and through. To take a shower, you not only had to walk through the hallway, which was unheated, at least in winter, you also had to sacrifice a shower token to heat the water. The shower token was, of course, chargeable. C. liked to describe the dimensions of his room as “9 cubic metres”. 331 or so, 1 was the height. My own domicile on the floor below was really exclusive: 12 square metres to be sure, and if you got enough oil, you could even heat it. However, I never really acquired the necessary technology. What was the point? After all, I now lived in the south. It rarely got below 6 degrees in the room. And that too plus!
By the way, there was even something as exclusive as a fridge on the upper floor! And if you registered in good time, you were even allocated a compartment! Well, I didn’t live there long enough to get one. But I did: when someone was away, I could use his locker temporarily. And that wasn’t enough luxury: there was even a landline in the house! Of course, it was seldom free and when it was, you had to meticulously record the units you had phoned and pay the sum at the end of the month, and you also had to put up with up to 10 people listening in, because this device was also in the hallway. As you can see, it was a wonderful time all round.
So it wasn’t just day and night playing, I used the really sparse free time I had as a result in two ways: Calculating the probabilities for all possible dice combinations or evaluating the slips of paper submitted to me by the other crazy people. A real study of maths “al gusto”. Because: We had founded a real club, so to speak. Unofficially, but still. And I was the evaluation centre. You could achieve standards in the Yamb. There were title norms like in chess. A score was calculated for each player, a bit like the Elo system. And the champions received their honours in the form of titles. It was all down to my (inadequate) organisational talent. But still: for the duration of this daily madness, I even created a certain order.
So now I already had several filled caroblocks. At least one that contained all the probabilities for possible throwing combinations and at least one in which I kept the data of the other participants. Who has how many standards? Who has what current rating? Who has just become FIDE Master or International Master in which discipline? And so on. And there were new games to evaluate every day. In short, there was really no time at all for official studies at university. Right and important as a motto in life: I just have to set priorities.
Yamb, by the way, is a game similar to Kniffel. You roll 5 dice. There is an up column and a down column, in which you were only allowed to enter at the corresponding place. There was also a free column and an announcement column. In the free column you could enter anywhere and whenever you wanted, in the announcement column you had to announce after the first throw that you would enter there and at that place. The art of the game was, of course, to decide in time to strike at the up and down columns so that you could get over the “difficult” throws. To do this, of course, you always had to weigh up the probabilities well, whether you would now rather go for straight or full house with this throw, etc. In principle, it was quite a demanding game and would have been very interesting as it was, even as a money game, if it had become more widespread. Above all, we still introduced the much more demanding variant, the “three-settler”, where the game could confidently be called a “strategy game”. You had three slips of paper at the same time in which you could/must place your throws. You always had one option. The trick was to find the best of the possibilities.
By the way, my absolutely faithful companion was my head, no, no, just kidding, it was my calculator. And it was really my pride and joy at the time. There were hardly any other calculators, not yet in 1983. Mainframes yes, but who had a PC anyway? And what did it do? My HP 41 CV calculator, a Hewlett Packard, was the first really freely programmable calculator. And I used it to the full. You had to be careful with the memory allocation, but there were 4 slots at the back for memory expansion. And I used the space economically. The important functions were placed on freely definable keys and so on. It was a really advanced device for its time. And what’s more: I had really familiarised myself with it.
2) Black Jack
Even the best of times comes to an end. But there is always something new. That was also the case with me. I’ve already told you about the backgammon I learned. But a friend and team mate suddenly sent me a book about Black Jack.
But before I could start studying this game, a few things had to be sorted out privately: Mr Elbin, my landlord in Lehener Strasse, had all his tenants on his back. Including C. and me (by the way, the rent for my suite was 120 DM per month; a more than reasonable, almost cheap price, with so much luxury, I think?!). But Mr Elbin was probably surprised by his own magnanimity and planned to increase the rent to DM 140. A quarrel ensued, because the handsome gentleman was not prepared to make any concessions. He almost threatened me in my room. I took flight.
A little surprise when I returned home: my room had been completely cleared out. All my belongings were in front of the door in the hallway. A mortise lock in the door denied me access to my room! But for one day I was able to testify to the advantages of German bureaucracy: I immediately went to the court, which was still open late on Friday afternoon for special cases. I immediately got a temporary injunction confirming that I was entitled to enter my room. The locksmith who was then called immediately removed the mortise lock. I was able to re-enter my room and spend the night there after my things had been put away again in a makeshift manner. And Mr Elbin was later ordered to pay me a hefty fine and a certain amount of damages.
Nevertheless, it was impossible to maintain this “tenancy”. I went in search of a flat. And soon I found one. A really nice room, basement, situated directly on the railway tracks for long-distance traffic. But I liked it there and I really liked it in Wiesenstrasse. The visitors always asked me if the noise of the long-distance traffic wasn’t annoying. But it wasn’t, there was something pleasant and calming about it. In my memory almost my nicest domicile ever. Price: 135 DM, but it was also much more spacious than the previous room, and it was also heated, I moved in on 1 February.
And apart from the long-distance traffic, I had absolute peace and quiet there. The Wiesenstrasse was a bit out of the way, C. was also a sufficient distance away, the daily Yamboss games were on break. I took up Edward Thorpe’s book on Black Jack. Mr Thorpe had found a winning strategy. At least he was the first to write it down.
This winning strategy was based on counting the cards dealt and waiting for favourable situations. In addition, there was the so-called “basic strategy”. The basic strategy had to be followed first anyway. And if you did that, then at least you had reduced the disadvantage to a minimum.
I opened the book rather randomly somewhere. You could also call it “I read it diagonally”. Then I had a recognisable fable for combinatorics and probability theory. Paulilein was, as always, rebellious. And instead of blindly following the Black Jack Pope, I began to mathematically check any combination of cards with numbers. And I discovered that the results did not match. That irritated me a little. I checked my calculation again. But I had not made a mistake.
I had accidentally come across the problem of whether one should double with 11 against an ace. Mr Thorpe was convinced that it would be right. My conclusion was that one should not double. It seemed totally absurd to me. At best, you could insure the bet and then double, including the insurance (which would be allowed even here), with the consideration: either the bank gets a 10 or you get it (both do no harm; insurance pays back everything for the bank in the case of a 10). But that was not right either.
The solution, which I only came across a little later, was that in the USA in the 1960s, the rules were different. The banker placed the second card next to the first, but the second card was face down. After all players had made their decision whether to insure or not, the dealer looked under the second card. The players only saw the card if it was a 10. If it was not, the game continued as normal. Now you didn’t know what the banker had when it was your turn, but you knew what she didn’t have. Of course, under these circumstances, doubling was more than correct. But for me there was only one consequence: if there was a mistake here (the cause of which I did not know at the time), then there might be more. So simple conclusion: I calculate everything on my own.
I put on a few more caroblocks. My calculator was never “cold” anyway. And in this combination – Wiesenstrasse – very cosy room – Karoblocks – pocket calculator – I set to work. I simply calculated all possible constellations one by one.
This may sound unbelievable or almost like a joke. But it is not a bit less true because of that. That was my contribution to the topic of “applied mathematics”. The check blocks filled up little by little. Frankly, it took me several months, about seven, to really get through it all.
Regrettably, however, this “work” did not remain with me and was lost during one of the quite numerous later moves. Today I regret this, of course, and if I had put a photo in this book, it would have been the one with these blocks of squares, bulging with numbers.
By the way, I take Mr. Thorpe’s word for it: many of his figures are the result of simulations, which is really an absolutely reliable means of obtaining such figures. Later, at university, I also programmed Black Jack and simulated all the numbers. Many correlations are also highly complex, and yet the result in decimal places is absolutely irrelevant. Moreover, the book was written in the 1960s. And at that time in America, the game was played with only one deck of 52 cards (in my time in Baden-Baden, the game was played with 5 decks, later often with 6; today, with mixing machines, the number of decks is again irrelevant). That also changed some of the odds. In addition, many rules were simply different (you can read about these rule variations in the chapter “Black Jack Rules”).
My version of the “exact calculation” became more and more sophisticated. I then added up all the possible combinations to determine exactly the mathematical disadvantage of the player. The special thing about this: I had included the individual rule variations so that I got an answer as to how valuable a rule was from the player’s point of view, provided it was offered. For example, this resulted in a disadvantage of 1.3% for the rules in the Berlin casino in the Europacenter at the time. In a way, the rules were almost maximally unfavourable. In Hamburg, on the other hand, the disadvantage was only 0.9%.
If I remember correctly, it was because you were allowed to continue splitting after the split and, if you had a suitable card, you were also allowed to double up. This is also very important when splitting the aces. There is nothing more frustrating than splitting two aces, actually the best possible split, you then have two times 11, +10 would result in a 21 (that didn’t count, anywhere, as Black Jack), almost the maximum. And then one more time you get what feels like the best card, another ace, and you have a 2 or 12 or even 0, because that’s all it’s worth anyway, and you’re not allowed to split any further!
An example of redoubling: You have two 8s, which are worthless as such, because: who needs 16? But the cards individually are not so bad, if you get a 10 in addition, you still have 18. But if you then get a 2 or 3, you could theoretically double. But that wasn’t the case in Berlin, for example, but it was in Hamburg.
By far the best rules I experienced were in Monte Carlo. There, in addition to all the other privileges, which were similar to those in Hamburg, but in Hamburg you were not allowed to insure, the “soft double” or the “double any two cards” was allowed. In total, this resulted in the dream value of a 0.7% disadvantage for Monte Carlo.
And the whole thing was calculated for me by my faithful friend, the HP 41 CV, my almost consistently faithful friend, mathematics, and my absolutely unreliable and not even friend, my head.
Would I be where I am today if I hadn’t really “studied” so diligently back then? If you want to hear one of the kind quotes from my wife: “If I didn’t have you ———- I’d have someone else.” You understand what I mean?