The organiser wins -> the player loses?
That the organiser of each game wins in the long run is in principle self-evident. Or rather, there were certainly those who lost. The emphasis here is on “gave”. These disappear again. But the conclusion that the player always loses is at least not trivial, rather incorrect. The sum of the players loses. But each individual has the opportunity to use his or her skills and possibly switch to the winning side. I will try to explain how this works in the individual games in the following sections.
But at least one thing is certain: you can play every game “well”. Whether in the long run with a profit advantage that is also enough to feed oneself is another question.
First of all, roulette: How can you play it well? Yes, you can. If you really haven’t played it yet, I’ll explain a rule that beginners often don’t know and if they do, they (may) even think it’s meaningless: If you play simple chances (that’s the chances red/black, even/odd and top half/bottom half, that just sounds better in French: Rouge/Noir, Pair/Impair, Manque/Passe), then you win when your chance comes and lose when yours doesn’t come. You also win exactly the amount of your bet. 10 euros bet on red, red comes, 10 euros win, black comes, 10 euros loss.
But if zero comes, the little green square, the bank number, the zero, then you lose. No, you are right. That’s the special rule for the easy chances. You don’t lose, not completely. Your bet is blocked until the next roll of the dice. Then, when the chance you had bet on comes, it becomes free again. You even have the option of getting half your bet back after the zero comes. So, loosely translated, this means that you lose only half of your bet on zero (all other bets lose completely when zero comes). This makes the following difference, using a practical example: If you bet 37 times and each number comes exactly once (I would like to present you the probability for this event: it is 1,304 * E-15, i.e. approx. 1/1 quadrillion), mathematicians like to refer to the laws of large numbers, where this is supposed to be the case in the very long term. (As we have seen above, however, he may be starting from false premises. Are all numbers really equally probable? But that doesn’t belong here now). All right, now you have bet 37 times, each number came, by a giant coincidence once, then you have won 18 times your stake, which was 10 euros, the payout is equal money, so odds 2. 0, makes 180 euros profit, but 18 times you have unfortunately lost, then the 180 are unfortunately already gone, and the one time, at Zero, you have also lost half (you have wisely taken half down after the appearance of Zero, used your option), makes a total of -5 euros (and the whole thing for 35 minutes of fun, that is probably called expensive fun? By the way, the calculation looks quite different for lucky people…). So you have made 370 euros in turnover and have lost 5 euros on this turnover. Your loss is therefore 5/370 = 1.35 %.
The person who bet on a number at the same time won only once, but got the payout ratio of 36.0, i.e. 350 euros profit. But he lost the other 36 games, which makes a loss of 360 euros. Then we calculate the sum, 350-360, and that equals -10. So the player lost 10 euros on a turnover of 370 euros, which makes a loss of 10/370 = 2.7%. So you played twice as well as he did, because you only lost half as much. In the long run, it should look like this, always assuming that all numbers come with the same probability (and in the end with the same frequency). Then, in the long run, the above result would come out.
I have already described the second example, the recording of permanents and the search for boiler errors. But I wouldn’t try to do that, because then this kettle, of all things, where you have taken notes for half a year, will be replaced?
If you want another example of good roulette playing, here you go: There is supposedly a man who makes a very good living from roulette. He does it like this: he watches the ball as it spins in the cauldron. And he has developed amazing skill in predicting in which part of the kettle the ball will land. You don’t believe it? To understand, you should realise that only a tiny shift in the probabilities in his favour is enough to give him an advantage. So the calculation would be this: The normal disadvantage is 1.35% on easy chances and 2.7% on other chances. He can only play the other chances because the simple chances are alternated in the pot. So he has to make up for the 2.7% disadvantage by observation. But to make this profitable, it is enough for him to shift the probability of occurrence for one of his numbers (he must then play large-scale, but this is possible, one can play kettle areas, the casinos offer this; they are called small series, large series and Orphelin) from the “normal” chance of 1/37 to 1/35. Obviously, he would profit from then on. And that shift is so small that that seems to me to be very realistic for someone to tease that out by observation. So by no means does he have to see where the ball lands every time he throws it, he just has to say, “As it is, it’s more likely to fall there, in this half of the cauldron,” and with a half-small improvement in the chance of hitting it, he’s already at an advantage.
By the way, I occasionally hear the discussion whether you should play with the bench or against the bench. What does that mean? Unfortunately, it is obvious here that the discussion is almost always about colours, red or black. It also quickly becomes clear why this is so: in every casino, above the roulette tables, even elsewhere, the last throws are recorded. So you can trace back the last, say, 20 throws, which numbers came up. Of course, you can go into detail about that or not. But one thing is clear: you can also see from a distance whether the last number was red or black. They are displayed that way, in the colour. And then it always causes quite a stir when a longer series of one colour or the other appears. Then those two chances are played more. The turnovers increase, just watch. So, for example, if black was in a series 6 times, then both chances are played more at the table where it occurred. This may sound curious, but it soon becomes obvious: one party plays against the bank, the other party plays with the bank. And why do they do that? Yes, what would you do? So one party says to itself, now it’s been black so often, now red has to come at some point, right? That’s right. And the other party says to itself: Maybe something is rotten here? Or: The bank has a black run, I’ll jump on it.
You already know my theory: a) if, I would only play with the bank. Because if there is an indication, then it is indeed that the probabilities are shifted in favour of the side that is now coming stronger, b) but especially with simple chances, the prospects are not good that this theory is correct. Because: all simple chances are arranged alternately in the pot. So there is always a red field next to a black one, a manque next to a pass, a pair next to an impair. And that’s where it just seems random to me. If you are looking for indicators, as already mentioned, then exclusively those on kettle areas. As I said, my recommendation. Otherwise, however, this remains guaranteed: if you are already playing, always only with the bank.
But I emphasise again for safety’s sake that the casino is basically at an advantage in all games offered there. So even good gambling does not protect you from long-term losses here. If you do not have any of the above-mentioned options, the only advice I can give is: Don’t gamble. Or be lucky, that works too.
b) The Blackjack
Blackjack, as I mentioned once above, offers the player other forms of decision-making possibilities. And, of course, the quality of the individual decision has a long-term impact on the financial outcome. However, the option I mentioned above of playing the game with an advantage on the player’s side, i.e. your side, no longer exists.
Very briefly the rules of the game? All right: Up to 7 players and a casino employee, the so-called dealer, sit at a gaming table. Each player places a bet between the minimum and maximum stake. This varies from gaming table to gaming table and country to country, casino to casino. But let’s assume you are allowed to bet between 10 and 250 euros and, according to your nature, you bet the minimum, 10 euros. Then each player gets one card face up, then the dealer puts one card face up, his card, the dealer card (most later decisions depend on it). Then each player gets a second card. The dealer initially stays with the one.
Then the dealer asks one player after the other what they intend to do. The card values are as follows: Ace counts 1 or 11, you may choose, 2 to 9 count their card value and 10, Jack, Queen King all count an identical 10 eyes (in case you thought you recognised the game so far: no, it is not 17 and 4, where Jack counts 2, Queen 3 and King 4 eyes, precisely because in the casino it is played with a 52 game; there the values 2 to 4 are already taken and even 5 and 6 exist). The aim is to get as close as possible to 21, ideally 21 or even Blackjack, an ace and any card with a value of 10, i.e. 10, jack, queen or king. Blackjack is better than 21, so if you have one of these combinations, your bet is paid out immediately if the banker does not have a 10 or an ace in turn, and can still “standoff”, i.e. tie. And you even get paid more than your stake, namely one and a half times. So for 10 euros you get 15 euros profit.
So, after two cards you either have Blackjack or otherwise at best 20, with 2 tens. Otherwise, you have a decision to make: Double, split, buy or stand still (English: double, split, hit or rest). You may double if the sum of your two cards is 9, 10 or 11. The bank offers this because it is a favourable constellation and it is generous. The most common card is the one with a value of 10. If you get this, you will have 19, 20 or 21, i.e. a very high, profitable value. You can split if you have two identical cards, two 7s or two 8s, for example. You may, but you don’t have to.
Otherwise you may buy or stand, hit or rest. If you have more than 21, if you have sold out, your bet is lost. If you have not sold out, i.e. you have any card total greater than or equal to 12 (you may of course stand still at a lower value, but that would obviously be stupid, because you can only improve) and less than or equal to 21, the game is repeated for each of the other players. Everyone makes their decision. Then it’s the bank’s turn. The bank has very fixed rules according to which it must buy: It has to buy less than 17, and it has to stand still if it is greater than or equal to 17. Soft 17, e.g. ace and 6 (since the ace counts as 1 or 11, you could safely buy a card with this hand), the banker must stop. After all, there are 17.
Now for the strategy: There are a few obvious decisions. For example, not splitting 10s. Although the 10 is a very good card, and you would have it twice after the split, your expectation of winning is much higher if you stand with the 20 you have and collect the easy win (often). So, in a nutshell, there is a basic strategy. However, it only ensures that you lose very little in the long run when you apply it. The basic strategy essentially looks like this: Against the small cards of the bank, 2 – 6, you should not risk selling out, i.e. stop at 12 (with 12 against the 2 or 3, it is minimally better to buy after all, but that is just marginal). For this you may double against these cards and split many cards. A split is good with 2s, 3s, 6s, 7s, 8s and 9s. Aces you have to split anyway. And against the other cards, 7, 8, 9, 10, ace, you have to buy until you have a hand. So even at 16 you still have to buy, even if it seems hopeless, pointless or even wrong.
Now there are lots of subtleties that you can learn in addition. But I actually wanted to explain how you could win, why and why not today.
Well, from the rule description you can see that there are certain card constellations that are favourable for the player. These are all the situations where you need aces and 10s. Doubles and blackjacks. There is another reason why it is favourable for the player if there are many high cards, i.e. 10s, in the deck: If the bank has one of the small cards, i.e. a 2-6, then they are forced to buy to 16. You, on the other hand, have the option to reshuffle before, i.e. at 12 to 16. So, imagine the following situation: The bank has a 6. 7 players are sitting at the table. No one has anything, they all have a 10 and a small card, so 12, 13, 14 or 15 say. No one buys a card. Then it’s the banker’s turn. The bank buys a 10. The bank has 16. The bank would collect all the bets. And what happens? The bank has to buy, that’s the rules, buys a 10, is sold and has to pay all the stakes. This additional option of resten in dangerous card combinations (where you could sell out), also favours you, the player, if there are many, more than usual, 10s in the resten pile.
This resulted in a simple winning strategy: you had to count the cards (cardcounting). But this counting method was very simple, in principle anyone could learn it. You only counted plus one and minus one. Plus one for each card from 2-6 and minus one for each 10 and each ace. Both are 5 cards of the 13 of 2-ace. 7, 8, 9 were not counted, so with zero. So on average it should come down to a balanced count. But if the count became clearly positive, i.e. plus 5 or plus 8, just examples, then obviously more of the coveted 10s and aces were in play. The two together also come occasionally, you have Blackjack. And although they also come more often at the bank, of course, the bank only wins single and you win one and a half times. All these little things added up in such a way that from a certain positive count (which also depended on the remaining cards) you had an advantage. Then, instead of playing the minimum stakes as usual, you played the maximum (you only played the minimum stakes to keep your place, because usually there are other players waiting for a place; you have to play to keep your place). So you played the normal games with minimum and the advantage games with maximum. This resulted in an overall positive expectation of winning.
Unfortunately, the casinos also gradually (never seen a film? There are good ones, honest) also knew that there was a winning strategy. And they even hired the best players for their casinos to identify the professional players. Personally, I was only once literally thrown out of a casino and banned for life (reason: “You know why” “Why?” “We told you at least twice, that you are not allowed to play at the Black Jack tables.”), but it wasn’t that attractive in my time either. Another time, obstacles were put in my way, I was prevented from playing until I voluntarily surrendered.
So: the casinos knew, they made the rules worse, more and more, they took more stacks of cards (earlier in Vegas one game, later up to 6), that doesn’t make counting more difficult, but the situations come less often. And then part of the deck is always marked out. This was originally only meant so that in the last game the cards would not suddenly run out, so the dealer saw the red card that he initially gave to stake out in the pile, and when it came, it had to be reshuffled after the game. However, there were still enough cards for each player after the staking card. But this staking was later used to take more cards out of the pack, it was called “cutting” or “cutting out”. I have played in casinos where half of 6 card games were staked out. Not only do you run out of steam, but there’s just no advantage anymore. Then when you could play, in the middle of the deck, play, so bet maximum, play an advantage game, then they reshuffle. So that already made it almost impossible. But then even “on top of that” the shuffling machines were introduced. They simply shuffle the cards after each game, they shuffle during the game, there is no advantage any more.
Should you ever go to a table anyway, please at least use the basic strategy, that saves a lot of money.
But I can’t resist one question: Do you know why the bank wins in the long run with this game or why it offers it at all? What is the advantage?
With roulette, it is, at least apparently, easy to understand. It has to do with the zero. But with blackjack? There is no zero there. And if you think about it for a moment, you will surely realise that the game is also extremely fair in other respects. In the case of a “standoff”, i.e. a tie, nobody wins. Your bet remains on the table. So you have 18, the banker also makes 18. That’s standoff. Your money stays put. And apart from that, you have all kinds of advantages: You can double in favourable constellations, which can only be a good thing, since it is not obligatory. You get paid one and a half times your money on a blackjack, the bank, for its part, only collects your single bet. You may even split if you think it is convenient. Not compulsory either, but there are the favourable situations. Otherwise, everything evens out. So go ahead and play, you will win.
Or should you think about it first? All right, you’ve figured it out, but I’ll say it anyway: when you sell (“bust”) there is no standoff. So if you are sold, your stake is gone. If the bank subsequently sells as well, you don’t get your stake back (unlike the other standoffs). That is the bank’s advantage. And, if you play optimally, you sell out at about 17%. The bank, by its rules, sells itself at about 28%. So, then multiply those probabilities and you get a disadvantage to you of 0.17*0.28=0.0467. so about 4.7%. If you are nodding in agreement now, I have to disappoint you. This is not correct. Multiplying is only correct if the events are independent of each other. That is not the case here. You are following a strategy depending on the bank card. So against one card you sell more often, against the other less often. I never get bored with that, by the way, how about you?
So your playing behaviour has an influence on the combined probability of the events “player sells out” and “bank sells out”. In fact, your strategy is specifically designed to exploit that in your favour. You sell out much more often against the cards where the bank sells out less often. And against the cards where the bank sells more often, you cleverly don’t sell at all. This leads to a reduction of the disadvantage from an apparent 4.7% to 3.7%.
Of this 3.7%, we can gradually get some back through the other rules.
The biggest advantage you get from other rules is that of blackjack. After all, a Black Jack comes in one out of 21 games (calculation method: 1/13 for an ace, 4/13 for any 10, the whole times 2, as the order doesn’t matter, so 1/13 * 4/13 * 2 = about 1/21).
So in one out of 21 games you get half a bet for free. That makes 1/21 * 0.5 = 1/42 or 2.38%. So now we are only at a disadvantage of 3.7% -2.38% = 1.32%. Unfortunately, the remaining advantages are only minimal, so that one plays with a disadvantage of about 1% when using the “basic strategy”.
Now, of course, I have to explain the basic strategy briefly: Always buy up to and including 16 against cards 7, 8, 9, 10, B, D, K, Ace. Never buy against 2, 3, 4, 5, 6. Always split the 8s except against 10s and aces (against 10s it doesn’t even matter). Otherwise only the splits of 2s, 3s, 6s, 7s and 9s are interesting. The first 4 always split against 2-7 and the 9s even against 2-9. Doubles are only interesting against 10s or 11s. Doubles against 9s bring almost nothing, only against 4s, 5s and 6s a minimal profit. Doubling 10s and 11s is good against 2-9 (so not against 10 or ace). These are the most important rules. There are only tiny subtleties (buying with 12 against 2 and 3 is minimally better than rested for example).
Unfortunately, it is also not so easy to compare the strategies in percentage terms. Nevertheless, I will give you a few examples:
For example, if someone always stands from 12, then he has the following disadvantages: With 12 against the ace it costs 21% of his bet. This calculates that the disadvantage is big when buying (equity -0.55 units), but much bigger when not buying (namely -0.76 units), so it costs 0.21 units. Another example: If you stand with 16 against the 7, it costs you 6% of your bet. Again the calculation: -0.475 units if you stand still and only -0.415 units if you buy. These are examples of rather gross mistakes.
Others are also very significant: If you buy with 13 against the 3, for example, it costs you only 0.039 units (-0.291 hit, -0.252 rest). But if you buy with 16 against the 5, it costs you a whopping 0.28 units (-0.45 hit, -0.17 rest).
So in conclusion: I cannot calculate the difference between a bad and a good player exactly here, because completely different types of players can make completely different mistakes. But every mistake, every deviation from the basic strategy, costs money in the long run. So if you play, why not play well?
I can also give you a justification for gambling in general: After all, if you do any kind of undertaking, it will almost never work without spending money. So a visit to the cinema or theatre, a carnival, even just going out to eat, everything involves spending money. So if you go to a casino and make a turnover of 1000 euros, on roulette, as suggested above, or blackjack, it will cost you about 10-13 euros. That is just a figure that will be noticeable in the very long term. In one evening, you may very well win. That’s the fun, the attraction of it. But if in the long run it becomes noticeable that you get what you are entitled to, as mathematics promises in principle, then in the long run you would come to a financial cost of 10 euros per evening of play. And that’s a manageable amount, like going to the cinema, which one likes to invest for so much fun, isn’t it?
I don’t want to bore you, especially by telling you things that have been known for a long time. But I have to mention it at least once: Yes, you can also play the lottery well. If you play unrelated numbers above 31, you don’t improve your chance of getting the 5 or 6 correct numbers, but you do improve the payout rate. Because in lotto, the payout rate is based on the number of correct picks. And the number of correct picks decreases with these number combinations. The reason is this: Many people play numbers that represent dates of birth. These are always less than or equal to 31. But some also play patterns, for reasons of simplicity. So numbers that are related to each other are played more often, you would have a higher number of fellow players who also guessed it if you hit it. Is that convincing? It is even possible to gain an advantage in this way, i.e. that playing the lottery is profitable if the above rules are applied. However, I don’t have the figures to be able to judge that exactly. You would have to analyse the payout rate over a very long period of time. And even then, a lot of things can just be coincidence. Actually, I would have to see all the tips received. Then a judgement would be possible. That leads on to…
d) Totalisator principle, horse betting and Toto
Ok, you have probably already guessed, if not known: Toto and horse betting can also be played well. But first I will explain the totalisator principle using the example of horse betting.
The totalisator principle works in such a way that the organiser does not announce fixed odds. At the racetrack you get current odds, which are calculated from the current distribution of bets at any given time, but these odds can change again with each new bet on a horse (no, they will certainly change). So you don’t know at the time of betting which odds you will get in the end. After all bets have been placed, i.e. at the start of the race, the odds are based on the sum of all bets on the various starters. The organiser retains part of the stakes and distributes the rest “fairly” to the winners. Let’s take a simplified example: Let’s say there are four horses at the start. On horse 1, a total of 5000 Euros are received on the win (for the sake of simplicity, we will only consider win bets, not run-in bets or place bets; with run-in bets you try to predict several horses in the correct order, with place bets you bet that your horse will be among the first 3 horses). On horse 2 you bet 1000 Euros, on horse 3 only 500 and on horse 4 again 3500. Now there is a total stake of 10000 Euros. The organiser, for example, retains 20%, i.e. 2000 Euros.
Now there are 8000 Euros available for payment. These are paid out in full to all those who had horse 1 on the win. So you divide the payout amount by the stakes on this horse. In this case 8000/5000 (8000 total payout, 5000 total stake on horse 1). This gives 1.60.
Then, if horse 1 wins, he pays out 1.60 euros per euro bet for each person who bet on the win. So the odds at which the bet was placed are 1.6, we check this: A total of 5000 euros was bet, each person, even if it was only one, gets 1.60* bet, here 1.6*5000, so a total of 8000 euros is paid out. That is exactly 10000 reduced by the 20% of 10000, so 10000 – 2000 = 8000.
However, should the biggest outsider, horse 3, win, the payout ratio would be 16.0. 8000/500.
Test: total stake of 500, the whole *16, gives 8000 again, right.
Since the actual chances of success of the horses are unknown here too, difficult to determine, a real expert can possibly work with an advantage here too. So if the actual chances of winning of horse 1 exceed 1/1.6 = 62.5%, one would have an advantage. If the chances of winning horse 3 are actually higher than 1/16 = 6.25%, one would have an advantage there too. I have never bothered with this game as I do not know for sure if all races are run fairly. If the jockeys or others should agree on who wins, then they will work it out that way. I’m not assuming anything; I don’t know, so I don’t do it.
A mathematical hint derived from logical reasoning goes like this: Common sense, which only appears to be common sense, tells us that, as mentioned several times above, do what is certain. As safe as it can be. In the case of sporting events, it tells us: play what comes. And what do we assume is coming? Correct, the favourite event. If Bayern Munich plays Hansa Rostock, why should I play Hansa? I hear someone yelling out to me, “What did you bet on that game, you expert?”, I answer “Hansa, it’s obvious.” Answer: “Nice expert, you keep on calculating, I’ll play what’s coming. And that’s Bayern.” And: Who wants to contradict that? “The experts are only discussing the amount of the victory.”
At that moment I was struck by the thought: What have I been feeding on all this time? I always play the wrong ones!
So my mathematical mind tells me: If you want to win on the racetrack, you can hardly do it by playing favourites. But as I said, I don’t have the insight.
To the pool:
Again, the question is whether you can actually play it with advantage. But I have given up trying to find the advantage. The data that led to the determination of the good tips are not made available by the Lotto/Toto company, as I found out when I called them. But I don’t think it’s impossible that it can be done. And after all, with Toto you have the opportunity to make high turnovers. I’m talking about profitable turnovers, of course. All right, how would one have to proceed? Of course, you have to take advantage of the (mis)behaviour of other lottery players. The tendency is definitely to include some clear outsiders in the tips. My idea would be the following (by the way, I did some research on Spanish pools with two acquaintances. There are indications that it is possible to place such bets that promise a profitable turnover; however, the tool, computer programme, for calculating this is already highly complicated and new questions always arise): One has to pick out the supposed bank tips. Because almost every player in Toto plays like this: 3-5 banks, games where you commit yourself. They have to come, otherwise all is lost. The rest is filled up with 2s and 3s. Depending on your budget, because many 3-way games also mean a lot of capital investment (you cover all possible outcomes, which costs money). The idea with this way of playing is this: Banks come and from the rest there will be something from time to time. And maybe I’ll have the 11. So, but I can tell you about at least five people who have already told me: “Do you know what happened to me? Three weeks ago I finally had the 11, and then I just collected 80 euros.” Have you ever heard something like that? That would really not be a coincidence then (and I have already read many definitions of this word, the simplest and closest to the origin of the term is: “coincidence” stands for a rather improbable event. And I guess I’m a little lucky to be sitting out of your reach, because: how can I of all people use the word “improbable”? I must be slapped), because the very fact that you have already met one who made the statement suggests that there are a great many of them. And this is confirmed by the low payoff: only really many had this tip. And what’s more, all of them, guaranteed all of them, think their sad fate is worth telling. But what remains worth telling, we agreed, are the extraordinary events? And that’s just not one. So, pick the bank tips, bet against them in these games. That would be my suggestion. But you don’t have to do it for all the games. Because: It is enough if you manage to be the only winner or have to share with very few. And for that it is enough to get two or three outsider tips through. But please bear in mind that you then have the disadvantage of a very low probability of occurrence. After all, can you remember a matchday when Werder Bremen, Bayern Munich and Borussia Dortmund all lost at their own ground, and against Duisburg, Bochum and Bielefeld?
But I didn’t say that after studying the book you only have to open the window to let the money rain in, did I?
By the way, how is the advantage calculated? From a purely mathematical point of view, you would always have an advantage on a single tip if the ratio of tips received on one of the 3 chances (by this I mean 1 – X – 2) in relation to the total tips is in favourable proportion to the probability of occurrence. It looks something like this, to stick with the example above. Let’s say we had determined that the victory of Bayern Munich against Hansa Rostock has a probability of 76%. If now, for example, 8800 of 10000 tips, i.e. 88%, are on Bayern winning, then it would be advisable not to bet on it, even on the contrary, the advantage would then be on side X/2, i.e. that Bayern does not win. The odds at which you then bet can even be calculated. This would then be 10000/1200 = 8.33 (here the 1200 is the number of tips received on X or 2, 10000 – 8800). That’s really great odds, and you get those on the “Bayern doesn’t win” event, so to speak. If you assume that you only decide on X, and 700 tips are received on X, then you would get the gigantic odds of 10000/700 = 14.28. You would not get odds like that in any betting office or with any bookmaker. My guess, but certainly not unrealistic, would be the maximum odds of 6.0.
(All 9 out of 11, we had already calculated, betting with a bookmaker would result in the number of 11 over 9 = (11109876543) / (987654321), in this case you quickly realise that you can immediately shorten several factors from the numerator and denominator. And you can also see that 11 over 9 = 11 over 2, the remaining factors. Namely 11*10/2 = 55).
After all, you already get a payout for 9 hits. I don’t want to bore you with the formula of how big the advantage on a game has to be in order for the whole game to be profitable, but I will at least note here what the result would be if you had a 5% advantage on each game. That would be something like 1.05 to the power of 9 and that = 1.55. So if you have a 5% advantage on each of 9 games in a combined bet (hence the 1.05, which is more or less 105% back), you would already have an advantage of 55%. Thanks to the multiplication. As I said, this is not necessarily realistic on Toto, because there are often a lot of “balanced games” where you are guaranteed to have no advantage, because the Toto players also assess them as balanced, so the distribution of tips will also be balanced. For me, the biggest drawback was that I couldn’t get an insight into the betting distribution even after the end of a match day. Because with the help of this, one could at least have determined the “standard errors”. So what was the actual distribution of tips for Bayern – Hansa? Without this information, I only have the payout ratio as an indicator, and that is simply too little.
e) The stock market
Perhaps I should hold back even more on topics I know nothing about. Nevertheless, I also have my views on this, but I really haven’t seriously dealt with this “game”. Yes, it is a game for me. It’s just considered more serious, isn’t it? After all, you are betting on large to very large, successful (or not so successful) business enterprises. I also know that you can definitely make or get good forecasts on how the values will develop. But for me, the whole game remains more like a modern form of chain letter. So one acquires a value. You pay the market price for it. So far, so good. You look at the development. You have even analysed well, the price movement is positive. You can sell at a profit, you sell. Ok. But: from whom or what have you profited? First, you have to subtract the percentages that are retained for trading there as well. Then you even have to pay tax on these profits if they are profitable. That costs further percentages. But where does the profit come from then? If you buy the value, it is because it is undervalued. You have determined that. If you sell it, you should only do so if it is overvalued at the time. Otherwise you would have to hold it and let it go up. My concerns are not moral. For even in my business I profit (or: intend to profit) from the fact that someone else has a worse, shall we say, wrong assessment of the event on which I am betting, putting my money. But I ask: where is the true value of the share? What is the economic equivalent? And here I am of the opinion that the traded values do not correspond to the real ones. The profit can only come from the market laws of “supply and demand”. I formulate it for myself like this: When I buy a value, I do something stupid. But I do the stupidity consciously because I know that another person is willing to do an even greater stupidity later. The stupidity is that I pay too much. The equivalent value does not exist. I still make a profit: someone else does an even bigger stupid thing. And that is like a chain letter.
The effect of the mistake is also quite obvious: the stock market crash. Somewhere, someone starts to realise that he has done something stupid. He sells. The values slide, everyone still wants to get something out of it, the stone, ah, the avalanche starts rolling.
The probability of a stock market crash, which usually damages a large part of the investors (by large part I mean 99%; a few may save themselves in time; by the way, these are the same people who hear fleas coughing). And this crash probability is obviously a quite realistic probability in relation to the super-GAU. Because I’ve already heard of a few. And stock exchanges are far fewer than nuclear power plants. So every time you buy a security, you not only have to calculate the brokerage percentages that accrue when you buy and when you sell it, as well as the taxes you have to pay when you make a profit, but you also have to calculate the crash probability.