What is the Event Space?
Did I actually promise somewhere to entertain you well? Well, if not, I would like to and am working on it. In mathematical terms, the event space in a random experiment consists of all the possible outcomes that can come out of this particular experiment. The sum of all the individual probabilities must be 100%, or even 1. That is simple, yes. The mathematician makes it simple. So when he picks up a dice, he says it can come up 1, 2, 3, 4, 5 or 6. Or with the roulette wheel. 0 – 36, each number in a box of the same size if possible. So 37 possible outcomes.
Even simpler, as already explained above, he makes it with the distribution of the chances. I have a die here, it has six sides, I don’t see anything out of the ordinary, so each chance is 1/6. 6 outputs, 6*1/6=1. Done. Other cases are not considered (neither is shifting the odds, but more on that elsewhere).
Now comes the pain in the ass again, and I really qualify as such: what if the die falls under the couch and you can’t find it again? I’m not serious? Yes, I am. It’s never happened before? But what if you find it, but in the process the dice falls over, you don’t know what number it was? It doesn’t matter, you say? Repeat? But what if the cube “burns”? Yes, now it’s getting “dicey”. Then the question arises: When does it burn? How is burning defined? Have you never had an argument in a dice game about whether a dice burns or not? Well, if it wasn’t about money, it’s okay. But even then, you could…
There are even quite a few dice games that are played with more than one dice. I just always notice that it’s not considered or settled until the first event. It doesn’t fit into the event space. And then when it does happen, you worry about it. Between friends, no problem, right? But when money is involved, it simply has to be defined.
Anyway, the event space should actually look like this: Cube is lost, cube burns, cube shows a 1, 2, 3, 4, 5, 6. And the probabilities of occurrence! If you can still approximate them quite well for the six numbers, then you lack any feeling for the other two events. And the sum remains at 100%, you simply can’t get any more, or any less. So these 1/6 are wrong anyway.
You should see how often the dice burn in a backgammon tournament. There are no statistics on that. Fortunately, there is (almost) never a dispute. And also a rule, so that the significance becomes relatively small: The throw is repeated. Yes, that’s right, in backgammon both dice have to be thrown again, even if only one of them burns.
But if you now insist on your view that this is irrelevant, then I will give you a few more examples. By the way, they all serve the same purpose: the elimination of prejudices, the softening of thought structures. I want to make you compliant, hehe.
And I’m working on it so that one day you’ll say: the man is somehow right, I never thought of it that way.
So I can give you two more examples on the subject of event space: There was the memorable quarter-final match between 1 FC Cologne and Liverpool in the 1964/65 European Champion Clubs’ Cup. After the first and second legs, the score was still a draw, both games ended 0:0. At that time, there was no extra time but a replay. Replay 2:2, extra time, still 2:2. There was no penalty shootout. There was a coin toss right after the game, at the centre circle. The ground was totally ploughed. The referee threw the coin, it actually landed on the edge, stuck like that! But maybe it was tilted? Cologne’s side up? It can’t have been completely vertical. But I don’t know of any protests, the throw was repeated – Liverpool won. Fate? Meaningless? Even if it was, but at least entertaining? Oh, please.
I once witnessed a scene in a well-known gamblers’ pub at an advanced hour: the protagonists suddenly had the idea to play a single game for 1000 DM. But it was supposed to be a fair game. It was a kind of test of courage. Like this: “I don’t think you dare to bet 1000 DM at once.” “Of course I dare.” Kindergarten. But it came to pass. Both put 1000 DM on the table, a dice was brought in, a referee, one took the even numbers, the other the odd ones. Now don’t say that wasn’t spectacular. The referee threw, the dice rolled, across the floor, tension, tension, and then: it rolled under the radiator. What now? Does the number on top count? No one could see it, but discussions were about to take place. Luckily there was a referee, replay, Mike won. The smart guy had just taken it!
So this is how the event spaces, so pleasant for the mathematician, originally look: N outcomes, all equally likely. Yes, you can rub your hands together. That’s what makes mathematics fun. All these disturbing factors in the practical examples? Nah, we don’t want to have anything to do with that. But as a player or on the way to becoming a successful player, it is often precisely the task to find the weak points in the games.
And above all, there are a lot of events whose probabilities of occurrence are completely unknown. The event space often remains clear. The addition of the probabilities remains at 100%. But how probable which outcome is is open, even indeterminable. How is it that people can still feed on this? Even if it is only the providers identified as winners by the average citizen (i.e. not by you). How are they supposed to manage? Navigating their way through a gigantic guessing game?