‘A game with negative mathematical expectation or The worst secret in the exchange's closet’ (part 1)
Since I've spent a lot of time studying game theory, and I am a Gambler by nature (I try to keep myself within limits, but drowning in the game, I've tossed lots for seven-digit sums $), so the topic came easily to me
I should note that 99% of traders do not pay attention to it and don't know what I'll describe in details now, and exchanges in their turn keep this secret behind seven seals and at any dialogue at any level, it is only worth starting a conversation on this topic, as the leadership and management change their faces, blush and deny by all means, and the proposal to make simple mathematical calculations is received with hostility
Before we start to study and calculate in detail, we need to define the terms and give a full explanation of each of them:
🤨 A zero-sum game is a situation in which one party's gain depends on the other party's loss, and the net change in wealth is zero
Let me explain with the most obvious life example - ‘Poker’ (and it's conditional on the game being played between players). You sit down at a table, let's say 5 people with $10,000 (totaling $50,000) and at the end everyone's take out will total $50,000
All trading on the spot goes at the same zero sum (if you don't take into account commissions - quite a fair income for the exchange, if anything), i.e. all purchases are someone else's sales and vice versa. In the end, most of the market remains out of business still, because there are Insiders, Manipulators, Market Makers - call it what you want, but this is the class of people who play with the marked cards and essentially predetermine the growth and trends for the season, but that's another story, today is not about that
🤨 The mathematical expectation (expected value) is the average outcome of a game given an infinite number of attempts
Any game in the casino is calculated from the negative mathematical expectation, for example roulette has the highest rate for players and it's not difficult to calculate it: (36/37)x100%= 97.3%. Quite a high probability %, isn't it, but on that negligible 2.7% deviation, the casino wins fabulous money all over the World. Of course, we're talking about fair play scenario, because there are also ‘Tricksters’ let's say, but that's another story as well
The meaning of what is required to understand: At the slightest deviation of mathematical expectation from 100% and large turnovers - the amount of players' losses can be counted in any figures
In general, if we talk about the mathematical expectation in casinos, it will vary within 93% (keep this value in mind, we'll come back to it later)
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