Betwinner Luck and Bad Luck: The Fine Line of Expectation Luck often plays a big role in the betting process Sometimes luck can be the key to our success, and bad luck is the reason for failure. It is important to understand the role of the luck factor in the betting process. But how thin is the line between luck and bad luck? Randomness plays an important role in the sports betting process. The winners almost always owe their success to luck, but bookmaker margins and the law of large numbers almost always negate that success in the end. Those of you who have read my articles over the years are aware of my uncompromising attitude when it comes to the likelihood of long-term profits for bettors. I do not expect that you will necessarily agree with my opinion, since it is the basis of the conflict between hope and reality that any player faces. This is why many of the articles in our Betting Blog or Guide are educational in nature and are designed to help gamblers gain the prediction experience. Nonetheless, the rules of probability apply even to the few who manage to compute a profitable long-run expectation. In this article, I will go into more detail on how this happens. In particular, I will illustrate how thin the line is between luck and bad luck. Classic example of a coin toss We all know that a coin flip has a 50/50 chance of getting heads or tails. We also know that if you flip a coin 20 times, there is no guarantee that it will land ten times heads or ten times. ”, Although this is the most likely result. Sometimes there are 12 heads and eight tails, and sometimes vice versa. It is very rare that a result of five heads and 15 tails is possible. In order to accurately determine the probability of each possible outcome, the binomial distribution can be used. For 20 coin tosses, it looks like this. In most cases, the range of likely outcomes ranges from five heads and 15 tails to 15 heads and five tails. What happens in case of 100 coin tosses? The distribution will look like this. This time, the range of likely outcomes is wider. If we visualize the result, then for 20 coin tosses, the distribution of values will be in the range from five to 15 “heads” (the difference is ten). For 100 coin tosses, this range will roughly double to 40 to 60 heads. Does this mean that as the sample size of the coin toss data increases, the range of possible outcomes also increases? Yes and no. When the mathematician Jacob Bernoulli experimented with this scenario, he noticed that while the absolute numerical difference between the number of heads and tails may increase with increasing sample size, the percentage of heads approaches the 50% mark. Five “heads” out of 20 is 25%; 40 out of 100, however, is 40%. This second explanation, which defines the basis of the law of large numbers, is very important for the players to understand the rules of probability. Standard deviation for binomial distribution You can measure the range or variance in a distribution using the standard deviation. For a binomial distribution, the standard deviation (σ) can be expressed using the simple equation below. n is the number of binary repetitions (for example, tossing a coin), p is the probability of success (hitting heads), and q is the probability of failure (hitting tails). Since p + q = 1, we get the equation below. And for the simple case, when p = q (that is, 0.5), it will look as follows. For 20 coin tosses σ = 2.24, and for 100 tosses σ = 5. The standard deviation gives an idea of the range of most possible results. For example, if you flip a coin 100 times, then just over two thirds of the cases will be within ± 1σ (45–55 heads). We confirmed Bernoulli's first conclusion: the larger the sample size, the greater the absolute variation. But what happens if we use percentage heads instead of absolute numbers? In order to calculate the percentage of heads, it is necessary to divide their number by the total number of coin tosses (n). Likewise, in order to calculate the standard deviation of percentages, we must also divide this value by n. The result for simple bets with a probability of 50-50 outcomes is shown below. If you now flip a coin 20 times, the standard deviation of the percentage of heads will be 0.11 (or 11%), but for 100 flips, it will be only 0.05 (or 5%).