arXiv subjects

Ralph Stömmer

Publications and source records attributed to Ralph Stömmer.

4 recordsLinked to original sources

arXiv2026

Tackling the 6/49 Lottery and Debunking Common Myths with Probabilistic Methods and Combinatorial Designs

At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This article compares objective scientific approaches to tackle the 6/49 lottery: probabilistic methods and combinatorial designs. The mathematical models developed herein can be modified and applied to other lotteries. The newly constructed (49, 6, 5) covering design is introduced, which meets the Schönheim bound. For lottery designs and for covering designs, a benchmark based on probabilistic methods is presented. It is demonstrated that common attempts to outwit the odds correspond to limitations of numbers to subsets, which disproportionately reduce the chances of winning.

stat.OT↗

arXiv2025

On the Lottery Problem: Tracing Stefan Mandel's Combinatorial Condensation

Stefan Mandel is said to have won the lottery 14 times. He never disclosed the recipe he called combinatorial condensation, which enabled him to hit the Romanian lottery jackpot in the early phase of his betting career. Combinatorial condensation is frequently mixed up with another strategy known as buying the pot, which Stefan Mandel was pursuing later on. On occasion, he dropped a few hints on combinatorial condensation. The hints are applied in this work to narrow down and assess his initial recipe. The underlying theory resembles what a weekend mathematician, as he once referred to himself, may have encountered in the 1960s. The cardinality of the (15, 6, 6, 5) and (49, 6, 6, 5) lottery schemes shows that Stefan Mandel probably wasn't aware of lottery designs. First concepts on such topics had been available at that time, but coherent theories on combinatorial designs took off only in later decades. There is no absolute evidence beyond doubt, but the size of actual covering designs and the associated efforts allow the following hypothesis: Stefan Mandel most likely pioneered in constructing a (15, 6, 5) covering design many years before others published about it, which he applied in the Romanian lottery. Calculations indicate that he took considerable risks that his method might fail, because he limited himself to a subset of 15 numbers out of 49 numbers. The risks explain why he later changed his strategy from combinatorial condensation to buying the pot.

math.CO↗

arXiv2023

Beating the average: how to generate profit by exploiting the inefficiencies of soccer betting

In economy, markets are denoted as efficient when it is impossible to systematically generate profits which outperform the average. In the past years, the concept has been tested in other domains such as the growing sports betting market. Surprisingly, despite its large size and its level of maturity, sports betting shows traits of inefficiency. The anomalies indicate the existence of strategies which shift betting from a game of chance towards a game of skill. This article shows an example for an inefficiency detected in the German soccer betting TOTO 13er Wette, which is operated by state-run lottery agencies. Gamblers have to guess the outcome (win, draw, loss) of 13 soccer matches listed on a lottery tip. Applying stochastic methods, a recipe is presented to determine hit rates for single match outcomes. More important, the recipe provides the number of lottery tips required to achieve a specific number of strikes (number of correct match forecasts per lottery tip) for any given level of safety. An approximation is derived to cope with large numbers in hypergeometric distributions, valid under certain constraints. Overall, the strategy does lead to returns exceeding the aggregated lottery fees, resulting in moderate, but consistent profits. It is briefly discussed if lessions learned from soccer betting can be transferred back to financial markets, because gamblers and retail investors face similar challenges and opportunities.

physics.soc-ph↗

arXiv2022

Soccer: a quantitative analysis of team resilience and the miracle of Bern

Resilience is the ability to positively respond to adversity. It has been studied in psychology for several decades, with focus on how individuals overcome traumata or cope with setbacks and obstacles in their professional career. Research on resilience in the sport context is rather new. Activities are based on insights that in highly competitive environments, tiny effects tip the scales. A key question of measuring resilience in sports is what parameters to measure. Here a novel concept is proposed to measure the resilience of soccer teams. The relative frequency of matches is determined, where a soccer team, which is initially trailing by 2 goals, finally succeeds to win the match or at least to reach a draw. The analysis is applied to the last 59 seasons of the German premier soccer league Bundesliga. The empirical data are compared with a theoretical model derived from Poisson distributions. It is shown how leading teams in the premier soccer league differ from the average with respect to resilience, which provides further insights into the hidden secrets of top soccer teams.

stat.AP↗