Data Analyst
The travelling salesman problem (TSP) is defined as follows, “Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?”. Increasing the number of cities increases the number of possible routes enormously which makes this…
Pictured above is a chart which shows the estimated probabilities of the league position of each team after a round of matches – in this example Round 16 of the English Premier League at the end of 2020. * Liverpool, then top were leading Everton by 3 points with a 10 goal goal difference advantage…
Apparently the Drunkard’s Walk, “falls into the general category of Stochastic Processes, specifically a type of Random Walk called a Markov Chain.“. That all sounds very complicated, so I’ll simulate it with an Excel Data Table. A drunk person starts at home at co-ordinates (0,0), and goes for a wander. For each step he takes,…
In my post http://www.neilmcniven.co.uk/european-roulette-simulation/, I looked into the amount of money you could expect to win or lose with a given bankroll and number of spins at European roulette. Here instead I will look at the number of spins of the wheel you can expect to survive before your bankroll is down to zero –…
In European Roulette there are 37 pockets in the wheel numbered from 0 to 36 inclusive – 18 black, 18 red, and 1 green. There are many possible bets that can be placed in the game of roulette. One of the simplest is just to bet on the ball finishing in the pocket of specific…
Stephen Wolfram is famous for many reasons. One of those reasons are his Wolfram Rules looking at cellular automata. One dimensional cellular automata are defined by very simple rules. Each cell is given a value of 1 or 0 depending on the values contained by the three neighbouring cells above (the cell directly above, the…
The Game of Life rules are very simple. You start with a randomly generated grid of cells (some ‘[a]live’ and some ‘dead’).What happens next is decided by the following rules:* Any live cell with two or three live neighbours survives.* Any dead cell with three live neighbours becomes a live cell.* All other live cells…
I ran a Monte Carlo simulation of coin tosses with Excel – simulating tossing a fair coin 20 times to see how many times the coin landed on heads, and repeating that 50,000 times. Above on the left shows one iteration of tossing the coin 20 times. On this occasion, heads (1) came up 12…
This evening (28th August 2020), popular YouTuber educator Veritasium (Derek Muller) asked the question of whether success is a result of hard work or luck. During the video (link below) he discusses how in January of this year, NASA selected 11 new astronauts from 18,300 applicants to join their corps.He wanted to know how much…
I downloaded ten seasons of Premier League football results and betting odds data (Bet365) from https://datahub.io/sports-data/english-premier-league (2009-2019 inclusive in ten CSV files). After drawing some charts with the data just looking at the relationships between the betting odds and the results, one potential strategy that stood out was betting on matches to be drawn under certain circumstances…