This is my announcement for a project I am doing on the side that is related to fighting games. A while back a conversation on SRK sparked my interest in the idea of “How does my chance of winning a round propagate through sets and tournaments?” This originally got started as “If I have a 4-6 match up how does that effect my chance of winning a 2 out of 3 set? A 3 out of 5?” In my first attempt at this problem I tried to derive a formula to deal with it, but found the math got too big too fast. I was able to get some useful results however which you can find at this link:
I realized I couldn’t actually find this answer for a tournament of any significant size (A 4 man bracket was already difficult to do). So to solve this I have actually written a piece of computer code that simulates a tournament using a Monte Carlo style algorithm. I know that sounds difficult, but the idea is actually very simple. Set up a bracket, run the matches according to set probabilities, determine the winner, send the winner/loser to the next round, and record the results.
A match is simulated on the computer rather simply. Let’s say I have a match against another player and in a long set I would win 60% of my matches against that player. The computer will simulate each game in a standard tournament set by selecting a random number between 0 and 1. If that number is less than .6 I win, if not I lose. We simply repeat this till someone wins the set. Then the rest of the program works exactly how a tournament would, advance the winner and knock out the loser.
With this you can sample thousands of tournament scenarios which allows you to figure out how different factors effect chances of winning.
Here are some of the factors I intend on testing
- If I have win rate of x% how does that effect my chance of winning an entire tournament?
- If there is a top player in my bracket how does that effect my chances?
- If I have a bye in the first round how does that improve my chances?
I’ll be posting some of my results as I finish them.