
BGonline.org Forums
A common fallacy about luck and skill
Posted By: Timothy Chow
Date: Thursday, 25 February 2016, at 11:46 p.m.
Let's take two commonly asked questions about games like backgammon that contain a mixture of luck and skill. For a given match length and a given pair of players,
1. How often does the more skillful player win?
2. How often does the luckier player win?
I think that most people tacitly believe, without thinking about it much, that the answers to these two questions must be negatively correlated. That is, if you tinker with the rules of the game so that the more skillful player wins more often, then the luckier player will win less often, and vice versa.
It may therefore surprise many people to learn that this is not necessarily true, assuming that we define "luckier player" in the same way it's standardly defined by backgammon bots. I'll phrase this in the form of an exercise.
Construct a simple game and a pair of players so that the more skillful player wins extremely close to 100% of the time and the luckier player wins extremely close to 100% of the time.
Once you see how to do this, you should also be able to see how to construct a game in which the luckier player wins X% of the time and the more skillful players wins Y% of the time for almost any values of X and Y in the range 50 to 100.

BGonline.org Forums is maintained by Stick with WebBBS 5.12.