G'Day, hoping someone out there is smarter than we are at calculating this kind of stuff.
At work during lunch, it's been custom to play a game of cards for two rounds - the person to lose the first round of cards has to do the dish washing for the rest of the day; and the loser of the second round dries the dishes.
We have eight people in our department, but from day to day the number of playing differs due to holidays, working during lunch or any other form of absence. The question was raised who was the best at cards, so for the past few weeks we have been noting down who played each day, who lost the first round and who lost the second round.
Based on this data, we want to figure out a way to rank who is best - but it's proving difficult for our uneducated minds as we're assuming losing in a game when 7 people are playing is 'worse' in skill then playing when, say, only 3 people are involved in the game (i.e. 14% likelihood against 33%). Also we're not sure how to account for those who have only played several games - i.e. if they've only played 3 games and hold a 0% loss rate, are they really better than someone who has a 6% loss rate over 30 games?
Any insight into the question would be most appreciated, even more if could be explained as non-technical as possible. Thanks.