# How to Best Determine Probability of Winning a Card Game

• Jan 5th 2012, 12:06 AM
whiterequiem
How to Best Determine Probability of Winning a Card Game
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.
• Jan 6th 2012, 03:29 PM
Maxim
Re: How to Best Determine Probability of Winning a Card Game
I guess you could use some kind of ELO rating system. Everybody starts off with a certain rating, e.g. 1500, and then when people play, they gain points (when winning) or lose points (when losing) depending on the ratings of their opponents.

You could use the formulas described at the wiki page, but any implementation of the general idea should do: before playing a game, determine a probability for each player to win the game (depending on their current ratings, and number of players). The less likely you are to win the game, the more points you gain if you do. And vice versa, the less likely you are to lose the game, the more your rating drops if you do.