Poker and Skat: More skill than luck
Are Skat and Poker games of luck or skill? According to economists at the University of Heidelberg both card games have a luck component of over 50 percent, but skill prevails in the long run.
In chess, the strategist wins; in roulette, chance decides victory or defeat. Prof. Dr. Jörg Oechssler and his team wanted to know what applies to Skat and Poker. Are they games of skill or luck? “The classification is difficult, as there are many shades between extremes like roulette and chess,” says Prof. Oechssler. The legislator states in the Glücksspielstaatsvertrag: “A game of chance exists if, within the framework of a game, a fee is charged for the acquisition of a chance to win and the decision on the win depends entirely or predominantly on chance.” But how can this be measured objectively?
The researchers addressed this question in a game-theoretical study. According to their own statements, they used data from over four million online matches of chess, poker and Skat. From this, they developed a rating system based on the Elo rating method used in chess. This number describes the strength of individual players. “Since chess is a pure skill game, the Elo ratings of players vary widely. They range from under 1,000 for a beginner to over 2,800 for the current world champion. The wider the distribution of player ratings, the more important the role of skill,” explains Dr. Peter Dürsch. With a higher proportion of luck and chance, these numbers would therefore not be so far apart.
Apply method to all games
This is exactly what the scientists’ results showed: For poker and Skat, this spread is significantly smaller. While the standard deviation – the average deviation from the mean – for chess is over 170, it does not exceed 30 for the other two games. To create a benchmark for a game that depends more than 50 percent on chance, the researchers replaced every second game in their chess dataset with a coin toss. In this case, they calculated a deviation of 45, which is still significantly higher than that of poker and Skat. “Both games thus fall below the 50 percent skill threshold, meaning they depend predominantly on chance,” says Marco Lambrecht. “Nevertheless, skill prevails in the long run. Our analyses show: After approximately one hundred games, a poker player who is one standard deviation better than their opponent would have a 75 percent probability of having won more games than their opponent.”
According to the scientists, the method can in principle be applied to all games where a winner is determined. For example, the skill component in the popular card game Mau-Mau is even lower than in poker, while the skill component in the Chinese board game Go is even higher than in chess.