Degree of Randomness vs Skill

Degree of Randomness vs Skill

Every game that is played is on a spectrum from a pure game of chance to a pure game of skill. A pure game of chance would be roulette. There are 37 (or 38 if you are playing a double zero wheel) possible outcomes in roulette. Each outcome has an equal chance of occurring. Meaning if you bet on a single number the odds of you winning are 1/37 or 2.7%.

Game of Chance

Since each event is independent of one other no statistics or skill can increase your probability of winning. This is a pure game of chance, your decisions do not increase nor decrease your chance of winning. No skill is involved. A veteran player will win just as often as a newbie in the long run. There are betting strategies, but the absolute chance of winning is not affected by your bet.

Game of Skill

A pure game of skill would be chess. There are no random outcomes in chess and players have perfect information. The only random occurrence would be who plays white and who plays black. The players have total control over the outcome of the game.

In chess, there are a finite amount of possible positions and moves. This is because of the 50-move rule and threefold repetition rule, which lead to draws. Because chess is finite that means it can be solved just like tic-tac-toe. We can determine the best possible move based on what the final outcome will be. The problem is how many possible moves and positions there are. Too many possible outcomes that no human can calculate. And our computers today even struggle with this if not allowed a crazy amount of time to “think”.

Check out my chess engine ‘Angel‘ I am currently building.

All games fall in between pure luck and pure skill spectrum. Some games fall more toward skill and others toward luck. A popular debate on if a game is more luck or skill is poker. Skill is involved with knowing when to check, bet, raise, or fold. Knowing your opponents’ tells and knowing when to bluff. But there is also a huge luck factor, you have no idea what card is coming out next. You can count cards to help narrow down the probability of what card is coming next but to an insignificant amount.

Critical Repetition Theory

There is a theory by Ingo Fiedler that there is a Critical Repetition Frequency (CRF) in mixed games.¹ Mixed games are games that have both luck and skill involved. The CRF is the number of times a mixed game must be played for the skill to be the greater contributor to the outcome. It’s the point when the reason you win or lose is because of ability, not randomness.

The idea is similar to the law of large numbers. In the long run, the randomness of the game cancels out thus the relative skill between players is exemplified. It’s important to note that he is talking about relative skill, not absolute skill. In the short run, the outcome of a game of poker is luck, but in the long run, it is based on relative skill. This is why a game of poker with your friends seems entirely based on luck yet there are professionals who play as their job. They just played enough games to surpass their CRF threshold.

Sports betting

Sports betting has become a hot topic of skill or luck-based games, especially when betting online. Some states in the US don’t allow for online gambling, so determining whether or not sports betting is skill-based or luck based determined if it was legal or not. Some states require a gambling license to host sports betting.

Draftkings and Fanduel ran into these legal troubles when offering sports betting on their app. But a petition by these companies claimed that skill accounts for the majority of the outcomes in the long run.

It does look like pure luck since any given team can win each game. But in the long run, the better teams win more often than the weaker teams. It’s the law of larger numbers that cancel out the luck in the end and reveals how much skill is required. Draftkings and Fanduel currently do not have a gambling license since it is not required because they run skill-based games, not luck-based games.

Sources

[1] Fiedler, Ingo & Rock, Jan-Philipp. (2009). Quantifying Skill in Games – Theory and Empirical Evidence for Poker. Gaming Law Review and Economics. 13. 10.1089/glre.2008.13106.