What needs more skill poker or chess

Is poker a game of chance or a game of skill?

The aim of this article is to shed light on whether poker is more of a game of chance or a game of skill and show, using examples, that this question does not make sense in itself. Poker is both luck and skill.

In the discussion of luck versus skill, it is often assumed that games can be arranged linearly on a scale, with pure games of chance on the one hand, pure games of skill on the other and mixed forms in the middle.

Such an arrangement could look something like this:

The question of whether poker is more of a game of skill or a game of chance is then limited to whether poker is more to the right or more to the left.

However, as I will show in this article, this representation is beyond measure, and I want to argue that a game can have both a very pronounced component of luck and skill. I took many of my arguments and ideas from Mike Stein, who wrote an excellent and very detailed series of articles on the subject on QuantitivePoker.

In order to be able to classify the game of poker, I first look at other games and check them for their luck and skill factor.

Chess - just skill

First of all, I take chess, the game that is considered the prototype of a game of skill. Chess is a game with complete information and, as Ernst Zermelo proved at the beginning of the 20th century, theoretically solvable. That said, there is a perfect strategy for both players. However, the game is so complex that it is not yet known whether this perfect strategy will result in a win for White, a win for Black or a draw1.

In chess, differences in the skill level of two players are very clear, so an amateur will almost always lose to a grandmaster.

However, it is still possible that a weaker player beats a stronger player in a game with luck. A player who always randomly chooses a regular move can, with a probability greater than zero, choose the best possible move in the respective situation. If a player acting in this way randomly chooses the best possible move enough times in a row, he can beat a significantly better player. Granted, the likelihood of this happening is extremely small, but it is possible, and it shows that in chess, too, it is possible that a weak player can defeat a strong player. Or in other words: chess also has a component of luck. Nevertheless, luck plays such a minimal role in chess that this game can be described as a practically pure game of skill.

Rando-Chess - Skill and luck

One can also modify chess so that it has a luck component. Dr. Richard Garfield, the developer of Magic: The Gathering, suggests the following chess variant, called Rando-Chess, as a thought experiment: The game is played like a normal chess game, but at the end a dice is thrown. If this shows a one, the losing player is declared the winner. Obviously, this Rando Chess variant now has a significant amount of luck. Even the worst player has a one-sixth chance of winning a game.

Is Rando-Chess a game of chance or a game of skill? If you want to classify the game on a one-dimensional skill-luck scale, you would have to consider the luck component and place the game further down the middle. However, the way of playing Rando-Chess is identical to that of normal chess. There are no new strategies, the game doesn't get any easier or less complex, and a better player will always prevail over a worse player in the long run. In this respect, it would be clearly wrong to attribute a lower skill component to the game Rando-Chess than to regular chess.

A better classification would be to assign Rando-Chess the same skill component as that of regular chess and to add a luck component to the game. The classification must be two-dimensional.

Nim game - neither skill nor luck

As the next variant, I will briefly consider the Nim game. This game works as follows: two players compete against each other and there are 20 matches on the table. Each player can take turns taking between one and five matches. Whoever takes the last match has lost2.

The game has a very simple winning strategy for the attractive player: He always takes so many matches that 1, 7, 13 or 19 matches remain on the table. Then his opponent cannot win this game.

Is this game a game of luck or skill? Obviously, there is no significant element of luck in this game. Although a player can play the winning strategy purely by chance, this luck, like in chess, does not play a decisive role. On a one-dimensional skill-luck scale, the Nim game would have to be placed on the skill side.

But to describe the Nim game as a game of skill is absurd. The winning strategy is so trivial for halfway intelligent players that at best it can have a minimal component of skill. In fact, this game is neither a game of luck nor a game of skill, which must also be shown when classifying the game. Just like Rando-Chess, this can be done in two dimensions.

Game of chance and skill

As the two examples Rando-Chess and the Nim game show, it is far more appropriate to assign games both a skill component and an independent component of luck instead of trying to arrange them one-dimensionally. If you want to classify a game, you have to take both components into account. Such an arrangement could look like this:

Two-dimensional arrangement of games. Bottom left: Nim player; neither luck nor skill. Top left: slots; strong luck and non-existent skill component. Bottom right: chess; in fact pure skill. Top right: Rando-Chess; Game of skill with a component of luck.

I left poker out of this arrangement because the aim of this article is not to classify the game of poker accurately. The main thing to note is that poker is both a game of luck and a game of skill and an either / or question makes very little sense when it comes to classification.

Poker is a game of chance

There is clearly a strong element of luck in poker. Regardless of the specific variant, the entire gameplay is designed so that the cards are randomly distributed and the players do not know which cards are held by the opponents or which cards are still revealed.

The outcome of a single hand in poker is also random as it correlates strongly with the cards dealt. In this respect, it is correct to refer to poker as a game of chance.

Poker is a game of skill

Nevertheless, poker also has a pronounced skill component. This is easiest to understand when you consider that in virtually every variant there is a very rich amount of possible game strategies.

Each player has the opportunity to carry out various actions at least once and, if necessary, several times during the game. These are structured in a comparatively simple way (usually they are limited to bet / raise, call / check or fold), but give every player the opportunity to have a significant influence on the further course of the game.

In fact, it is possible to specify different strategies for each of the random card constellations, each previous game and each opponent constellation at the table. In mixed strategies, there is even an optimal strategy for each constellation, which delivers the best possible expected value.

In fact, all forms of poker are so complex that it has not even been possible to begin with to describe such an optimal strategy. This is a strong indicator that skill plays a prominent role in poker. A simpler but equally powerful indicator is the abundance of poker strategy books available on the market - including very theory-heavy books such as "Theory of Poker" or "Mathematics of Poker".

There is a popular saying that poker is a game of chance if you only play one hand, but a game of skill if you play a few thousand (or ten thousand) hands. This statement is only partially correct - in fact, in most interpretations it is even wrong; Poker always has the same component of luck and skill. In the next article in this series, I will consider the conditions under which the skill component dominates the luck component in terms of results.

Relevant links
"Dr. Richard Garfield, Luck vs. Skill, video, English
“Mike Stein, QuantitivePoker, English

1 For other, less complex games with complete information, such perfect strategies can be given. In 2007 it was shown that a perfect strategy in the game of checkers leads to a tie. As early as 1988 it was shown that the attractive player at Four Wins can always win the game with perfect strategy.

2 There are countless variants of the Nim game. The one described here is a simplified Misère variant.