There are some misconceptions concerning the relationship between randomness and skill that have been expressed on this forum. I would like to give everyone some food for thought. As an aside, I am a published author on applied statistics in academic journals. While game theory is not my specialty, it is a subset of applied statistics and utilizes a statistical approach.
Another poster in another thread - arguing against the inclusion of random elements to the gameplay - asked how much skill is involved in guessing cards pulled randomly from a deck. While the answer is “None”, it is the wrong question to ask. To find the right question, we must decide what we mean by “skill”.
First, let’s look at a completely deterministic (i.e., no randomness) gaming example, like the original Mario Bros. Whether we measure skill as time required to complete a level, defeat all enemies, maximizing level score, or finding all bonuses, the measurement quantifies the ability to press controller buttons in the optimal sequence using visual cues to supplement memory. In other words, “skill” in Mario Bros. is a proxy for memorization ability, and the expected value of a successful outcome is entirely a function of memory, where expected value is the ratio of successful outcomes to total attempts.
Second, let’s look at a game where the gameplay elements are entirely stochastic (i.e., random), but are used only once and the total number is known, like Blackjack. When a new set of card decks are used, the expected value of a player’s successful outcome is less than 0.5 due to the house advantage. This means that, overall, the player will lose.
As the game plays out, however, the expected value changes. Regardless of the cards that have been played, the house must play in a defined manner. This manner is optimized for maximum house winnings based on random draws. As the cards play out, the actual odds change due to certain combinations of draws being no longer available. A player that tracks the cards played and adjusts his/her own play according to the actual draw odds at the moment can achieve an expected value greater than 0.5. So while this player will not win every hand, overall, this player will be able to beat the house.
Like the Mario Bros example, skill in Blackjack is a function of memory: first the cards played, and second a table of instantaneous odds. And though the game elements are completely random, an unskilled player will be a losing player and a skilled player can be a winning player. It is arguable that it actually increased the skill necessary to win, as one could argue that more people would be successful at Mario Bros than blackjack, given an equal opportunity to learn and play both games.
Third, we ought to make a brief mention of another stochastic game where the elements are used more than once: Texas Hold’em. For each game, the deck is randomized, and cards played on the previous hand do not affect the odds of cards played on the present hand - thus increasing the total randomness of the game play. Moreover, the game is played against human opponents of varying abilities (more randomness) who will not always act in the theoretically optimal fashion given the hand and community cards (bluffing, trapping).
Because of the human element, there is no theoretical solution for expected values beyond pre-flop play. While some have designed automatic playing software that can beat most human opponents, unless the software deliberately plays with some element of randomness, any reasonably skilled Hold’em player can beat them. Only the most sophisticated software approaches world class ability, and none have yet exceeded it.
Despite the large stochastic component to poker play - or, rather, because of it - most would say that playing world-class poker requires more skill than world-class Mario Bros or blackjack. Among non-humans, computers would agree.
However, what may have gone unnoticed is that the definition of skill has changed. In Mario Bros and blackjack, skill was a proxy for memory. While some amount of memory in poker is crucial, many other factors are just as important - or even more important. Interestingly, one of the most crucial factors is randomizing one’s own play rather than simply responding in the probabilistically optimal fashion based on the cards presented.
In game theory, randomizing game elements generally result in higher skill levels being required to maintain expected value above a certain level when compared to leaving game elements deterministic. Randomness generally also requires use of skills beyond memory, while deterministic games can, in theory, be mastered solely via memorization.
The general rule is the less deterministic the game elements are arranged, the harder it becomes to maintain high expected values. In many cases, randomness also reduces the dependence on the memorization ability (though not always; c.f. Mario Bros vs. blackjack). What is important in game design is whether the degree of randomization renders the likelihood of mastery negligible.
In terms of Halo, let us assume that we will measure “skill” in terms of K/D. The base case we will look at is very simple: Equal starts in an octagon with no AAs, ordnance, or specializations. Generically, two abilities will contribute to a high skill measurement: gun skills and movement skills. Given the simplicity of the setting, few other abilities will have a significant impact.
Now let us add in the ability for different weapon starts. This adds a random element (which gun did each player choose) and a deterministic one (the characteristics of each weapon). Now an additional set of skills are required to maintain expected value: first being able to select a weapon for one’s self that maximizes performance given the game situation, and second being able to recognize the opponent’s weapon and playing in a manner that minimizes whatever advantages it has. Since the outcome is no longer dependent solely on gun skill and movement skills, the relative importance of these two items decreases.
This can be viewed in two ways. If one defines “skill” as primarily gun / movement, then one can reasonably argue that the random element decreased the skill necessary for mastery. If one defines “skill” as all abilities that increase expected value, then the random element increased the skill necessary for mastery. As more and more random elements are added, gun / movement skills will become less and less important, and other skills will become more important.
In a game with a high degree of randomness, the number of “mediocre” players increases because the proportion of expected value determined by random factors increases relative to the proportion determined by skill. However, while this pushes more players into the “middle of the pack” (since it hides skill differences below a certain threshold), it enhances the differences between players with enough skill to stand out.
So the question randomness is not really a question of skill. It is actually a question of whether you want to more efficiently rank bad players or more efficiently rank good players based on a defined set of abilities.
