the skill factor

This is a slightly modified article written a few years back. It’ll be the last one for the foreseeable future.

Which version of poker requires the greater skill? We’re all biassed one way or another; prone, perhaps to vouch for which we know, or succeed at – whether it's because we witness greater depth or are driven to service our ego. Still, for others it will be the converse, the games foreign seem more complex, leaving us unsure underfoot. This article will at best only vaguely inform, on what is, a rather ambiguous and somewhat intractable question.

Poker, like most games, is a combination of both luck and skill. It is, it seems, entirely rational to state a game more dependent on luck to be a less skillful game. Classifications, of say, ‘80% luck, 20% skill’ are tempting, and arguably, provide some insight; however, it is not meaningful to qualify a game’s skill-level this way. Our personal ranking order of skillful games doesn’t, nor shouldn’t, faithfully follow some simplistic percentage-luck metric: compare snap and tic-tac-toe to poker, backgammon and bridge. Are the skillful games more or less reliant on luck? There are qualitative and quantitative attributes of skill in a game.

Those who’ve undertaken some basic measure of computer programming will likely recall being tasked to code a sorting algorithm. A common poser is to orgnaise a group of numbers into numerical order, and or, possibly, the more taxing version, to sort a list of words alphabetically. Each rinse of the program creates a more ordered list [1], until, the task is completed – within a determinable maximum number of loops.

One might argue a poker tournament serves as one cycle of a sorting algorithm for players, albeit a somewhat stochastic one: the list might easily become less entropic after one tournament loop. However, you’d figure, eventually, given enough tournaments to arrive at a perfect ordering of ability for 100 fixed-skilled players. Though, unlike, the word and number sorting algorithms there is no upper-bound on the number of loops guaranteeing a completed task. In the real world of poker, though, the very thing (skill levels) set out to be ordered in the first tournment, no longer exist at the start of the second: abilities change.

It appears quite apparent, in tournament poker, Limit-Hold'em (LH) orders better than No-Limit (NL) : skilful Limit-Holdem players should, like for like, expect to outperform their NL counterparts. Still, even were such an assertion shown to hold true, it in no way testifies to a more skilful game, or skilled players. What it would evidence, is limit-holdem discriminating better between players, than NL. Thus one’d anticipate the limit version of holdem to establish rank more readily than NL in our iteration of poker tournaments.

Perhaps one way of attempting to model Limit-Holdem would be to identify it as a series of multiple-choice questions; NL might also be approximated similarly, but of course with a greater number of choices, albeit approximated.

Now, it is without modesty, that I can currently claim to hold both a better vocabulary, mathematical insight than my 7-year old neice. However, it is, clearly, trivial to set 50 mutiple-choice mathematical questions, or tests of vocabulary, to which I could fail to hazard any sort of meaningful guess. Such questions might tax the knowledgeable, or brilliant, but they’d fail to discriminate between our respective abilities, or knowledge.

A continual lowering of standard, will, eventually, yield the odd problem I’d reckon on tackling, or guess at educatedly. Yet in spite of this edge, I could easily lose, since in only a handful of instances are my responses an improvement on outright guesses. But as the quality is relaxed still further, a point should eventually arrive, hopefully, where I’d anticipate confidently answering all 50 questions, and where she is still forced to guess at all of them. At this level the test discriminates very well (but measures poorly) between our respective knowledge of the subject.

Continued simplification will witness a juncture where we are both able to answer all 50 questions: once again the test fails to discriminate. Clearly, the level of difficulty mostly likely to discriminate between candidates isn’t the one offering the superior challenge or requiring the greatest degree of skill or understanding, or naturally, the simplest one either.

Bidding to analogise more meaningfully with NL/Limit hold'em tournaments debate, we might choose to spice up the multi-choice. Suppose in a discriminating multiple-choice test we implenent a scoring system tolerating 3 mistakes; the score awarded is the running score when the third error occurs. Then run it with, say, with 6 strikes, or one strike: which of the tests is likely to reveal a more representative order of ability?

While the questions are the same in both cases the penalty for failure isn’t. One could easily design a test that would both discriminate and challenge more than another on merit alone, but if the penalty system employed was stern enough, it’d be expected to do less well at sorting out the participants in order of ability: higher variance. It certainly appears NL hold’em has a higher penalty system for poor decision-making*: the limit version yields more lives. That said, employing a heavy penalty system could serve as a better discriminator too. In life, for example, one person may get more day to day life-decisions right than another person, but may have a tendency of getting the important ones wrong. Which of them will be the happier? But if a set of tennis were settled by the first unforced error from either player, what odds for Nadal at the French Open?

The weighting or importance assigned to different decisions or outcomes is crucial when trying to ascertain an individual's effectiveness, ability or, indeed, to establish a proper order of things. Calling down a possible bluff on the river in NL often holds a far greater penalty for failure than such a call in Limit-Hold’em. It might appear that the ‘weights’ are a little kinder to the limit player.

So, in conclusion: the skill factor in a game is measured in terms of quality as well as quantity; a game that more readily discriminates between players isn’t necessarily more challenging or more skilful; heavier penalties for poor decision-making can level the playing field; it is not a paradoxical to state a game to be both more luck and skill dependent than another.


*Note, by suggesting a game has a heavier penalty system one is not implying it is more reliant on luck. A game can be deterministic, free from luck and uncertainty, yet still employ a penalty system. One might consider the luck aspect of a game to be the extent to which poor decisions can be rewarded and, consequently, good ones penalised or indeed how much of the game is free from decision-making all together.