A Bad MetricThe first problem with the question: 'Is poker a game of luck or skill' is its phraseology. In the short-term, there is no such thing as a skill level sufficient to guarantee good results. In the extreme long-term, there is no such thing as a level of bad luck that can stop a winning player from winning or grant a losing player a positive win-rate. From this point on, then, we shall use four different terms instead of two. These will be short-term skill; short-term luck; long-term skill, and long-term luck. In doing so, the true nature of poker will become much clearer.
Short-Term SkillHaving a skill advantage in the short-term is simply being a little more likely to win than your opponents. When non-poker players ask me whether there is any skill in poker, I like to use the weighted coin analogy, which goes as follows:
Imagine that you and your opponent both hold a coin and are each going to flip your coin 50 times. The winner will be whoever flips the most heads. The other person's coin is a normal everyday quarter, euro, or pound – it doesn't matter – the chance of flipping heads is 50%. Your coin, however, is slightly weighted so that it will land on heads 52% of the time. It's difficult to imagine this 2% advantage constituting a certain win over only 50 flips, but it does make it a little more likely.
When a professional poker player puts in a short session against a few amateurs, his expectation is small but definitely very positive. As this session becomes longer and turns into two sessions, a week, a month etc. the professional starts to have a much higher probability of cleaning up.
Short-Term LuckLuck plays a very large role in the outcome of a hand, session, or even a week in the life of a professional. All of these time frames are relatively short compared with a year or a 200,000-hand stretch. It is these longer time frames that define success in poker.
One thing that makes win-rates lower on a poker site or in a casino than they would be in a home game with friends is rake. We have to pay a fee to the site in exchange for the gaming service we receive; just like we pay for a sandwich or some petrol. If there is only a 52% chance of winning because your win-rate is quite small after the rake comes off your winning hands, then a 50-hand sample could really go either way – just like the flip of the weighted coin. Think of it this way – imagine that instead of playing poker or flipping a coin that you were spinning a wheel that went from 1-100. You win on 1-52 and your opponent only wins on 53-100. Your edge only means anything when the wheel comes 51, or 52. If you exclude these two numbers then the chances revert to 50:50. This is how big a role luck can play in the short-term.
The overall picture looks like this, the more you play the smaller the influence of luck becomes:
Long-Term SkillWhat the sceptical beginner fails to realise is the reliability of what we call the law of large numbers. This law states that as we exponentially increase the number of instances of an experiment, the true outcome will move closer and closer to the expected statistical outcome. Take a break-even player, for example, his poker results will look like this:
Note that the X axis here is not to scale. We are accelerating from one hand on the far left through to a million hands on the right. Although luck still governs each short-term outcome, as we zoom out to view a longer-term picture, the break-even player is virtually guaranteed to break even. Everything that happened during the first few thousand hands, was due almost exclusively to variance and any conception that he was a winner, or a loser, was flawed. As we view stretches of hundreds of thousands of hands, however, it becomes almost impossible for this player to win or lose money unless he improves his game or tilts in a long-term way.
Contrast this to the results of a winning player over exponentially larger timeframes:
Long-Term LuckWe have learned that the impact of luck in poker is diminished over large samples and eliminated over infinite samples, however, most people still under-estimate the chances of running good or bad for a long time, particularly if they are low-volume players. Let's say that a slightly winning player plays for four months. This might seem like a long time, but if he or she is also busy with a full-time job and raising a family then poker time might be just a few hours every week. This could equate to only a few thousand hands a month. It might take this player years to amass enough of a sample to start to see the pure picture of his or her win-rate. Any judgments this player makes about his or her game or win-rate based on results over this timeframe will be an illusion. This player is very much still being blown around by the winds of variance. He or she is at the start of the two graphs above and at the far left of the bar chart above.
ConclusionBy now you might be thinking: 'Okay, Pete, this sounds reasonable, but why should I care.' In fact, it is crucial to your poker progress that you have a sound understanding of the balance of luck and skill and of the law of large numbers. Failing to do so can result in a warped sense of poker reality or an inflated or deflated ego, which in turn can lead you down the wrong path for moving forward.
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