# Strategy / The Luck Factor and Poker

## The Luck Factor and PokerSamedi, 28 juin 2014

Is luck a more important factor than talent in poker? How many times have I heard this question! While the question is always the same, the answers vary. Depending on their mood and their recent results, players opinions will vary from one extreme to the other. While some will swear that only luck dictates the results, others will whipe it out of the equation completely. To solve this debate, others will simply estimate a ratio of 70-30, or other subjective numbers, favoring talent.

Who’s right in this discussion, and more importantly, why?

The answer to this question rests on a basic statistical comprehension, as well as on the nature of chance itself. What is luck? In poker, luck simply is variance, positive (luck) or negative (badluck) compared with the sum of average results a player can mathematically expect to obtain with each of his decisions.

Of course, the expected sum total is impossible to evaluate precisely, except for all-in hands where all live hands are opened and known.

In poker, variance is a concept directly linked to volume of hands. Take a coin for example, when you are playing heads or tails. Your success rate, no matter wich side you choose, will always be 50%. If you throw it only once, your average win rate will either be 100% or 0%. The difference relative to your average expectation will always be 50%, no matter the result.! On a single trow, you will either be lucky or unlucky.

Now, trow the coin 10 times. Nothing garantees you that you will end up at 50%. It is very likely that your win rate will be 70-80%, as well as 20-30%. Very seldom will it be 0 or 100% but it will happen. Nonetheless, it will tend to nearer 50% than on a single toss.

Trow the coin 1 000 times now. You can now be quite sure that your rate will be nearer to 50% again. It will most probably be between 40% and 60% and will have steered away from the extremes. Trow the coin one million times now. The difference between the number of heads and tails will have increased but the sampling is so large now that it would be very surprising if the win rate was not between 48% and 52%.

In other words, the larger the sample, the less variance applies. This also means that the luck factor diminishes with each and evey hand played and always slides towards zero.

Of course, unlike in a coin flip, your average win rate will vary with each decision you take in every hand you play. Nonetheless, the same principle applies. If you make decisions with a positive expected value ( EV) more often than the opposite, you will be garanteed positive results in the long run. This doesn't mean that every session you have will be positive! You can play perfect poker for a whole session and still finish in the red. The opposite is also true of course. But you cannot cheat long term. Your results eventually will reflect on your level as a player, without luck having any role to play in the results.

So what does this mean in relation with our main question? There is no unique answer. The luck factor is very important on a single hand, then diminishes with every hand played. In the end, for a serious player who works on his game and plays a lot of hands daily, it means luck has no influence. He will still absorb it in each and every single hand, but in the long term, it will not be a factor.

Let me make a precision on this last sentence. If luck flattens out on long term, this does not mean that a losing session will be followed by a winning one. Is this paradoxical? Absolutely not. Your last result has no bearing on your next ones. If you suffer a 1000$ negative difference with your expected gain during a month, dont expect to get better results in the next month. As a matter of fact, the most probable possibility for the next month is that you will still have this negative difference. On the other hand, you will have doubled your number of hands played. Thus, it’s the volume of hands played that gives you your true EV. Don't make the mistake of thinking “you are overdue for a win”!

Every poker player will have both lucky and unlucky sequences. What this article shows is that there is nothing abnormal to this and, over long term, this factor will diminish until luck is absent from your results. The conclusion goes like this: no matter what your short term results, you can be certain you will drift towards your real EV in the long term. So it’s important to always play your best poker and to never let this daily variance affect you. By always taking the best decisions, no matter the results, you make sure your long term EV will be better.

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