Luck, Skill, Probability; They Interact to Bias Your Results

We all want to have luck – good luck, that is. We want to avoid bad luck. Luck comes and goes. Some days the cards just seem to fall into place, and you are a big winner. But other days, the opposite holds, and you go home a loser. Oh, well, tomorrow is another day.

Skill is the ability to use knowledge to achieve an objective. When playing poker, your objective is to win! By learning the rules and strategies for winning poker, you become skilled. Read books on poker, analyze hands, and discuss strategies with friends. Playing experience is a great teacher; while playing, observe and analyze hands to become more skilled.

Skill is forever and can grow; luck fluctuates. Once you have become skilled, you have a valuable asset that is yours forever. Cherish it! Unlike luck, skill won't fluctuate. Skill is either zero or positive. Unlike luck, skill is never negative. That's a big advantage – compared to fickle luck, which can vary from deal to deal: up one day (like the stock market), good luck; down the next, bad luck. You cannot control the luck factor, but skill is something over which you have control, and you have the power to gain yet greater skill.

Losers often blame bad luck for their losses. Luck is a factor in the short term, but skill makes the difference in the long run. What's more, skill can make a difference in the short term – even when luck is running against you. A skilled player minimizes his losses when his luck is bad. And, as a corollary, he maximizes his winnings when his luck is favorable. That's where probability comes in.

Probability is a part of statistical analysis that deals with likelihoods rather than absolutes, which are free from imperfections or control. What is the chance, the likelihood, the probability of something happening? Flip a coin; the probability that it will land "heads up" is 50-50; that's 0.50. In the long term, the coin will come up "heads" half the time. That assumes the coin is "fair" – not biased in some way. (I've seen a coin with heads on both sides.)

When you become skilled, you can bias the results. Luck can be either good or bad, although it may not seem that way sometimes. In the long run, it's even money: 50-50. The probability is 0.5 – just like flipping a fair, unbiased coin. You should have good luck just as often as bad luck. Assuming that all players are equal, the frequency of winning and losing sessions and the amounts won and lost should even out – neglecting the rake and tips to the dealers.

But, all players are not equal in skill; the more skilled player will win more often and more money than the unskilled player. Why? Think in terms of probability theory: Skill causes the luck factor to be biased; the frequency of wins and losses is skewed in the direction of wins. The more skilled a player is, the greater the shift in the curve. And when playing during a run of bad luck, the losses are less.

Skill can turn a bad-luck event into a win. Here's an example: You start with a three-card flush, ace high, in seven-card stud with a 9 as your doorcard. On fourth street, you pair your doorcard. Then you catch a fourth card to your flush:

A Q 9 9u 10

You are high on the board and bet. You then catch a rag on sixth street; you still have only the pair of nines and a four-flush. Four clubs have fallen in your opponents' hands, so there are five clubs still "live" out of about 30 unseen cards. The probability of making a flush is 5/30, or 1/6. The odds against making the flush are 5-to-1. With about $50 in the pot, your bet of $6 would offer favorable pot odds: For an investment of $6, you could win the $50 that's already in the pot. That's $50/$6 = 8.3-to-1 pot odds. There is also the chance of making three nines or two pair, which might be the best hand. There are lots of "outs," so your odds are even better.

You make a "semibluff" bet – betting with less than the best hand, hoping to force out your opponents, while having lots of outs that could make your hand. You are also establishing the scenario for a possible bluff on the river.

Alas, luck is not with you, as the river card doesn't help. You didn't make the flush, nor did you catch a third 9 or a second pair. You have only the pair of nines.

Two other players are still in the hand. Try to "read" their hands. One player is very aggressive, but he has just been calling your bets all the way. If he had a high pair, he would have raised. He's probably been drawing to a medium straight. You have observed that most of the cards he needs are "dead." It's not likely that he has the straight. The other opponent is a tight player; she doesn't show much on the board, but has been calling all the way. You put her on a medium or high pair in the hole. She doesn't have a pair on the board; hopefully, she didn't pair up on the river.

The chance of your winning with just a pair of nines is not good. If you check, you probably won't win. So, you bluff! It's a sound investment, considering the size of the pot. You had set the stage for the bluff with your previous betting. For added emphasis, as the cards were dealt, you picked up some chips and jingled them in your hand. You boldly make your bet, and then sit back and pray to the poker gods … oh, boy! They both fold. You win! You did not have good luck – yet you won the pot. That's an example of how skill can skew the results and overcome the luck factor. In effect, your skill biased luck – vis-à-vis the "two-sided coin" – to favor you.

On the other hand, perhaps you did have good luck, because neither of your opponents connected to improve his or her hand.

Editor's note: George Epstein is the author of The Greatest Book of Poker for Winners! See his ad in the Players Shopping Guide.