Everyone who gambles at anything - and, of course, this includes poker - should know at least a little bit about probability. The chance of an event happening is always between 0 and 1.0. An event that can't happen has a probability of 0. An event that is certain to happen has a probability of 1.0. The probability of a coin landing heads is 0.5. It happens half the time. The chance of a die landing on 6 is one-sixth, or about 0.17. The chance of an event happening is simply the number of ways the event can happen divided by the number ways that anything can happen. If 10 percent of the players in a poker tournament will cash, the average player has 0.10 chance of cashing. If there are 600 players in the tournament, the average player has approximately 0.0017 chance of winning (1 divided by 600).
My own research has shown that 90 percent of poker players believe they are above average. Almost 50 percent believe they are in the top 10 percent. This is impossible, or at least highly unlikely. If 10 percent never win and the remaining 90 percent are all equally skilled, that 90 percent are all above average. The real picture might be the reverse of this happy picture; 10 percent of the players win way more than their share, leaving the entire remaining 90 percent with below-average returns. Let's make some simplistic assumptions about the average player: In a cash game, he wins half the time. In a tournament, he cashes 10 percent of the time. If there are 600 players, he makes the final six players, 1 percent of the time, and wins 0.17 percent of the time. Given these assumptions, what are the chances of an extended losing streak, uninterrupted by even a single win?
I hope you already are familiar with the math that follows. If not, you should seriously consider brushing up on the basics of probability. If this is all beyond you, and you want to see some results, just skip to the chart below.
Let's suppose that we decide to look at the chance of having at least one win during a series of 10 games or tournaments. It is quite arduous to calculate all of the possible ways of winning. You could have one win in any of the 10 sessions. You could have two wins in a variety of ways, and so on. Instead, we need to calculate only one number - the chance of having no wins and subtract it from 1.0, since the chance of having no wins and the chance of having at least one win add up to 1.0. (As mentioned above, a certain event has a chance of 1.0. Since the only possibilities are no wins or at least one win, the two possibilities must add up to 1.0.) The chance of a series of failures is the chance of one loss multiplied by itself, the number of times we are interested in. For example, if you win 60 percent of the time, you lose 40 percent of the time. The chance of a player who loses 40 percent of the time losing twice in a row is 0.4 times 0.4, which equals 0.16. Three in a row is 0.4 cubed, or .064. Using this neat little trick, I have calculated the chances of losing 10 in a row and 24 in a row. Why these numbers? I chose 10 because it is a nice round number. I chose 24 because it represents about a month of playing five days a week or a year of entering two big tournaments a month.
The following chart looks at our average player. In a cash game, he wins half the time; therefore, he loses half the time. In a tournament, he cashes 10 percent of the time; therefore, he finishes out of the money 90 percent of the time. If there are 600 players, he makes the final six players 1 percent of the time, and wins 0.17 percent of the time; therefore, he fails to make the final six players 99 percent of the time, and fails to win 99.83 percent of the time.
Notice what this means: An average cash-game player will seldom lose 10 times in a row and, for all practical purposes, never lose 24 times in a row. The poor average tournament player has a much worse fate. He will go 10 tournaments without a cash more than a third of the time. He will even go 24 tournaments without cashing nearly 10 percent of the time. We all know that tournament payouts are very top-heavy. So, just cashing may not be worth much. What about making the final six players? Our poor average guy fails to do that 10 times in a row most of the time, 90 percent. He even fails to make the final six players, 24 times in a row nearly 80 percent of the time. Imagine that.
If he plays two big tournaments a month, in almost four out of five years, he will fail to make the final six even once. When it comes to winning, his situation is truly bleak. He will fail to win a tournament 24 times in a row 96 percent of the time. Playing 24 tournaments a year, he will fail to win one in 19 out of every 20 years.
Are there any morals to this sad story? Yes. First, the dire fate of an average player makes one appreciate how good (and/or lucky) the tournament superstars must be. Second, it should reinforce the fact that successfully playing the tournament trail requires not only a large bankroll and great skills, but also the ability to accept frequent defeats without sinking into a sea of depression. Third and last,
you will receive less glory as a cash player, but will have a lot more happy days. 
Steve "Zee" Zolotow, aka The Bald Eagle, is a successful games player. He currently devotes most of his time to poker. He can be found at many major tournaments and playing on Full Tilt, as one of its pros. When escaping from poker, he hangs out in his bars on Avenue A - Nice Guy Eddie's on Houston and Doc Holliday's on 9th St. - in New York City.
