Streaks

It seems like everyone and almost everything goes through streaks. By streaks, I mean a prolonged series of consistent results that seem significantly different than what you would expect. There is a theory that most results, that appear unusual, are really random fluctuations in large samples. If you are interested in this check online references to the Hot Hand Fallacy. The original studies focused on basketball shooting. There are also studies that contradict that theory and say that there are streaks. It certainly seems to me that there are many streaks in non-random events. When humans are involved, we are not random. Our psychology, practice and life style influence our results. When things are going well for us, we tend to be relaxed and confident, and continue to do well.

Obviously, the reverse is also true. The problem is telling random streaks from streaks due to specific causes. There has been a streak of global warming for at least the last 20 years. Most scientists feel that human activities, especially increasing CO2 in the atmosphere, is primarily responsible. But a case can be made that other factors, like solar activity or random variations in the earth’s orbit, are the main contributors. Instead of discussing humans trashing the planet, let’s discuss something important – streaks at poker.

First let me discuss my own recent streaks in cash games and tournaments. In cash games, I have been playing a lot of pot-limit Omaha at Aria and a lot of no-limit hold’em at Bellagio. Most of it has been at the $5-$10 level (the PLO is actually $2-$5-$10). I have played a little at higher and lower stakes but not that much. My normal session is from 3 to 6 hours long, and my big wins have been bigger than the amount I’d ever allow myself to lose in one day. I have played a few tournaments before the WSOP, and a variety of the smaller WSOP events. I usually entered the tournaments after the early levels. My tournament goal is to have a large cash, not grind my way to a min-cash. I have been on two streaks. In cash games, I have won 19 out of the last 20 plays.

Over this same period, I failed to cash in over 15 tournaments before finally cashing in the Seniors and Super Seniors. If you know the chance of something happening once, how do you calculate the chance of it happening a certain number of times in a row? You raise the odds to the power of that number of times. For example, what are the chances of five heads in a row? ½ to the fifth power or ½ times ½ times ½ times ½ times ½ or 1/32. It is important to understand that streaks are often random. If we flip 32 coins, and one comes up heads five times, it is not a more skillful coin than the one that never came up heads.

Let’s test some random streaks. I win around two-thirds of the time in these cash games. Here is a table showing the chance of some streaks: the first column gives the winning chance and each column gives the chance for a winning streak of a given length.

Winning Chance 10 in a row 15 in a row 20 in a row
65% .014 .0016 .0002
70% .028 .0047 .0008
75% .056 .0134 .0032

Notice how small all these numbers are. At a 70 percent win rate, if I played 10 sessions in a row 100 times, I’d only have about three streaks of 10 wins. The fact I actually had one losing session in the middle of this streak, makes the numbers much bigger, but my chance of winning 19 out or 20 is still very small. What about my chance of an extended losing streak? That chance is almost infinitesimal. I won’t bother with a full table, but if someone wins 65 percent of the time, he loses ten times in a row only .00003. A winning player should lose 10 in a row less that once in a thousand sets of 10 sessions.

Now a tournament chart:

Chance of no cash 10 without cash 15 in a row 20 in a row
85% .20 .087 .039
80% .11 .035 .012
75% .06 .013 .003

What should you take away from all this? First, streaks are unusual. Even if the event is relatively likely to happen, it is not likely to happen every time. Second, winning cash game players will seldom suffer a long losing streak without an occasional win. Third, tournament players should expect fairly frequent droughts. This implies that you need a larger bankroll for tournament play. You also need a lot more fortitude, since you will inevitably suffer some bad streaks. Remember that random variance causes most streaks. Everyone goes through periods where they lose races and miss flush draws. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years. With two WSOP bracelets and few million in tournament cashes, he is easing into retirement. He currently devotes most of his time to poker. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City -The Library near Houston and Doc Holliday’s on 9th St. are his favorites.