Expected Value at the WSOP

Almost every winning gambler thinks in terms of expected value (EV). EV is also often referred to as equity. The simplest way to think of EV is that it is how much you will win (or lose) on average. If you flip a coin for $100, your EV is zero. Even though no flip can result in a tie, and you will always win or lose one hundred, your EV is zero. If you bet your $100 on the Pass Line at the craps table, your EV is approximately -1.50. In general, you want to maximize your EV. (There are situations in which risk aversion, risk attraction, ego satisfaction, or a variety of other factors may lead you to make a choice that doesn’t maximize EV.) However, for routine daily situations in gambling, investing, or elsewhere in your life, your best result can be reached by trying to maximize your EV.

You should already be making decisions based on maximizing your EV on every hand you play. If your opponent has bet, you have three choices. You can fold, call, or raise. There is an expectation attached to each of these choices. Let’s say you flop a big draw, and there is already some money in the pot. Your opponent makes a bet of about half the size of the pot. Your are quite sure you have positive equity if you call, however you feel that raising will give you even greater positive equity since they might fold or you might miss the turn and still get to see the river for free when your opponent checks. The EV for each play might turn out to be: fold EV=0, call EV=50, and raise EV=100. Take time after a session to review some of the plays you made to see if there was a play with a higher EV that you might have used.

I usually try to write a Card Player column with some advice or suggestions for players before they head off to the WSOP. These have dealt with physical preparation, scheduling, bankroll and loss limits, and so on. This year, I want to focus my advice on EV. How can you maximize the expected value of your time in Las Vegas during the WSOP? First, it is essential to make all your decisions based on EV. Keep asking yourself what can I do to make the most money per hour for the hours I spend working. Don’t delude yourself into thinking it’s not work. It might be something you enjoy doing, but you are there to put in your hours and make some money.

I often hear players explain that they have decided to play in an event based on the size of first place or on the amount guaranteed by the casino. These are not really useful measures of whether you should play. Yes, it’s nice to imagine entering an event for $1,500, beating 3,000 or more players, and taking down a prize of $600,000. Even if you are twice as good as everyone else, you will still only win once in every 1,500 attempts. If you played one of these tournaments nearly every day, you’ll win it once every four or five years. Your average return would be $3,000. In reality, very few players are twice as good as the average player. A realistic estimate of your EV might be to win an average of 30 percent of your buy-in or $450. If you spend an average of six hours playing, you will make $75 per hour. Therefore, enter this tournament if you feel there is nothing else you could do that is worth more than $75 per hour. Perhaps you are averaging $100 an hour in cash games.

Notice that your EV of $75 per hour will only be realized after a lot hours and a lot of tournaments. Most often, you will enter for $1,500, and get back nothing. Even when you cash, there will also be a lot of times when you spend 15 or 20 hours, and get back $2,500 for a net gain of $1,000, so you might chose to play a cash game with a slightly lower EV, but with a lot less variance. There are some changes to events at the WSOP this year. Payments have been flattened out so more people will cash. This will lower your variance, but also make it harder to have a really big score. There will also be larger starting stacks. Both of these changes favor players who are capable of playing a solid style longer than they had to in previous years, but you will also have to invest more hours at the table.

Many players find that by starting late, their total EV is increased, even though their EV in the tournament might drop from $450 to $300. For example, let’s say you can average $50 an hour in a cash game. Now by playing four hours of cash, you will win an average of $200 to combine with $300 from the tournament, leading to a total EV of $500. On a typical day, your choices at the Rio might include two WSOP bracelet events, four WSOP small tournaments with buy-ins ranging from $135 to $365, one-table satellites with a variety of buy-ins, super-satellites, and cash games. There will also be tournaments and cash games at the Aria, Bellagio, Venetian, and many smaller venues. Before rushing off to play, try and decide where you will have the most EV. Not an easy task to accomplish, but well worth the effort. ♠

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.