Discipline: Part 12 – Bankroll Continued

I am nearing the end of this series of columns on discipline. So far I have discussed avoiding tilt, finding good situations, physical conditioning, and mental conditioning. The last two columns discussed the topic of building and maintaining a bankroll. It is impossible to succeed as a professional poker player (or in any profession that involves dealing with risking your capital in situations where is outcome is uncertain, like trading options) without being able to manage your bankroll. This requires knowing what to do and the discipline to do. These are my first two rules of bankroll management:

Steve Zee’s Bankroll Rules:

1. The larger your bankroll is, the less risk you should take.
2. Always know how much you can risk.

In this column, I am going add the third rule: The more unlikely winning is, the less you should risk. It is very easy to go astray trying to maximize your equity. In general, you want to make the bet with the highest equity, or stated simply make the bet that earns you the most. Let’s look at a simple case. You have a choice between bet 1 and bet 2. Bet 1: You risk $1.00. Half the time you end up with zero and half the time you end up with $3.00. On average, you will have $1.50. This bet has an expectation or equity of plus fifty cents. Bet 2: You risk $1.00. Two-thirds of the time you wind up with zero, but one-third of the time you end up with $5.00. On average, you end up with $1.68. This second bet has an expectation or equity of plus 68 cents. If you can only make one of these bets, and since .68 is greater than .50, you should choose Bet 2.

The choice above is relatively easy. The amounts you are risking are small, and the chance of winning is reasonably large. Now what about Bet 3? You risk $1.00. 99 times out of 100 you lose your dollar. One time out of 100, you get $200. If you play 100 times, you will average 99 losses of one dollar and one win of $199, for a net result of winning $100. This third bet has an expectation or equity of plus one dollar. If you can only make one of these bets, and since $1.00 is greater than either .68 or .50, you should choose Bet 3. Even though winning is pretty remote, this bet still has a much bigger equity than the others, and the risk is still small, so it makes sense to pick Bet 3. But you should have a nagging feeling that, even though this bet has more equity, it might not be as good as one of the others. You should be thinking, I only have a one percent chance of winning, and that is pretty bad, even if my equity is good.

These bets were all for miniscule amounts. Now let’s change the situation. Multiply the amount you can bet by 100,000. You are fortunate enough to have a nice fat bankroll of half a million dollars. Let’s say you have can make one of those three bets for $100,000. You can chose Bet 1, 2 or 3, but you are now risking 20 percent of a large bankroll. Each choice has plus equity. For Bet 1, it is plus $50,000. For Bet 2, your expectation is to win $68,000 (rounded.) For Bet 3, you will average winning $100,000. Even though your average win for Bet 3 is a lot bigger than for either of the others, even an adventurous plunger should know enough not to risk 20 percent of his bankroll on something he will only win once in one hundred trials.

For those of you, who enjoy or are interested in math, look up the St. Petersburg Paradox, which shows how little one should pay for something with an infinite expectation. Here is one reference: https://en.wikipedia.org/wiki/St._Petersburg_paradox
Don’t think these are really unusual situations. True, you will never face a St. Petersburg-style gamble, but you will frequently have to decide between two gambling choices where the one with more equity has a more remote payoff. Here is a decision players face all the time. Given my current bankroll, should I enter a $1,000 buy-in poker tournament where I will win an average of $50 per hour, but only cash around 10 percent of the time or should I use that thousand to enter a cash game, where I will win 60 percent of the time, although my average winnings will only be $40 per hour?

I will continue this discussion in the next column, but for now remember my rules for managing your bankroll.

Steve Zee’s Bankroll Rules:

1. The larger your bankroll is, the less risk you should take.
2. Always know how much you can risk.
3. The more unlikely winning is, the less you should risk. ♠

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.