James Keys is a professional poker player who boasts success both at the live and online felt. In 2007, he made the final of the inaugural WSOPE for £61,540. He also became the only player to cash in both main events when he made the money the following year.
I’ll begin this article with two possibly controversial statements:
1. Most poker players are motivated by money.
2. Most poker players don’t act rationally to maximise the amount of money they make.
The first statement is obviously a huge generalisation, but anyone to whom this doesn’t apply (e.g. play money players or Guy Laliberte), will be able to self-diagnose whether or not this is true pretty accurately. If this doesn’t apply to you, you can disregard this article and go find something on strategy. However, players to whom the second statement applies usually don’t realise it, and are often aspiring professionals struggling to make ends meet and don’t know why. Many players think that making money in poker is about playing well, when in fact this is only half the battle at most. I’m writing this article because this is a subject so many players, myself included, are too stubborn or blissfully ignorant to understand.
This article assumes you are a winning player: you know what cards to play, when to bet and why, when to fold, etc. Basically, you’re beating the games appropriate for your bankroll at a good rate. What next? Most players just keep learning about their chosen game - reading strategy or maybe trying coaching videos while practising new skills at the tables - but there comes a point where the law of diminishing returns kicks in and all the effort you put in to learning a new skill only marginally increases your win rate. How do you move forward from there and start earning more money per hour so you can work less and relax more, or move on up and eventually reach the status of pro on the European tour?
The three most important words in the English language for a full-time poker player are ‘Expected Hourly Rate’. Words like ROI, win rate, rakeback, sponsorship, volume, variance, EV and bankroll management are all a means to an end. The bottom line is that your expected hourly rate is the number you’re looking to maximise if you want to earn money from poker, as either a full-time or part-time player.
For poker players, the only scarce resource is time; everyone gets the same number of hours in a day and days in a year. In some circumstances you might want to use expected daily rate, but the same principal applies: you need to weigh up the things like ROI, EV, variance, etc and come to a decision as to what maximises your money earned over time. All poker players at some time or another have irrationally placed one consideration over others or neglected something that ends up hurting their expected hourly rate and, at the end of the day, their long term wealth.
Bankroll Management
“How does bankroll management affect your expected hourly rate?” I hear you cry. “Surely if you’re beating the game, the higher you play the higher your expected hourly rate?” Well, not quite. If variance causes you to go broke and forces you to quit the game that you’re beating, your expected hourly rate drops to zero and starts to cancel out all the big expected value you earned while playing. On average, your expected hourly rate will end up lower than if you’d beaten a smaller game indefinitely. The following example will make it much easier to explain:
Say someone offers you 1.5:1 on the flip of a coin. You have £1,000 to your name and this guy assures you that you can bet as much or as little as you like, as many times as you like and he’ll always offer these odds. How much should you bet on each flip?
Answer #1: It’s an unbelievably great bet, you want to stick as much as you can on, bet £1,000. After the flip, probabilistically speaking, in two parallel universes one of you has £2,500 and one of you is broke, so on average you have £1,250, a win of £250 for just one flip of a coin - not bad, eh? But half the time you’re broke, you’ve got nothing to bet and you’re going to have to let this great opportunity slip through your fingers. You could only get £250 of equity from his indefinite offer of a stupid bet. Surely you can do better than that? Maybe.
Answer #2: Provided you don’t go broke, this guy is giving away free money, just bet a quid each time and every 1,000 flips you’ll win very close to £500, indefinitely. The chance of losing money over 1,000 flips is totally negligible. However, it takes time to flip a coin and since this guy obviously has a screw loose, you need to make as much as you can before he realises his mistake or his carer finds him. You need to maximise your expected hourly rate.
So what amount should you bet to maximise your average return per flip? Now this is where I find most poker players get it very wrong. “Simple, that’s your ROI, it’s 25 percent.” True, but this is your return on investment, the amount of your bet that you’ll win each time on average. Your return per unit time will vary depending on how much you bet. The formula for maximising this value, which again I stress is the only important value to you as a money-earning poker player, is called the ‘Kelly Criterion’. The Kelly Criterion is essential knowledge if you want to be a full-time poker player and there’s a great Wikipedia article on it, including a mathematical proof if you disagree with me - go check it out. If you’re interested, in this case the Kelly Criterion recommends betting one sixth of your bankroll on each flip.
An important note: in the long run, overbetting Kelly is much worse for your bankroll than underbetting, so where precise ROIs and winning probabilities aren’t known it’s best to err on the side of caution and bet lower than Kelly. Overbetting the Kelly Criterion will very quickly lead to ruin most of the time. Also, the basic formula makes no account of the ‘utility’ of the money and so encourages a larger amount of risk than most people are comfortable with. When betting the full Kelly amount, at any one time the chances of losing half your bankroll are 50 percent, thus the chance of losing three quarters of your bankroll is 25 percent and so on. I doubt anyone with a $100,000 bankroll actually wants to risk losing three quarters of it 25 percent of the time if they could have a reliable income for life by betting way under the Kelly Criterion. Many professional gamblers use Kelly divided by 10 to size their bets, which leaves a decent margin for error and will still grow your bankroll relatively quickly.
The basic equation for the Kelly Criterion is f* = (bp-q)/b where:
• f* is the fraction of the current bankroll to wager;
• b is the net odds received on the wager (that is, odds are usually quoted as “b to 1”)
• p is the probability of winning;
• q is the probability of losing, which is 1 − p.
The Kelly formula itself is pretty simple, but adapting it to poker requires some complicated maths. However, there are sites out there (e.g. http://www.cisiova.com/betsizing.asp) that can make the process easier, but will require you to make a number of approximations based on the information you have available to you.
Roughly converted to a poker scenario, the Kelly Criterion therefore states you should be wagering no more than 5.4 percent of your bankroll for a 2,700 runner $1,500 WSOP event. The numbers implemented on this occasion were 84 percent for no cash, 15.4 percent for a cash at $7,000, and 0.6 percent for a final table at $250,000. Obviously these numbers are a bit haphazard given that the field only paid 10 percent but they can’t be too far a stretch from the truth.
I reckon the number of people in your average $1,500 WSOP event that have 20 times the buy-in in their bankroll will be a very small proportion. These people taking shots above Kelly Criterion are doing massive damage to their long term wealth in the process, yet I’m sure most of them will feel inside that they play poker to make money, making their decision to play this tournament completely irrational.
In Part Two, I’ll talk about how poor game selection can hold a good player back and cause a lot of wasted time. Much more than a lack of bankroll management, this is something I have really suffered with in the past so I hope to share the benefit of my experience.
If you would to ask any questions about what I have written in this article, please post on my board on my profile page.