Poker Strategy
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The Kelly Criterion: Finding a Balance Between Risk and Reward
A Life Raft With an Engine
Let me begin with a confession. The first time I heard someone mention the Kelly Criterion at the poker table, I thought it was the name of a Scandinavian online reg. The phrase “Just use Kelly” was completely alien to me but I made a mental note to look it up later that day.
Like most of the mental notes that I make, it wasn’t worth the paper it was written on and I forgot about it. That is until poker player Phil Laak started talking about Kelly on a highstakes poker show. I immediately googled it and it has since become the cornerstone of my entire approach to bankroll management.
Some within poker’s intelligentsia criticize Kelly, arguing that it’s too focused on logarithmic growth and doesn’t reflect real-world psychological factors. It is certainly true that variance in poker is multi-dimensional. Beyond the simple win/loss equation, there are risk of ruin, time horizon and opportunity cost factors. In tournaments, there are different payout structures which muddy the waters. There are also life EV considerations.
The biggest thing for me, however, is how Kelly is built on certainty, and poker is a game of estimates. The moment that I grasped the elegant beauty of the equation, it completely changed how I thought about risk, both negatively and positively. It wasn’t just a life raft. It was a vessel with an engine that allowed me to power myself through a sea of variance - guiding me, tempering me, emboldening me.
What is The Kelly Criterion?
Put simply, The Kelly Criterion is a formula used to determine the optimal size of a bet in order to maximize long-term bankroll growth. It is not about survival, nor is it about short-term gains. It’s about compounding at the fastest possible rate while minimizing risk of ruin.
This is the basic formula for even-money bets:
f = (bp - q)/b
Where:
- f is the fraction of your bankroll to wager
- b is the odds received on the bet (expressed as a decimal)
- p is the probability of winning
- q is the probability of losing (1 - p)
For example, if you’re getting 2:1 on a proposition that you estimate to hit 50% of the time:
f = (2 × 0.5 - 0.5) / 2 = 0.25
To put in words, you should bet 25% of your bankroll.
In poker tournaments, however, you are not directly betting on binary win/lose outcomes with fixed odds. Kelly should therefore be adapted by modeling the Expected Value (EV) of a particular action or tournament entry and comparing it to your total bankroll.
The Kelly formula becomes:
f* = (EV − C)/B
Where:
- f* = fraction of your bankroll to spend on entries like this
- EV = your estimated expected value (in dollars)
- C = cost of the buy-in (including fees)
- B = your current bankroll
For example, if your buy-in is $100 and your estimated EV is $110 (you have a 10% edge) and your bankroll is $5000, then:
f* = (110 - 100)/5000 = 0.002 = 2%
To put it in words, you can allocate 0.2% of your bankroll toward this tournament (which in this case equals the buy-in, so it is just about okay to play).
Kelly: A Razor Thin Tightrope
In 1956, a Bell Labs scientist by the name of John L. Kelly Jr. penned a paper called ‘A New Interpretation of Information Rate’. His objective was to optimize signal transmission through noisy channels but the application of the formula contained within soon found its way to traders, financial advisors, hedge fund managers and eventually to poker players.
In a game in which we understand that variance is a feature, not a bug, the importance of a wealth creation strategy cannot be underestimated. Bet too little and you are under-utilizing your edge. Bet too much, and the volatility could eat you alive. The genius of Kelly is that it mathematically proves there is an optimal risk level for growth. Between timid and reckless, there is a razor-thin tightrope than can be walked.
There is a beauty when you find the balance between risk and reward, when there is a reliable lens through which every buy-in and every bullet can be analysed. Game selection doesn’t just become easier. It becomes ruthlessly efficient.
Cowards and Dreamers
On one end of the spectrum there are the players who shoot for the stars, the dreamers who put their case money on a cash table or satellite into a $10K Main Event with a $5K bankroll, believing that they are destined to run it up. They are not wealth-creators thinking in terms of EV. They are people with main character syndrome thinking in narratives.
On the other end of the spectrum, there are cowards who onboard a lot less risk than they should. The fear of going broke looms large in their minds. They too are living a storied existence, except theirs is a tragedy and they are the perpetually unlucky protagonist foredoomed to failure.
It would be easy to say that The Kelly Criterion provides the solution for the players at both ends of the spectrum and I can say from personal experience, as a person who natural tendencies are on the nittier side, that it became my solution. That is, until I discovered fractional Kelly.
Fractional Kelly
Kelly assumes perfect knowledge of your edge and for poker players, that requires some guesswork. With the best will in the world, it is easy to over-estimate your abilities and underestimate those of your opponents. There are other variables too. Will the field be as soft as it seems? Will it get as many runners as you think? What is the payout structure? Will you be playing your A-Game?
Poker isn’t played in a vacuum and poker players are imperfect. They are human beings, subject to fear, tilt, tiredness and lapses in concentration. However hard they try to repress them, they also have cognitive biases and emotions. If you use full Kelly in a tournament context, you are putting a lot of faith in your ability to evaluate yourself, as well as the size and composition of the tournament field.
The practical solution is to use fractional Kelly, usually half-Kelly or even a quarter. Think of it as a safety buffer or cushion. You probably don’t know your exact edge and that edge could fluctuate based on extraneous factors. Life can throw you a curve ball and when it does, you will be grateful that you showed some restraint and deployed fractional Kelly as a prudent hedge.
The Occam’s Razor of Bankroll Management
For almost twenty years, the questions that I get asked most about, particularly from up and coming poker players, are on the topic of bankroll management. It will always be an important subject because no matter how good players get at the game, they can always mis-manage their money by game-selecting poorly.
A hard-to-swallow truth is that poker players, even the best ones, do not have a stable, knowable ROI, especially across varying field sizes, structures and formats. Even if you are a crusher, the variance in big-field tournament poker is brutal and prolonged. You can play well for a year and still lose money. When that happens, it’s easy to put it down to poor fortune but it’s not bad luck. It’s math with a knife and it’s utterly predictable. It is therefore vital that you deploy a bankroll management strategy that can withstand the swings.
Kelly will offer that because it forces you to be disciplined on the way down just as much as it will stiffen your resolve to bet bigger on the way up. Fractional Kelly will go a step further in safeguarding your bankroll. It still requires moments of honest self-appraisal and a good read on the competition but it offers an additional bulwark.
It’s the Occam’s Razor of bankroll management, slicing through delusion and allowing you to see your financial reality for what it is. It won’t make you win. It won’t save you from suckouts. However, it will, if deployed correctly, keep you in the game long enough to let your edge compound into something real.
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