Applying the Kelly Criterion to Tournament Poker

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If you were paying attention to poker Twitter on the night of Mayweather-McGregor, you’ll have seen plenty of pros discussing the wagers they made on the fight. While some were admitting to having placed bets amounting to massive portions of their net worth on the ‘sure thing’ of Mayweather winning, others could be found discussing betting strategies in more precise terms.

Dig into some of the conversations a little below the surface, and you’ll see a curious piece of terminology pop up repeatedly – the term ‘Kelly’, along with ‘half Kelly’, ‘quarter Kelly’ and other variants, was commonplace. But what does this term mean, and why was it so relevant to these discussions in particular? Let’s take a look at the Kelly Criterion.

What is the Kelly Criterion?

The Kelly Criterion is a theory utilized by high-level gamblers to establish how much of their existing bankroll should be used for any one bet. The specifics involve too much algebra for me to elucidate here. It’s more common in sports betting or other forms of gambling than it is in poker, for a fairly simple reason – its most common usage is in calculating the parameters of a bet with a finite, win-or-lose result. Where poker is concerned, there are a huge number of variables in play that complicate the issue of results, and thus Kelly becomes applicable only in a more broad sense.

The general idea of the Kelly Criterion is that in order to minimize one’s risk of ruin and ensure long-term profitability as a gambler, certain risk management techniques must be employed – for example, just because a bet is profitable doesn’t mean it makes sense to risk your entire net worth on it, because the portion of the time you lose will be so harmful in the long-term.

Kelly’s answers to specific problems are usually framed in terms of a percentage of one’s bankroll – for example, a Kelly Calculator will recommend that if you have a 40% chance to win and you’re getting 2 to 1 odds on your bet, you should consistently bet around 10% of your bankroll in order to maximize profit in the long run, while minimizing risk of ruin. Obviously if your first bet loses, you’ll be betting a smaller amount if you make the same bet again, while if your first bet wins, you’ll be betting a larger amount.

Applications in game selection

The biggest complexity in poker is that, of course, we don’t always get to choose how much of our money we invest in any one hand while we’re actually playing – we’re often responding to our opponents’ bets. This, however, is not true of overall game selection in and of itself. While we may not be able to come up with a Kelly equation to tell us what stakes of cash games we should be playing or what tournaments we should buy into, its overall philosophy should provide a guiding light for us.

It seems logical to train ourselves to perceive our tournament or cash-game buyins as a percentage of our overall bankroll, since that’s not a hard thing to do. The hard part with game selection comes in the adaptation – many players, for example, will say to themselves at a certain point, “okay, that’s it, it’s time to move up in stakes”, and from that point on, they’ll be playing a $20 average buy-in instead of $10 online, or they’ll jump into the $5/$10 game at their local casino instead of the $2/$5.

The problem these players encounter, is that they simply don’t adapt sufficiently after that – they’ve moved up in stakes, so moving back down again simply because they had one losing session is counter-intuitive. Buying into a $5 tournament again seems like a waste of time – why would I do that, now that I’ve moved up?

The players who are too stubborn to accept the necessity of flexibility in these situations end up getting punished for it. If you move up in stakes because your bankroll crossed an arbitrary threshold you’ve put up, and you don’t move back down again when you drop below that threshold, you never really had rules in the first place. You’re not necessarily a better player than you were before you crossed that threshold, so there’s no guarantee you won’t run bad and slide back down below it – for this reason, a flexible bankroll-management approach is needed.

While it can’t help us pick one specific game over another, the Kelly Criterion can at least teach us that in theoretical terms, we should be treating our tournament (or cash-game) buyins as a percentage of our overall bankroll, rather than as a clearly-defined category of games which we’ve given ourselves blanket permission to play. Adaptation is fundamental to survival in poker, and fluctuations in our bankroll are no different.

Picking our spots in-game

While it may seem like the complexity of an in-game poker decision might render the Kelly Criterion irrelevant at the table, there is one regard in which it can be useful. It essentially teaches us the value of being able to put other players at risk for their tournament lives. Where we have the possibility to force them to risk a high proportion of their resources while we’re not risking much of ours, we can gain a significant advantage.

This is where the concept of ‘leverage’ comes in – if we can make a bet, raise or 3-bet that forces our opponent into a situation where their next decision will be a shove-or-fold spot, we’ve utilized a small portion of our resources (our chip stack) in order to put them under a great deal of pressure. We’ve made a bet that’s very efficient according to Kelly standards – the significant growth in our resources when our bet is successful is enough to offset our losses when it isn’t.

There’s a lot of room for potential discussion of tournament situations according to this metric. Imagine a situation where we’re considering a river bet, and evaluating it according to exploitative reads on our opponent. We might consider that the most +EV play could be to make a larger river bet for value, getting paid off bigger when we have the best hand, in trade for losing more chips on the occasions when we’re behind. Of course, this may well be the highest EV option, in which case we should take it – but another option might allow us to gain similar EV while risking a smaller portion of our resources in the event that we are wrong, potentially allowing us to avoid risking our tournament life in this eventuality. In these rare cases, our desire to avoid spots where we risk a large portion of our resources for minimal gain might encourage us to modify our approach, and reduce the volatility of our play in exchange for more consistent growth.

An aggressive 3-betting strategy preflop is actually one of the most Kelly-efficient approaches to tournament poker in existence – or at least, it would seem to be. We risk small portions of our resources to make profitable bets, in the hope that we will later be able to leverage our opponents into risking larger portions of their resources in spots where they’re uncomfortable.

Guidelines, not rules 

Finally, it’s crucial to remember that just like many other transferences of theory from non-poker gambling games or other fields, the applications of these ideas that I’m suggesting are merely guidelines. Kelly itself is merely an advisory guideline in the first place, for those gambling on more straightforward outcomes – hence the tendency for gamblers to adopt more conservative, half-Kelly or quarter-Kelly approaches, where they bet less than what an aggressive Kelly strategy would suggest.

The relevance of these theories to poker has not yet been fully explored – nor may it ever be. But by opening our minds to these ideas, we give ourselves space to expand our understanding of how the game of poker works, and allow new concepts to take root that may shape our poker experience over time.