The phrase ‘game tree’ is one with which many beginner- or intermediate-level poker players are unfamiliar. Its usage is becoming more commonplace as our understanding of poker theory and strategy grows, but it remains a mysterious and misunderstood concept in the eyes of many. Since even a rudimentary understanding of this concept can provide a big boost to a player’s poker knowledge, it’s important to get a good grasp on it if you aspire to reach the highest levels of the game.
What is a Game Tree?
Imagine a specific poker situation. Maybe it’s the very beginning of a hand, where the UTG player has the first decision. Now imagine every single conceivable thing that could possibly happen after that. It’s an immeasurably massive number of possibilities, right? Every potential bet sizing and board runout, every potential choice of action.
Even for a very powerful computer, it’s not possible to map out these possibilities with any degree of accuracy – there are simply too many variables. This is one of the many reasons why No-Limit Hold’em will ever be ‘solved’ in the way that Limit Hold’em already has been.
And yet, despite this, the game tree still has a myriad of uses as a theoretical concept. It can help us to understand the relationship between one part of a hand and another, and give us much greater insight into how to maximize the efficiency and profitability of our decisions – especially when compared to most people’s usual method of poker analysis, which involves looking purely at things that actually happened, instead of all the other things that could have happened.
The game tree can be displayed as a graphical representation of each potential decision, or as a linear list. In graphical form, it looks a lot like a family tree – one decision at the top, and a whole host of other decisions branching out from that one. A program like CardRunnersEV or HoldemResources Calculator can do a good job of introducing you to both preflop and postflop game trees.
The influence of early-stage mistakes
One important fact that an awareness of game tree concepts can teach us almost immediately, is that a big mistake earlier in a hand – i.e. higher up the game tree – can have a massive knock-on effect on later parts of the tree. For example, opening too wide of a range of hands preflop can have a huge impact on postflop EV – this is a very common leak among MTT players, particularly in late position.
The assumption players make is that if the blinds are folding too much, we should open wider, which is of course true in theory. It’s also true in theory that if someone is folding too much to c-bets, we should c-bet wider. However, these two situations are only two parts of the game tree, and they neglect other areas.
Since the EV of one root point in the tree is a function of the EVs of all the branches that come from that point, c-betting a high frequency might lead to a gain in EV in the, let’s say, 80% of spots where we do c-bet, but an even bigger loss in EV in the spots where we don’t – particularly when we c-bet all our strong value hands and our checking range consists of mostly air hands.
What happens with a lot of players is they c-bet the flop extremely frequently, but then rarely barrel the turn, because they simply don’t have a big enough proportion of good turn barrelling hands available to them – this allows the caller to realize more equity after calling the flop, and thus makes life extremely difficult on the turn and river for the person who c-bet too much.
In this example, a player opening too wide and c-betting too much was simply unable to capture enough EV in the spots where their opponents don’t fold, in order to back up the EV they gain in the spots where their opponents do fold. The entire situation would be more profitable by giving up a little bit more preflop fold equity in exchange for a lot more postflop EV.
Of course there are spots where this isn’t true – if your opponent is making a ton more mistakes than you are postflop, you’ll obviously want to play more hands against them – but generally it can be relevant with a surprising frequency. Not every crushing high-stakes regular is hyper-aggressive, and with good reason.
Simplicity versus complexity
Another reality we must bear in mind when utilizing game tree concepts to help us with decisions, is that our decisions become exponentially more difficult as the game tree becomes more complex. If our opponents are making a ton of mistakes then this isn’t an issue, but against better opponents, a more complex game tree is going to make it much harder for us to avoid leaving gaps or weaknesses in our game for them to exploit.
The process of simplifying the game tree is actually surprisingly simple in itself – just try to reduce the number of ranges you have to worry about. For example, in a situation where you have a massive range advantage on the flop, such as raising under the gun and getting called by the big blind, a GTO solver would probably advise you to c-bet something like 90%. In this instance, you lose virtually nothing in terms of EV by simply c-betting 100% instead, and you don’t have to worry about building an appropriate checking range. Similarly, if you don’t even have a range advantage at all, c-betting 0% might be better than trying to figure out which 25% of your range should be betting. This is particularly true OOP in multi-way pots.
However, it can be dangerous to apply this principle in the wrong situations – if a situation arises where your flop range advantage is marginal, or where it may not be advisable to simply play push-fold preflop, over-simplification can be dangerous. C-betting 100% or 0% when a solver advises 50% is likely to be costly. Identifying what your optimal c-betting range should be in a certain spot is tricky without access to a GTO solver, but loosely speaking, the bigger your range advantage, the more a solver will advise you to c-bet.
Using the tree to exploit opponents
The other side of this coin comes when we’re playing against weaker opponents, versus whom we don’t mind making more difficult decisions as part of a more complex game tree. We can even go so far as to make adjustments to our preflop raise sizing, c-bet the flop with different sizings for value and as bluffs, or to make unusually large bet sizings on the river in a variety of spots with individual hands.
These additions to the game tree take advantage of one fundamental reality – the optimal strategy for any given situation will be the one against which our opponent is going to make the most mistakes. If we’re able to identify a bet sizing against which our opponent will fold 100% of the time, then that should be our bet sizing with our bluffs. It might not be balanced, but in these spots, we don’t care.
We can also use the early parts of the game tree in order to put ourselves into better positions in the later parts. For example, if we know our opponent c-bets too much but doesn’t barrel the turn enough, we can start calling the flop wider than we usually would – in fact, we may consider never folding at all on certain flops, with the intent of targeting specific river leaks on the part of our opponent.
In the event that our opponent didn’t have these river leaks, the EV of never folding a specific flop would most likely be pretty low. But the EV we gain from printing money on the river versus this villain may be enough to compensate for it. There’s no real way to specifically measure this without a GTO solver, but even being aware of the concept will bring your game forward if you can apply it in certain spots.
Building lasting improvements in your game
Finally, we have to consider the structure of our learning processes in order to get the most out of this concept. If we can develop learning practices that allow us to understand the earlier parts of the game tree, and the more simplistic ones – preflop raising ranges and adaptations, 3-betting, push-fold play (this, in particular, is the simplest part of poker strategy) – and put in a large number of repetitions playing those situations effectively, we learn those skills to the level of unconscious competence, and free up mental space and energy to improve our ability to play the more complex spots.
If we can guarantee ourselves a baseline standard of play and a baseline EV in the earlier parts of the game tree, our capacity to improve our play in the later parts has a platform for growth.
If you’re studying complex turn and river spots without studying the preflop and flop spots that led to those turn and river spots, you’re missing opportunities. You’re probably making preflop and flop mistakes you don’t even know about, which mean that your EV in all the parts of the turn and river game tree will be lower.
Fixing a leak in one individual part of the tree that doesn’t happen very often is inherently less valuable than fixing a leak in an earlier part of the tree, with more branches stemming from it. Recognition of this factor could help you improve your study processes by leaps and bounds. You can also apply this concept in other areas of life – it doesn’t amount to much more than “don’t try to run before you can walk”. Get to know the early parts of the tree, the basics, like the back of your hand, and use that as a platform for the future.
omar2nd
Wow! This is very good! TY.