We’ll start with the assumption that the reader already appreciates the value of exploitative play relative to equilibrium solutions (i.e GTO play), which in truth, might not be the case. The relation is simple, exploitative play is all that matters. A nash equilibrium is simply a subset of exploitative play when employed correctly. In other words, we should only employ GTO solutions if just so happens to be maximally exploitative to do so. We should never try to “play GTO” arbitrarily or for the sake of “balance”.
Sometimes debates arise on the forums in the style of “GTO vs Exploitative”. Players proceed to inform the community whether they are “GTO” or “exploitative” players, and why they feel their particular brand of poker is the most profitable. The reality is that such threads should never exist if the posters involved understood where the value in a game theory approach actually lies. Any elite player only cares about max-EV lines. If a player is attempting to utilize a GTO approach against everyone, they are quite simply, not the elite players they might try and have us believe.
Mode of Operations
This is not to say that a GTO understanding of the game of poker is not important. Elite players understand game theory concepts well and more specifically when to use these concepts.
For example, it’s somewhat straight-forward to exploit an opponent who has clearly exploitable stats. Attempting to utilize an equilibrium strategy in such an instance would clearly be a mistake, since there is a higher EV alternative. Unknown opponents provide a slightly tougher case. With no clear exploitative opportunity facing us, it might seem that it makes sense to use a GTO style until further information presents itself. Here is where the error lies, there is nearly always a higher EV alternative before we need to resort to pure GTO approach.
After all, is it true that we know nothing about an unknown opponent? Actually no, it’s reasonable to make some assumptions even about unknown opponents. By analyzing a large sample size of hands, we can establish what the average player is likely to do in each spot. This allows us to generate lines which perform better than a GTO solution on average.
It is hence recommended to subscribe to the following mode of operations:
1. Exploitative play based on info (stats)
2. Exploitative play based on population data
3. GTO / Equilibrium Solutions with zero data
We take care to prioritize approaches at the top of the list over those at the bottom.
If we were therefore to find ourselves in a player-pool with no stats on our opponents; rather than follow a GTO approach it would make sense for us to take exploitative lines based on how the average player plays.
So when would we actually resort to the GTO approach? It would be exclusively scenarios that we haven’t analyzed population data for. Naturally an elite player will already have analyzed the highest frequency spots, so the implication is that we will be facing a somewhat rare situation. This could perhaps be caused by an unorthodox bet-sizing. We are not sure what the average player will show up with because we don’t have a decent point of reference in terms of sample size. (Or even if we have the sample, we haven’t run population analysis on the spot due to its low-frequency nature).
In short there are currently 3 primary ways of performing population analysis. We’ll list them in order, starting with the worst option first. In each case, a large database is required. Usually 1M hands or more.
1. Mass aliasing techniques. (Create an alias including all the players in our database and then check out the stats). The downside is that it takes a rather long time to make the mass alias in the first place without the use of scripts. We are also limited to the stats that are provided by the tracking software in most cases.
2. Notecaddy. Notecaddy is now available with both Hold’em Manager and Poker Tracker. It’s possible to create custom stats and use them to analyze the population. The downside is that it takes a very long time to code all the required stats for a decent population analysis. This is complicated by the fact that the software is laggy and contains very few shortcuts in terms of mass-producing similar stats. It is possible to speed thing up by purchasing stat packages.
3. Hand2Note. Easily the best option and comes with a built-in Range Research feature which is designed especially for population analysis. Downside is that it’s more expensive and the general consensus is that the support team is terrible. It can hence take a while to figure things out. This is by far the best option for elite players however. The H2N software has rapidly overtaken Hold’em Manager and Poker Tracker in recent times. Elite players have already begun making the switch.
By ‘hotspot’ we are referring to a scenario where the average player is making a significant error. Establishing the location of these hotspots is a key technique in maximizing our winrate. We can improve significantly on a GTO solution in these areas. Naturally, the larger the leak, the larger the incentive to deviate from the approximation of an equilibrium solution. We’ll now look at some examples of finding hotspots through interpreting population data.
Let’s take one area where players typically have mental blocks and see if we can improve our default approach. We’ll take the area of 3bet pots. Let’s first look to see how the population plays as the caller and look to improve our play in 3bet pots as the aggressor.
Note that pretty much all of the stats are exploitable in some way, but we are primarily interested in significant deviations from good strategy.
For example, take something such as fold to cbet IP. The population is folding 45% of the time. This typically allows us to generate automatic profit by betting any 2 cards. But to arrive at the conclusion that we should cbet 100% of flops would be missing the point. Our goal is to generate the maximum expectation, not to simply take any line which is +EV.
We should always consider the alternatives. If we skip our (profitable cbet), we can see that the playerpool will be float-betting a mere 39% of the time, allowing us to see a decent number of turns. The population then folds even more frequently to a turn delayed cbet, 51% of the time. Simulations usually demonstrate that going for the delayed cbet with garbage holdings is more profitable than relentlessly c-betting the flop with any 2. Besides, Cbetting 100% of the time won’t always fly below the radar; villain may attempt to counter such an aggressive approach.
This is why we are mostly looking for stats which look significantly out of line (hotspots). The more exploitable the values, the less likely it is that there will be an alternative line that generates a higher expectation. Take a few minutes to look over the stats in the image – do you notice anything else that we can exploit?
If your poker radar is finely tuned, you’d probably have been especially interested in the following.
1. Villain folds rivers too much after calling a delayed cbet. This means that we should typically two-barrel air across turn and river and reasonably expect to make a profit. Notice that villain folds significantly more frequently OOP. This is true regarding a large number of river situations in NLHE. Presumably the reason is that villain is less likely to slowplay by just check/calling the turn when OOP. His IP range will be slightly better defended with premiums.
2. River bluffing frequencies are super low across the board! The average player is simply not comfortable bluffing rivers in 3bet pots. A river bet after probing the turn is a bluff 8.1% of the time. A river probe bet is a bluff 8.5% of the time. A river bet after float-betting the turn is a bluff 14% of the time. A river float-bet is a bluff 13% of the time. How high might we expect these numbers to be from a GTO point of view? If we assume the average bet-sizing on the river after two-barreling is 50% pot, then a balanced bluffing frequency would be closer to 25%. We can exploit this by folding the vast majority of our bluff-catchers
3. Probes and Floats are low in all situations.
We probably notice that probe-bet and float-bet stats are generally quite low across the population. While it might sometimes feel as if our opponent is stabbing the turn wide to take the pot away after we skip our cbet, the data suggests otherwise. Keep in mind that the values are not ultra-low by any means so the goal is not to be making big hero folds here. We simply want to generate an awareness that the average player is more passive than he should be in these spots.
Now let’s take a look at population play as the aggressor in attempt to generate exploitative lines as the defender.
Take a moment to identify any areas that appear to be hotspots.
1. The population is folding too much to float bets, especially turn and river. The population is folding a huge 64% when facing river float bets. This is also a situation where many players find it difficult to pull the trigger on a bluff. The implication is that we have already called a preflop 3bet along with a flop and turn cbet. The pot is already very big and a river float bet would often constitute an all-in shove. It’s not a big surprise that a lot of players are reluctant to shove their entire stack in on a bluff, but the numbers suggest it will be extremely profitable.
2. The population is folding too much to probe bets, especially river probes. When we see the population is folding 44% of the time to a turn probe that may seem somewhat low. However, given that we will typically be using a half-pot sizing, this falls well within the realms of generating automatic profit. The population proceeds to fold 43% of the time when facing a river follow up bet, again meaning that we can generate a small amount of automatic profit if we select our bet-sizing carefully. Note that the population also folds rivers too much after calling a turn float-bet (45%).
3. The population is over-folding to river Onebets. “Onebets” is term we created to described a situation where the flop and turn get checked through and someone fires the river. It’s actually pretty rare for these type of spots to get analysed which is why we have created our own terminology. We can see that if flop and turn get checked through, a half-pot river stab with air will clearly generate profit in the long run.
4. Disinclination to fold against raises. People don’t like to fold a lot to raises in 3bet pots. Semi-bluffing without a large amount of equity seems a bad idea. Raising is less in important in 3bet pots than single-raised pots anyway, but it’s probably a good idea to be especially cautious about bluff-raising vs unknowns in 3bet pots.
We have analysed how the population plays in 3bet pots. We have seen clearly how we can increase our efficiency over that of a GTO approach by exploiting common mistakes. Of course, this constitutes just one small subset of the game of NLHE.
Elite players cover all spots in explicit detail to produce unbeatable default gameplans.