Game Theory Optimal vs Exploitative Strategy

In poker, there are two primary types of winning strategies you can choose to play by in any given situation:

Exploitative: This is where you play in a way that you maximize your expected value (EV) in any given situation by appropriately countering your opponents’ sub-optimal plays and weaker tendencies. Yes, playing this way often opens yourself to be exploited, too, but often times the weaker opponents you’re targeting with this strategy will not change their game to appropriately counteract this, allowing you to reap maximal profits over the long run.

GTO (Game-Theory Optimal): This playing style is where you essentially attempt to play perfect poker yourself, which in turn only allows for your opponents to make mistakes against you (which is where almost all of your profit will be derived from). It always incorporates having bluffs or semi-bluffs mixed in with your value bets, can help clarify bet sizes to use, and more.

Which Play Style is Best in Poker: GTO vs. Exploitative?

Before delving into strategic concepts regarding GTO poker, it’s important to understand which of these two very different play styles is going to be more profitable for you to use as a beginner or more advanced player. The simple answer will likely be a combination of both, but usually more of an exploitable approach.

Simply put, most of the player population do not play GTO poker and often times open themselves up to be exploited in some facet of their gameplay and strategy, allowing for more profits to be made from them using an exploitative approach. In fact, it’s only in some of the largest games at the highest stakes that GTO concepts are fully utilized and seen in practice, and even then, exploitative plays are still sometimes used.

That said, though, knowing, understanding, and being able to apply GTO poker basics is going to help create an incredibly sound, solid foundation for your poker game – no doubt! Additionally, it’s important to have that baseline of GTO knowledge so that you can know how to appropriately deviate from it when necessary in order to maximize profits. 

Poker GTO Strategy

As illuminated in Ed Miller’s book, “Poker’s 1%,” the most fundamental concept that only the most elite poker players truly grasp and understand is that regarding frequencies, which could be in relation to cbets, bluffs, folds, calls, raises, etc. .

GTO poker solvers (downloadable online software – something that will be talked upon in a later section of this article) often will give solutions for how to play as optimally as possible in any given spot, and often, they recommend using a mixed strategies based on select frequencies. 

For example, in a given river situation, a solver may tell you to call with a specific hand within a range 70% of the time and fold it 30% of the time. It might also tell you that in a given spot, you should call 50% of the time, fold 35% of the time, and raise 15% of the time (with a certain range of hands).

Frequencies are such a fundamentally important and often unrecognized part of poker, but the concept of this runs true through the following 5 poker GTO concepts:

Preflop Starting Hand Ranges
To make up for positional disadvantage, players must open up tighter hand ranges than otherwise the further they are out of position. That said, it’s never enough to just open premium starting hands. Considering GTO poker ranges and principles, you usually want to have a good, balanced starting hand range from each position with at least some hands that will allow you to have a very strong poker hand regardless of how the texture of the flop comes (low, mid, high, disconnected, etc).

Below is a poker GTO preflop beginner poker chart for starting hands for online 6-max play, showing which hand ranges one should open-raise with, after the action has folded to them. The table is coded by colors representing different table positions (see key below).

[chart 1: poker GTO preflop beginner poker chart for starting hands for online 6-max play]

NOTE: It’s advisable for GTO play to use a mixed strategy for opening in the small blind, combining some open-limps with open-raises for various hands in the range, something that cannot be illustrated with the color system used for this chart.

Often times, the correct solution of deciding which hands to play is simply a math problem, which is something discussed below.[1]

Other preflop GTO poker charts can include which hands should be played after a raise, which hands to 3bet, which hands to continue with after raising and now facing a 3bet, etc. Using solvers can assist you with choosing which hands to continue with preflop and in what capacity (call / raise / re-raise / etc).

Pot Odds

As a poker player, you should always be looking to make +EV decisions that render you profit. Understanding and applying principles of pot odds (and equity) can certainly help you out with that.

 Poker GTO Examples: Postflop Pot Odds

Let’s say that we have JhTh on a board of 9h8h2s4c (open-ended straight-flush draw). There’s $50 in the pot and we have $40 left in our stack. Our opponent has you covered, and he goes all-in.

Playing GTO here would simply involve making the calculations to determine whether or not a call would be +EV or –EV, as calling or folding are our only options. (There would be no further action in the hand.)

We assume any remaining heart, Queen, or 7 will give us a win on the hand. This means that we have 15 cards (outs) to improve out of 46 remaining unknown cards, meaning we’ll improve 32.6% of the time.

 However, what if our opponent has a set already some portion of the time? In that case, if the 4h or 2h came, it could improve our hand to a flush, but it also might improve villain’s hand to a boat. If we reduce the number of outs from 15 to 14.5 to account for this, this would bring our equity to 31.5%

Now we must calculate the pot odds we’re getting.:
(bet amount / (our bet + pot)) = pot odds = $50 / ($40 + $90) = $50 / $130 = 30.7%

This means we must have greater than 30.7% equity to make a profitable call. As we have 31.5% equity (even when we’ve taken the possibility of villain having a set into account), we can see that this is a profitable call.

Yes, the majority of the time we will lose, but over the long run, we will show a small profit from calling here, thus rendering a call to be correct.

NOTE: Additionally, it should be noted that the concept of pot odds is not only applicable to draws. If an opponent bets 50% pot, you are getting 3 to 1 odds on a call, this means you should win 25% of the time in order to make a call profitable. Therefore, if you take your current hand (and use an equity calculator like "Equilab" on a PC or "PokerCruncher" on a Mac) and it has better than 25% equity against your opponent’s perceived range, then you should call.

 Poker GTO Examples: Preflop Pot Odds

Assume you raise to 3bb preflop and get 3bet by the button to 9bb. Action then folds to you, and you must decide how to act. In situations like these, we can actually use pot odds to assist our decision-making.

In this case the size of the pot is:
= (our open + 3bet size + small blind + big blind)
= (3bb + 9bb + 0.5bb + 1bb)
= 13.5

This means that we need to call 6bb to try and win a pot of 13.5bb, meaning we would need to have equity of approximately (6bb / (6bb + 13.5bb)) = 30.7% against the range of the 3bettor in order to continue.

 However, there are at least 3 additional factors that need to be considered:

1. Positional Disadvantage: Being out of position on our opponent, it will be much more difficult to realize our equity in the hand, as our opponent will be able to effectively utilize his position better in order to put us in tough spots. As a result, we should usually add ~7% points to our equity needed in order to profitably continue against villain’s hand range.
2. Implied Odds / Reverse Implied Odds: This is the ability to win or lose a significant amount of more money post-flop (than what we invested pre-flop) as a result of the remaining money in our stack.
3. Villain’s Hand Range: While statistics on 3bet stats can be gained with a big enough sample size (i.e. 8% 3bet stat from button), the numbers don’t tell us which 8% of hands villain could be 3betting with. Both of the charts below represent 8% of possible hands, using both a polarized and depolarized approach.

Depolarised Hand Range (7.4% of hands): [chart 2]

Polarised Hand Range (7.54% of hands): [chart 3]

You can see that the contents that make up each hand range is vastly different. Additionally, we don’t necessarily know if he’s 3betting some hands a certain amount of the time and calling or folding those same hands another percentage of the time.

 However, knowing how to correctly proceed against a specific hand range comes down, in part, to using an exploitable strategy. Sticking with GTO, the next concept will help allow you to continue with ease.

3. Minimum Defence Frequency (MDF):

This concept refers to the % of hands in our range that we must continue with (either by calling or raising) in order to not be exploited by our opponents. It should be noted that this concept is most commonly used in off-table study and can be difficult to apply in-game.

However, studying these beginner GTO concepts off-table will assist with your decision-making during a hand, especially against opponents who show relentless aggression.

The formula to determine MDF is: POT SIZE / (POT SIZE + BET SIZE) = MDF

To help simplify this, here is a poker GTO chart of common bet sizes you may encounter in a poker hand, and the corresponding minimum defence frequency you must apply.

 Bet Size relative to Size of Pot (%)
Minimum Defense Frequency (%)
100%
50%
75%
57%
66%
60%
50%
67%
33%
75%

To determine which hands, you want to continue with, take the number of hand combos in your starting hand range and then use the MDF to calculate how many combos you should be continuing with. Generally, you should be choosing the hands with the best playability and highest equity against your opponent’s betting range.

As an example, suppose you open-raise in the HJ and the BB calls. The flop comes Qh9h6c. Your opponent takes the unusual play of leading into you for a ½-pot bet. Based on MDF, we should be continuing here with 67% of our range.

Using the starting hand chart above, we can determine that we’re opening 254 combos from the HJ, something that looks like this: [chart 4]

According to MDF, we must be defending 67% of these hands, or 170 combos to be unexploitable. Hands that we should continue with are those that retain the highest equity and playability, including:
Flush draws
Open-Ended Straight Draws
Gut-Shot Straight Draws
Over cards
Any Pair or better
That means that perhaps our flop continuing range will look something like this:

[chart]

Highlights to note include the following:
We eliminated pocket pairs of 4’s and 5’s, as these have little chance of improving on the turn or river. Additionally, we’re only continuing with AX combos of hearts (with a flush draw) that don’t have a pair or better to go along with it.

Lastly, we’ll include 4 combos of AJo, all 3 which have the Ace of hearts, as well as AcJh, which can block a backdoor nut flush combo.

For simplicity, let’s suppose we call with all these hands and that the turn is a blank (2 of spades). Our opponent bets full-pot. Now to remain unexploitable, according to MDF, we must defend 50% of our flop continuing range, which means we must leave ourselves 85 of 170 combos. This strategy should be comprised of our best flush draws, our best straight draws, and our best made hands, which might look something like this:

Notice here, we’re continuing with all of our combos of:
Nut flush draws
Pair + flush draws
GS + flush draws
Second Pair, Top Kicker+
One combo of JJ that doesn’t block the flush draw or backdoor flush draw.

 The same exercise can be repeated on the river, however this time, we’d be able to fold all of our missed draws to a bet and keep all of our strongest made hands. Be sure to think about blocker effects and card removal when calling with some weaker hands (to avoid overcalling and to decide which specific combos are best to continue with, according to MDF.

4. Finding Balance: Poker GTO Bet Sizing

To remain unexploitable (and to remain balanced and unpredictable), you must balance the number of bluffs to your value bets when you bet. The number of bluffs you include in your betting range is dependent on how big of a bet you make (in relation to the pot). This concept is solely applicable for river situations, as draws (“bluffs”) on the flop and turn still have equity, whereas on the river, busted draws have no equity (and are therefore total bluffs).

NOTE: For the flop, generally, you want a bluff to value bet ratio of about 2 : 1. This is because there won’t be as many made hands on the flop as on the river and also because your bluffs will usually still contain equity. For the turn, a “bluffing” ratio of ratio of about 1:1 is advisable. As for the river, use the chart below to determine GTO poker bluff frequencies (relative to your bet sizing choice):
Bet Size
Value Bet %
Bluffing %
25%     (1/4-pot)
83%
17%
33%     (1/3-pot)
80%
20%
50%     (1/2-pot)
75%
25%
66%     (2/3-pot)
72%
28%
75%     (3/4-pot)
70%
30%
100%   (Pot)
67%
33%
150%   (1.5x-pot)
62%
38%
200%   (2x-pot)
60%
40%

The way this chart works is in relation to the pot odds you’re laying your opponent. If you bet 50% pot, your opponent is then getting 3:1 pot odds and must therefore win 25% of the time, if he wants to call. As a result, poker GTO theory says that you should have 25% bluff combinations included in this betting range, so that you’re indifferent to your opponent calling or folding.

The best bluffs to include in a river betting range would be ones that don’t block the hands that you want your opponent to have (or not have). For example, in the case of missed flush draws, betting with missed Ace-high flush draws would often be a mistake because you block a missed flush draw that you want your opponent to have when you’re bluffing on the river (meaning that it would subsequently be less likely he would have it, if you held two of the flush draw cards). In addtion, ace-high usually carries with it some showdown value still on the river.

 If a 3-flush came on a river and you wanted to raise, bluff raising with some AX combos holding the Ace of the bluff suit on the board would be an acceptable option. If you block the nut flush, it means that your opponent cannot have that nutted combo in his range.

5. Cbetting Frequencies and Bet Sizes

 GTO beginner concepts and strategies do not only consist of bluffs and value bets. They will also allow you to see how often you should be cbetting in certain spots and also show which bet size to use! Poker solvers have helped top players dramatically with these aspects, which is exactly what we’ll discuss in the next section.

Poker GTO Software

Various poker GTO solvers have been released in recent years to assist beginner, intermediate and advanced players in showing how to correctly play poker from a more balanced/GTO standpoint poker in various situations.

PokerSnowie and PioSolver are the most common programs selling on the market right now to assist with GTO work and poker study behind-the-scenes.

 While you won’t be able to compute the various hand ranges of players and what hands to bet or check with in real time, taking the time with these programs to study in-depth GTO play strategies will ultimately pay you dividends. It will also help increase your level of thinking and understanding to be more GTO for poker.

The GTO methodologies that you’ll improve upon from using solvers can include balancing ranges, choosing optimal bet sizings, mastering cbet frequencies, and more.

Poker Tournament GTO

Tournaments often have shorter stacks in later stages than what will be typically found in cash games. As a result, in order to follow guidelines for GTO poker, Nash charts have been created, tweaked, and used over many years in order to know what hands to shove with (and also when to call, depending on what number of big blinds you have when you find yourself shortstacked).

Do note that the charts provided below are push/fold charts for heads-up play. Therefore, if you’re in a table with multiple players the “pusher” chart can only be used if play is folded to you in the small blind; as such, the “caller” chart can only be used if you’re in the big blind, and also would assume a small blind “pusher” (with a much wider range than if a player in another position was open-shoving).

For the pusher chart, if you divide all the numbers by 2, you can see which hands you should be pushing with from the Button. By the same thought, if you divide all of the original numbers on the chart by 4, you’ll find a solid pushing range from the CO. Do note, though, that some of the figures will be impossible to calculate accurately for the CO or positions further to the right of the blinds because the highest figure that the chart provides is “20+” big blinds, which is also a figure used for quite a large range of hands in the push chart.

Both of the GTO charts below are ideally applicable for heads-up play, but sometimes, using an exploitable strategies for HU shortstack strategy could lead to more +EV decisions against certain opponents. Simply following the charts below, though, will lead your play to being GTO and unexploitable.

 Within the spectra of possible push/fold charts, poker pro Max Silver created a super helpful GTO push/fold software called SnapShove. (It’s available for access online via desktop at www.snapshove.com or as iOS or Android apps (most common).)

With the full version, players can access poker GTO examples for shove ranges for a range of situations. (There’s full customizability for # of bb’s you have, what position you’re in, how big the ante is relative to the big blind (if applicable), and a plethora of other options.)

In Conclusion

With the constant evolving landscape in the world of poker, players are always developing their skills to improve and get an edge in the game. While often times, using an exploitable strategy will render higher profit margins than using a GTO-based approached all the time, knowing and understanding GTO beginner and more advanced concepts can certainly help you can an edge for a few primary reasons:

It creates a solid baseline and foundation for your gameplay.

It makes it easier to know how to deviate your strategy (re: exploitative) for certain villains when you have such a baseline established.

It allows you to avoid levelling wars with your opponents, because you’ll be making sound poker decisions based on reliable, unexploitable GTO strategy.

It doesn’t require that you to make assumptions about your opponents’ play styles.

It doesn’t call for you to be results-oriented.

This article is simply the tip of the iceberg for GTO concepts and poker theory. Continue studying these strategies provided, and also seriously consider investing in the GTO poker solver software listed above, as these can assist you in making incredible improvements to your game.

https://www.888poker.com/magazine/strategy/beginners-guide-gto-poker

I NEVER BLUFF

[caption id="attachment_11" align="alignnone" width="248"] Mr Lucky Poker[/caption]

Hollywood Park Casino Celebrity Sit N Go

HPC (Hollywood Park Casino) has a new Sit-N-Go Tournament, currently only on Tuesday @ 8pm (2107)
$3,000 Guarantee. $330 Entry Fee. It's a 10 player, single table event, with $300 of the entry fee going to the prize pool. The $330 entry fee will get you $10,000 in chips  with 20 minute levels starting at 50/100.

Tournament Value:   38.54,
Anything under 50 may not be worth playing and more likely designed to get you back to the cash game tables, but then again, it's on Tuesday.
Could be worth playing with an ROI of 4.94, but being that it's on a Tuesday it's more of a Predator/Prey Tournament.

http://www.mrluckypoker.net/2017/02/hollywood-park-casino-celebrity-sit-n-go.html

Sit and Go Tournaments are not spread very much anymore in the local card rooms. The best one I played in was as Hawaiian Gardens Casino, a three table tournament on weekends. Sadly it went away. Commerce Casino and The Bike run them sometimes during their big event tournaments.
This one is on the fast side but not Turbo, with 20 minute blind changes or 3 times per hour and not deep stacked @ only 100 Big Blinds for an "M" of 100, with a Utility "M" of about 67 Big Blinds.

You reach the Minefield at about Level 4,  which now lowers your (M) to 29 Big Blinds, since you need a minimum of 60 Big Blinds at all times to be competitive, you have to play much more riskier hands.

If your average win/loss rate is 50% and with the ante kicking in, you have only about 30 hands left before you have to play a Kill Phil kind of game. The Minefield section is about 1.5 hours and should end about Level 9, where you will need at least $72.000 in chips to continue at the Bubble Phase and on to the In-the-Money Phase. This tournament only pays the top 2 out of 10.

The Minefield is not too deep at about 6 levels, which means that's where most of the action is going to be as players try to improve their stacks. At level 7, about 2.33 hours into the tournament, it should start getting exciting as short stacks are going ALL-IN and medium stacks get cautious.

You only have about 2 hours to Double Up your stack, which means changing gears could be problematic when you are getting short stacked.

Being a tournament more geared to Luck at 81% than Skill, at about 18%, Tight Passive players are likely to have to make bigger bets than usual, but this one could go on for about 3 hours or more. Haven't seen the results, I don't think Hollywood Park Casino publishes them.

It would be interesting to see if a deeper stacked tournament, with 30 min blinds, and paying 3 players would make the tournament more popular, especially on a weekend.
Maybe 3 tables with 30 players and the top 3 chip stacks at each table make the final 9 and pay the 3 finishers.

I NEVER BLUFF

(M) # big blind bets you can make based on your chip stack size. An indicator of how aggressive you can be on each hand. (named after Paul Magriel.)

(UM) Utility of M, effectiveness of your chip stack size based on total blinds and ante for each round.