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• Today we wrap up my mini article series, modestly titled the ultimate guide to GTO poker solvers. It’s my hope that this article will be the most valuable to you of them all, as we explore some often overlooked ways to get more value from your poker solver study sessions. I’ve identified 6 features of PioSolver (my own weapon of choice.
• Genuinely Game Theory Optimal (GTO) play does not exist in poker. There are a few important things to notice from this approach: 1) both exploitative and GTO-based strategies made common sense adjustments to attempt to maximize against a specific villain, but 2) exploitative poker tries to maximize each hand's maximum EV with no guaranteed minimum while GTO poker tries to maximize each range's.

The following article is mostly theoretical in nature. I will draw on my years of experience as a poker player who played primarily No Limit Texas Holdem cash games at Low to Mid Stakes Live games before transitioning into mostly coaching. These stakes are generally considered minimum $100 buy-ins to as high as $2,000 or $5,000 depending on who you ask (USD). Anything higher is generally considered to be High Stakes, of which I have no experience whatsoever nor desire to play as it’s simply too stressful for me to consider playing that high. Of course I always paid any taxes due on time like a good US citizen, but sometimes the lovely folks at the IRS can be very determined. As such I will not discuss anything related to potential winnings and or losses so please do not ask. I know players who have been burned by doing so as the IRS will find even the very slightest discrepancy.

CHOOSE THE RIGHT GTO POKER TOOL At Simple Poker we take pride in producing professional GTO Poker Tools for professional poker players. We are constantly working to improve our existing applications and create innovative, new programs to help your game and increase your poker skills. The past decade has brought a wave of books, articles, and videos about applying Game Theory Optimal (GTO) strategy to poker. There are reams of mathematical calculations to support the potential usefulness of GTO-based poker play. There are also highly skilled professional players able to execute at least some of the strategies to positive effect. V132 (7/12/2020) - New engine. Almost 2x faster on our machines. If more RAM is needed while solving, then compression is applied. Several internal changes to the engine.

I will use my poker background to discuss Game Theory Optimal and Exploitative Gameplay, and theorize how one might apply that framework to Eternal. I will cover the theory of bluffing, and conclude by discussing Variance, and how to handle the inevitable tilt that ensues.
Before we begin, consider this article by Finkel a required prerequisite reading:
https://eternaltitans.com/finkels-playhouse-was-busy-thinking-about-bluffs/
In case you’ve been living under a rock, Finkel is one of Eternal’s top minds. This is a terrific article covering with examples, situations in which Finkel has run bluffs. What I will cover in my article is the theory behind why you need to bluff, and how to develop a frequency for bluffing consistent with a Game Theory Optimal strategy.
If you are interested in a more in-depth mathematical look check out https://en.wikipedia.org/wiki/Zero-sum_game and the links within that page. I will keep the mathematical calculations to a minimum and try to provide a practical summary that is easy to understand and apply without a high level mathematics background. In some examples I talk about Expected Value (EV) check out https://en.wikipedia.org/wiki/Expected_value if you are unfamiliar with the term.
This article will be applicable to Ranked Play, Draft, and Gauntlet. Gauntlet examples will be the most frequently used when covering Exploitative play as the AI makes a ton of mistakes. Game Theory Optimal play (GTO) should be strived for when playing against players of equal or greater skill to oneself. If you can identify mistakes in your opponent’s play, you can shift from GTO to playing Exploitative. Be cognizant of the fact that by playing an exploitative strategy, you are actively doing something that can in turn be exploited. Your strategy would lose against a player playing GTO.

So, what is Game Theory Optimal play? Simply put, it is playing a strategy that will break even (50% winrate in Eternal context) against other people also playing GTO, and will win (money in poker or >50% winrate in Eternal) against anyone deviating from GTO play. Neither poker, nor Eternal (a game with considerably more moving parts) have been solved in the sense that perfectly optimal play is known. Against players who deviate from GTO, if you can identify their leaks then playing an Exploitative strategy will allow you to win more than staying with GTO play over the long run. A “leak” is a term poker players use to describe a mistake that others have in their game, and usually something that is consistently done wrong. An Eternal example of a leak might be ALWAYS playing Wisdom of the Elders on your opponent’s turn when sometimes drawing on your turn will be more valuable. A more common leak might be simply never bluffing when attacking. If that is the case you know to always play around the fast spell that they are representing. By always giving your opponent credit for the combat trick and never calling his or her (nonexistent) bluffs, you are playing Exploitatively.

To get better at the game, and get your play as close to optimal as possible, I would suggest studying high level players play, watch ETS games (especially Invitationals and Worlds), chat with some of the best ladder players or streamers too, and read/watch their articles and videos. Chat with players who are also around your own skill level. You may both improve as a result. Of course, in game experience is a vital component as well. I am NOT a top ladder player, so I will not give advice in this regard. I will say though, that throughout my time in Poker, time spent outside the game studying and discussing the game was increasingly important as I rose through the stakes. This includes reviewing every noteworthy hand I played, which is admittedly harder to do in Eternal. So if you’re ever unsure of a decision, screenshot it, and make a note to review it later. Never be afraid to ask for help. Even the very best players in any game can always improve (until achieving the theoretical GTO play).

What I will talk about is why bluffing is vital for an optimal strategy, and how to put your opponent on and consider a Range of hands when making decisions, as well as considering how you would play your own range of possible hands on a given board state. This is where the concept of the long run comes in. The result of a given play is immaterial. What matter is the expected value of that play over the long run. Poker is a much easier game to quantify than Eternal, which is why I am going to be using poker examples throughout the article.

Lets first define what a range of hands is. A range of hands is all of the possible hands one can have in a given situation. Ignoring the way power is handled in Eternal, an opening hand range can be defined as all of the possible random seven card draws at the start. It will be easier to think of this in a best of three scenario so you know the decklist ahead of time. But one can usually determine the opponent’s deck approximately within the first few turns of play, at which point Ranging will be applicable.
You might be thinking, why do we need to consider a range of hands, and the long run outcome when I’m playing one game at a time against one hand from my opponent? To answer that, lets look at a simple example from Eternal:

You’re on Stonescar aggro with at least three open power and an Annihilate and a Torch in hand. It’s your turn and your opponent is on AP Midrange and played an Unseen Commando, then passed the turn with no power open. Lets assume you need to kill the Commando. There are two options. Torch it or Annihilate it. Torch may seem obvious at first glance but Annihilate is likely the better play. Why? Most lists these days are playing Crownwatch Traitor. Lets say 75% and the other 25% are on Impending Doom. If you Torch the Commando, Annihilate will do nothing against Crownwatch Traitor, and a Bloodletter follow up is likely gg. If you Annihilate the Commando, your opponent (over the long run) will play Traitor 75% of the time and then you get to torch Traitor when it’s still a 5/3. So, you played the Annihilate, killed Commando and your opponent slams Impending Doom. “Ah, why didn’t I just Torch Commando? Then I’d have killed Impending Doom!” This is FLAWED THINKING. You made the right play against the field, and it didn’t work out. While it is hard to calculate numerically for a game like Eternal, this was the play with the highest Expected Value. Do not deviate from this line in the future, even if it happens two, three or even ten times in a row. Assuming the 75%/25% meta split is still correct, then over the long run you were making the right play, the profitable play. Do not let variance get you away from optimal play. This is an extremely common pitfall in Poker, and in Eternal as well and is a sign of tilt that I discuss later in the article.

Lets talk about basic ranging in poker as this will give you a better idea of how to take that to Eternal. If you need to read about the basics, including hand rankings check out https://en.wikipedia.org/wiki/List_of_poker_hands
In No Limit Holdem (NLH), there are four betting rounds (unless all other players fold on any given round). There is a round before the flop, then on the flop (first three cards), turn and river which each give one additional card. The flop, turn and river are shared by the other players, and each player is first dealt a two card starting hand (hole or pocket cards which are unknown to other players) which they use to make hands with the cards on board (shared cards).

Preflop opening hand ranges are quite simple. At a table of nine other players if you are first to act, you should open with the following hands (approximately) at lower stakes. Two of a number like 22 are a paired hand like 2 clubs, 2 hearts (2c2h). A = Ace, K = King, Q = Queen, J = Jack. Those paint cards out rank tens – twos (deuces).
You would be correct to, on average table conditions open raise something like 99+ (that is 99, TT, JJ, QQ, KK, AA) and AQ+ (AQ, and AK). The percentage of hands you open is a simple calculation. There are 1326 total hand combinations in a 52 card deck and 2 card hands and is solved as 52!/(52-2)!2! = 52 *51 *50!/(50!*2!) =52*51/2 = 1326 combinations. ! denotes factorials https://en.wikipedia.org/wiki/Factorial
Each of your paired cards are 6 combinations (4!/(4-2)!2! = (4*3*2)/(2*2) = 6.
Your unpaired cards are 16 Combinations (4 Aces * 4 Kings = 16).
Sum the combinations we have 6*6 + 16*2 = 36+32 = 68 combinations. Divide by 1326 and we get approximately 5%. That means we are folding the remaining 95% of hands when first to act. As you are later to act you expand the hand range played, but that’s not necessary knowledge for this article (you might play 25% in later positions).
So we open raise our 5% hand range and action goes to a player who re-raises (3-bets) us. All other players fold. What do we do? If you are up against an average player at the lowest live stakes, they are folding preflop or calling your bet with way too high of a frequency. What that means is if they 3-bet you, they usually have a very strong hand on average. Here’s the scenario. You are holding AQ both of the same suit, and get 3-bet. What do you do? First, put your opponent on a range of hands, don’t guess a hand. Lets say they would only 3-bet AQ,AK, and JJ or better (this has been my experience against average live players at these stakes). Your preflop equity is only 36.59%:

Therefore, you should fold (yes, even after having folded every single hand dealt to you in over an hour). You can confidently fold because your opponent is playing way too few hands for a 3-bet. That is, they are playing an exploitable strategy and deviating from GTO by never having bluffs in their 3-bet range. You exploit them by folding AQ in that spot every time.

If you are playing against an Eternal opponent who never bluffs, say by attacking into a larger unit, you can exploit them by only blocking when you want to trade your unit for the combat trick, or can hold up a removal to get a two-for-one.

Lets talk about something closer to GTO play that you would use at higher stakes against more optimal players, and then we will pull these concepts into discussion of Eternal.

You are opening slightly more hand combinations now (again, an approximate range). 55 or better, AJ or better, KQ, and a few hands like 98 or 87 of the same suit (suited connectors), maybe some hands like A2 or A3 of the same suit. Your opponent is 3-betting you more often as part of a (near) GTO strategy, which means they are including bluffs in their range of hands. Imagine you are folding all but your very best hands to a 3-bet. If I 3-bet 100% of the cards dealt to me, I will essentially be printing money off of you because you will be folding the bulk of your opening hands. Say my 3-bet is $100 and you opened to $25 and fold to me 90% of the time and 4-bet (re raise my 3-bet) 10%. Lets assume my 3-bet is always a bluff and I always fold to that 10% for simplicity. The EV of my play is easily calculated as $25 *90% – $100*10% = $22.50 – $10 = +$12.50. I am exploiting you by playing this way. If you want to break even against me, you need to 4-bet me as a bluff some percent of the time. How often? Not very often to break even. You must continue with that percent (again, in practice sometimes you might call rather than 4-bet but we want to stay simple). At 20% 4-bet you win $100 and lose $25 80% which breaks even (100*.2 – 25*.8 = 0). Again, assuming I fold to 100% of your 4-bets. My 100% 3-betting is highly exploitable. You could easily counter my strategy by 4-betting an extra amount (way more than GTO dictates) because there are so many trash hands in my range that I would fold. If I were playing by 3-betting way too much and see my opponent adjust by 4-betting, I would go back to 3-bet heavily for value against that player and greatly reduce my bluffs.

In Eternal, if you go up against a player that you know always thinks you have the combat trick (or maybe also doesn’t read pauses well) you can bluff them a lot more than would otherwise be optimal. This would be an example of exploitative play by deviating from the GTO frequency of bluffs (whatever that number may be in Eternal).
For poker, In terms of GTO preflop play, you would raise a perfectly constructed Range preflop (premium hands, decent value hands, and hands that have decent potential to pick up equity post flop like suited connectors), I would 3-bet a perfect range, you would 4-bet the perfect amount of premium hands and bluffs (known as a polarized range) , call with some middle strength hands (and a few premiums mixed in for balance) and fold the rest.

An incredibly important concept in determining which hands to bluff with involves not just considering your current hand against a guess of what the opponent has, and not even just your current hand against their range (though that is much better thinking). Instead you need to think about your entire range of hands in that situation in relation to your opponent’s entire hand range, given the current board state.

Now we can focus our discussion on applying these principles to Eternal! If you were able to follow my poker write up, you now understand that bluffing the right amount is key to optimal play, and that playing in an exploitative (in itself exploitable) way (deviating from GTO) can win you more games against players that don’t understand that you are exploiting them who are not playing GTO themselves. You understand that to make optimal plays you should consider your entire range of hands for a given board against your opponent’s entire range (easier said than done – I make no claim to understand how to apply this theoretical concept optimally in Eternal). But the general idea is this: Given the current board state, what are the possible range of hands that my opponent can have? How should I play my current hand (extremely important) against that range? If I want to make bluffs however, that’s when I should be considering the range of my own hands. This will allow me to figure out what spots are better for bluffing than just guessing when to bluff against my opponent’s range of hands.
Your range and your opponent’s range are not just random cards given total number of cards in each hand. Consider things like what did I or my opponent play out so far. Would I/they be holding back specific units? Used certain tricks or weapons or can these be in our respective hands? Think about whether you would have used spells or played units already so you can understand what your own range looks like to your opponent (always assume your opponent is very skilled until they show otherwise from making in game mistakes, and assume that they are capable of putting you on a range just like you are with them).

Lets look at a practicle Eternal example for why we need to bluff. I have a Valkyrie Enforcer on board and you have a Rindra. Most players would attack here with Enforcer without a combat trick because you don’t want to chump block Rindra losing Enforcer, and may as well push what damage you can. If I don’t attack with Enforcer and have open power, there is a strong possibility I am looking to Block + Finest Hour. If I never bluff, then you should only swing with Rindra when you have a kill spell to 2 for 1 me, or you value getting the trick out of my hand more than your Rindra. If I never bluff, and holding back Enforcer means I always have Finest Hour to block + Finest Hour kill Rindra then my hand may as well be face up. I should therefore sometimes not attack even when I don’t have the Finest Hour to represent having it (but only with a pause for some spell – doesn’t have to be Finest Hour). Considering your range of hands in that situation, your opponent’s range, and his or her perception of your range can help you decide how often to bluff. Again, this is a theoretical concept that may be very hard to apply in Eternal.

The general takeaway here is to bluff to avoid allowing your opponent to get a perfect read on what your hand is. Bluff the right amount and you and your opponent will net zero EV if both are playing GTO. Poker is easier to quantify so here’s an easy example. We’re on the river and I bet $100 into a pot of $100. You are risking $100 to win $200. Assuming I am bluffing and value betting optimally, calling or folding yields 0 EV. You are getting 2:1 on a call, and need to win 1/3 times with your hand against my range to break even (1/3 *200 – 2/3*100). When I make a bluff for that bet size on the river, I need to bluff exactly 1/3 times to be GTO. This is why you need to study outside the game, look at your hands, board textures (board state in Eternal) and determine what your entire range looks like on the river to bluff optimally (or in Eternal, your perceived range for a given play). Otherwise how are you going to know which 1/3 of your range to bluff with if your cards are[X,Y] in that spot?

Lets go back to Eternal to talk a little more about exploitative play, and we’ll first look at gauntlet for an easy example. I have a 6/6 Carnosaur and want to go on the offensive against the AI board of a 3/3 and 2/2 (Marisen’s Disciple) and a 1/4 Archive Curator. The AI has six damage to kill Carnosaur, and assumes you have no fast spell. It blocks expecting you to kill just the 3/3 and 2/2 or the 1/4 and 2/2. The AI loves trades like these. If you don’t want that trade, wait until you have a Torch or Equivocate or whatever, and then 3 for 1 the AI. Knowing that the AI will take that attempted trade means you should play exploitatively by offering it with a fast spell up, even if a GTO player might punish that strategy by letting the Carnosaur through. The AI is about as far from GTO as you’ll find in the game. You should NEVER play GTO against the AI or you’re hemorrhaging winrate by not playing exploitatively.

I will conclude discussion of exploitative play by looking at a recent draft game I played against (presumably) a player just starting out. This was last month and because not that many people were playing we were matched despite MMR differences. I drew really badly. I had a decent quickdraw unit, with two weapons attached and a hand + board of 12 power (17 power deck). That setup was really my only way to play, all in on one unit. Meanwhile, my opponent (naturally) stopped drawing power at 6 and had nothing but gas. I’m supposed to lose this game 99% of the time. But, I had noticed something early in the game. My opponent took a really long time blocking, hovering over each of his or her units before deciding to chump block. The correct play for him or her in that spot was to let the damage through and crack back to try to race. Later on I started just attacking with my 7/4 Quickdraw unit, with no pauses over and over. If I hadn’t taken that risk based on my earlier read, I would have quickly been overrun. By now there was no way for me to win the race, and I had no blocks against his fliers. At this point, he or she had an easy double block to kill my guy and win the game from there but I kept attacking. I exploited him or her by recognizing that he or she struggled with quickdraw math. I ended up picking my opponent’s board apart with reckless aggression, and finally drawing my top end to lock up a game I had no business winning. I would have lost that game playing GTO, but by playing Exploitatively and capitalizing on a leak in my opponent’s game I was able to secure a win.

Again, everyone has leaks and it is up to you to find them. I have no doubt that I have some leaks and better players than myself could capitalize on them.

Finally, I’d like to conclude this article with a brief look at (negative) Variance, and how to handle the ensuing tilt and recognize when you are tilted or likely to become tilted. In poker, playing tilted is how great players lose money. In Eternal, playing tilted is how you drop ranks quickly. When I say Variance I really mean the swings. The clusters of losing five, six, seven games in a row. This differs from the mathematical definition of variance. Handling negative variance is key to your growth as a player, but even the very best players can struggle with this:

(Image and quote from Rounders -Miramax, Spanky Pictures)

To illustrate variance, here is a picture generated by https://www.random.org/coins/ of 20 coin flips. I put a line through clumps of three or more, shown either horizontally ordered or Vertically ordered so you can get an idea of variance. It doesn’t go Heads, Tails, Heads, Tails, Heads, Tails or even something like Heads, Heads, Tails, Heads, Tails Tails Tails, Heads, Tails. Take a look at the flips:

Note the clumps. There are several instances of three in a row, and even a five in a row in just a twenty flip sample. With larger samples, even more extreme clumping will develop. Random is Random! If you just lost ten games in a row with a 50% winrate what is the probability of winning your next game. It is still 50%. It is easy to fall into the trap of feeling entitled to win. There is no entitlement when it comes to games of Variance. You could go on to lose another twenty in a row, or win forty games in a row. With an infinite sample size these streaks are GUARANTEED to happen at some point.
The probability of losing thirty in a row is 1/2^30 or 1/1,073,741,824. Over an infinite sample this is guaranteed to happen (no I’m not going to prove it mathematically).
So, you now understand variance but have to learn to handle the swings emotionally. Over Thanksgiving many years ago, I played for nearly thirty hours straight (with breaks to eat etc) at a very profitable table of players easy to win against. I consistently got my money in as a favorite from odds ranging from 55% to 95%. I lost. EVERY.SINGLE.TIME. I ended up losing around twenty buy ins in just over a days play. My EV would have had me up maybe ten buy ins (just a guess) so I ran thirty buy ins under EV. I was forced to drop in stakes and grind back up which took over a month. Every poker player has a story like that because we play huge volumes of hands and experience some freak variance in there at some point. I take pride in the fact that my play never suffered (or not that I noticed) and I got the money in good every time and could keep making the right decisions despite getting punished by RNG repeatedly. This example illustrates a painful fact. The long run is REALLY long. You will have ups and downs along the way.

So how do we handle tilt? The first step is taking the lessons of variance to heart. Recognize that the swings are natural, and embrace them. Care to guess how many players would play poker with me if there was no RNG and they would always lose? You guessed it, zero. Only players better than I am would play with me and so on until no one wants to play. The game would die out. Variance is a good thing because it keeps players playing who otherwise wouldn’t unless they enjoy always losing. It allows weaker players to still have fun at the game. Learn to love Variance!

(Variance is a good thing!)

Losing sucks. No one likes to lose. It isn’t fun and it feels like you are wasting your time (assuming you are trying to win instead of just playing a list for fun in Casual where winning isn’t the main goal). Losing over and over messes with your mind. Doubt about your skills can creep in, you might stop taking risks where you would before and were correct to take them. Your play suffers, your winrate drops and the swings get worse. You have to get out of the tilted mindset.

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Recognize when you are tilted. Maybe your heart rate goes up, or your mouse clicks can be heard by the neighbors across the street you’re clicking so hard from frustration. Maybe it’s something more obvious like smashing a Computer Mouse, or just coming home from a bad day at work wanting to “crush some noobs”. These are all signs of tilt and will cause you to deviate from your “A Game”.

“Detilting” can be as simple as taking a break for an hour or a day, having a glass of water or going for a walk. It may take longer but everyone is different. The best advice I can give you is don’t even worry about your Rank or your wins (frustrating to miss dailies of course). Competitive Eternal, just like Poker, isn’t actually about winning. It’s about consistently making the right decisions. Do that and the results will come, in the long run.

I hope you enjoyed reading this (lengthy) article. I know it is highly theoretical but perhaps it will get you thinking about Eternal in new ways, and elevate your game. I hope to be able to apply this theory to my game one day, but it’s certainly no easy task.

Thanks for reading!

Poker tools are a variety of software or web-based applications that allow the statistical analysis of poker players, games or tournaments.

Hand converters[edit]

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Poker hand converters allow players to take text-based online pokerhand history files from online cardrooms and convert them into formats friendly to the eye and suitable for posting on online message boards. Hand converters are often used to show played hands to other players for analysis and discussion. Depending on the converter used, the output may include the pot size per betting round, blind level, seating order, and stack sizes.

Most online cardrooms store played hands on the computer of the player, allowing players to analyze and track their own performance or to discuss poker strategy with other players. Statistics a player can track include showdown percentage, frequency of aggression, percentage of check/raise etc. Most major poker sites such as Full Tilt Poker, PokerStars and PartyPoker provide players with hand history files, while a few such as the Playtech network offer hand histories, but not in text file format.

In addition to using hand history files to analyze and improve an individual's game,^[1] they can also be used to gather statistical data about opponents, both those a player has played against and even opponents never faced.^[2] Whether the latter constitutes cheating depends on the Acceptable Use Policy (AUP) of the cardroom. Sharing the raw hand history files is generally considered collusion and a violation of the AUP.^[3] Even though some sites don't offer readily available hand history files, you can usually request a transcript by e-mail.

Heads-up display[edit]

Multiple third party applications exist for the purpose of displaying simple to complex stats on online poker tables. These stats display observed information to allow the user to play multiple tables without paying close attention to the individual action.

Odds calculators[edit]

Numerous programs allow people to run 'hot and cold' simulations where two to ten hands are run against each other to show the approximate winning percentage for each. The first such simulator, Poker Probe, was developed by Mike Caro in 1990.^[4]

Solvers[edit]

Programs which produce Game Theory Optimal (GTO) solutions for some variants of poker. Most commercially available programs solve Heads-Up No Limit Texas Holdem with some predefined betting structure. Online poker sites often forbid use of solvers in-play, but allow them as a learning tool.

Tournament databases[edit]

Several commercial websites data mine the results of online poker cardroom tournaments and then offer rankings and return on investment statistics for players who have participated in these events.

Game software[edit]

Several commercial companies offer personal game software products where players can play against a table full of programmable robot opponents.

Gto Poker Wikipedia

Bots[edit]

Pokerbots are computer programs that play online poker disguised as a human opponent. Online poker rooms normally prohibit their use.^[5]

Datamining tools[edit]

Datamining tools, also known as hand grabbers, record the game play information of online poker games without requiring the user to play in the game. This data is usually stored as a text or XML file in a format which can be parsed by analysis tools. Note that in science and market research the term 'datamining' is used for the act of extracting knowledge from data, not for collecting raw data.

See also[edit]

Notes[edit]

Gto Poker Wiki Game

1. ^Full Tilt Poker: Hand HistoryArchived 2015-09-30 at the Wayback Machine
2. ^Explaining Winning Poker: A Data Mining Approach
3. ^PokerStars: Prohibited Online Poker Software FAQ
4. ^Poker1.com About Mike Caro
5. ^PartyPoker.com: PartyGaming's Unfair Advantage PolicyArchived 2007-10-16 at the Wayback Machine

External links[edit]

Gto Poker Wiki Play

• Poker Software and Tools at Curlie