Poker Combos Calculator
2021年5月25日Register here: http://gg.gg/upqjp
This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities
*Poker Combos Calculator Cheat
*Poker Combos Calculator Speed
*Poker Combos Calculator Game
Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.
___________________________________________________________________________Preliminary Calculation
Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.
Casino subtitles. No one stays at the top forever. Master director Martin Scorsese depicts the sloping depth of a casino mafia boss’ fall. Filmed in a semi-documentary fashion; about the life of the gambling paradise Las Vegas and its dark mafia underbelly. Watch casino 1995 online free.These are the same hand. Order is not important.
Poker Combinations Calculator table game is just as exciting to play online. Roulette requires no skill to play, although it is helpful to learn the best bets to make. Live dealer roulette is the most exciting game to play on online casinos, but bettors can find other roulette games to play online, too. The poker combinations calculator will help you calculate the poker hands of your opponents, sort the poker hand rankings by strength and tell you the exact chance of getting a royal flush. This software, like the turn tracker, is used by all advanced users to gain an advantage. A poker odds calculator is a piece of poker software that lets you run any scenario that you might see at a poker table. You can fill in your own hand and calculate the chances of you winning. A poker hand range calculator is a great tool to help make smarter decisions when playing for real money. Get in-depth knowledge of calculating hand ranges, equity, and combinations to improve poker strategies. This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog - multiplication principle, permutation.
The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.
The notation is called the binomial coefficient and is pronounced “n choose r”, which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.
Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is
This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.
The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.
If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.
Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.
Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of “3 diamond, 2 heart” hands is calculated as follows:
One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.
___________________________________________________________________________The Poker Hands
Here’s a ranking chart of the Poker hands.
The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.
Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.
The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.
Definitions of Poker HandsPoker HandDefinition1Royal FlushA, K, Q, J, 10, all in the same suit2Straight FlushFive consecutive cards,all in the same suit3Four of a KindFour cards of the same rank,one card of another rank4Full HouseThree of a kind with a pair5FlushFive cards of the same suit,not in consecutive order6StraightFive consecutive cards,not of the same suit7Three of a KindThree cards of the same rank,2 cards of two other ranks8Two PairTwo cards of the same rank,two cards of another rank,one card of a third rank9One PairThree cards of the same rank,3 cards of three other ranks10High CardIf no one has any of the above hands,the player with the highest card wins
___________________________________________________________________________Counting Poker Hands
Straight Flush
Counting from A-K-Q-J-10, K-Q-J-10-9, Q-J-10-9-8, …, 6-5-4-3-2 to 5-4-3-2-A, there are 10 hands that are in sequence in a given suit. So there are 40 straight flush hands all together.
Four of a Kind
There is only one way to have a four of a kind for a given rank. The fifth card can be any one of the remaining 48 cards. Thus there are 48 possibilities of a four of a kind in one rank. Thus there are 13 x 48 = 624 many four of a kind in total.
Full House
Let’s fix two ranks, say 2 and 8. How many ways can we have three of 2 and two of 8? We are choosing 3 cards out of the four 2’s and choosing 2 cards out of the four 8’s. That would be = 4 x 6 = 24. But the two ranks can be other ranks too. How many ways can we pick two ranks out of 13? That would be 13 x 12 = 156. So the total number of possibilities for Full House is
Note that the multiplication principle is at work here. When we pick two ranks, the number of ways is 13 x 12 = 156. Why did we not use = 78?
Flush
There are = 1,287 possible hands with all cards in the same suit. Recall that there are only 10 straight flush on a given suit. Thus of all the 5-card hands with all cards in a given suit, there are 1,287-10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108.
Straight
There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is . Then we need to subtract the number of straight flushes (40) from this number. Thus the number of straight is 10240 – 10 = 10,200.
Three of a Kind
There are 13 ranks (from A, K, …, to 2). We choose one of them to have 3 cards in that rank and two other ranks to have one card in each of those ranks. The following derivation reflects all the choosing in this process.
Two Pair and One Pair
These two are left as exercises.
High Card
The count is the complement that makes up 2,598,960.
The following table gives the counts of all the poker hands. The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960.
Probabilities of Poker HandsPoker HandCountProbability2Straight Flush400.00001543Four of a Kind6240.00024014Full House3,7440.00144065Flush5,1080.00196546Straight10,2000.00392467Three of a Kind54,9120.02112858Two Pair123,5520.04753909One Pair1,098,2400.422569010High Card1,302,5400.5011774Total2,598,9601.0000000
___________________________________________________________________________
2017 – Dan Ma
You might have heard of game theory optimal (GTO) or GTO poker solvers before. You might have also heard that you shouldn’t try to play GTO, that you should only play an ABC poker strategy - a simple yet effective that should beat your incompetent opponents. However you would be wrong.
GTO solvers are basically a super calculator for poker which allows players to set-up a hand scenario and find the optimal solution to that situation. You basically ask the solver a question and it gives you the GTO answer.Has poker been solved and turned into a game like Tic Tac Toe?
There are still limitations to what GTO solvers can do.
For example, they currently only solve for heads-up confrontations. But there’s a lot of benefits to using a GTO solver. They aren’t cheap. And often the learning curve deters people.
This article we’ll weigh up the benefits and pitfalls of using a GTO poker solver. And reveal how to get the most out of using a GTO solver.Is GTO the best poker strategy?
When it comes to beating poker, the term ‘GTO’ often gets thrown around like it’s the ultimate strategy. The idea of pure game theory optimal solutions (i.e. equilibria) works most effectively when players are playing perfect strategy. However, that isn’t often the case.
I HAVEN’T studied Tic Tac Toe, but I’m confident as the player going first, selecting the middle box as the first move would be optimal.
I HAVE studied poker for years, and sometimes I’m still not sure of the best play in a certain situation!
Poker is a complex game. As human players, we don’t consistently make optimal decisions. Some rarely do!
So what good is an equilibrium strategy when our opponent is deviating far from using an optimal game plan? After all, the importance of adjusting to your opponent and the mantra of ‘play the man’ has been at the crux of winning poker strategy since Cowboys on tilt were drawing pistols in saloons.
Here’s a short video that addresses the role GTO plays in the poker world.The power of GTO poker solvers
Well firstly, there are still certain takeaways from observing a GTO solver work its magic and plot an equilibrium solution. And secondly, solvers do allow you to set parameters so you can calculate an optimal strategy when playing a non-perfect player.Poker Combos Calculator CheatBenefits from eyeballing equilibrium play
Being able to eyeball a perfect strategy is a useful learning aid. It’s not always practical for the specific game type and opponents a player encounters in their regular games. But seeing a perfect strategy being modeled can be very thought provoking.
Especially when a players style of play differs in spots from the GTO mold. Players in a sense are forced to reflect on their own play and question why they exhibit certain tendencies.
Are they exploiting a certain opponent weakness or population tendency? Or is it a bad habit that’s developed that their opponents can capitalize on?GTO Poker Solver Example
Let’s take cbetting small pairs on the flop as an example. Solvers like to bet very small pairs in a lot of instances on the flop. These marginal holdings benefit greatly from taking the pot down on the early street. They have few outs to improve, and so the board texture usually develops unfavourably for them.
It makes sense to protect them in a lot of situations. But some players might frequently check back the flop rather than cbet figuring they just want to try to showdown with a weak hand.
Identifying these types of smart strategical patterns helps players modify and improve their own play. Here’ a few more examples;
*How is middle pair played?
*Should BB check-raise low boards a lot on the flop?
*What’s the role blockers play in spots?
*Backdoor flush draw play
*When do solvers over-bet the river?
*Should ace high cbet dry flops?
Some of which might be instantly beneficial if incorporated into a players gameFree MTT Poker Training:The Underused MTT Skills Essential For Success
*5 Day Email MTT Poker Training Course By Poker Pro Kelvin ’Acesup’ Beattie
*3 Key Skills That Will Take Your MTT Poker Game To A New Level
*1.5 Hours Of Professional Poker TrainingBenefits from locking opponent strategies
Frequently as we observe opponent play we notice tendencies they have. Additionally using a HUD or poker tracking software online will sometimes expose bad habits.
Once you’ve locked on to what you believe to be an opponent weakness, you can configure the poker solver to plot a new optimal strategy based on this information.
This approach of analyzing a GTO strategy for the specific opponent you’re playing against is a powerful tool solver’s offer and is usually referred to as ‘locking a strategy’ or ‘setting a strategy’.
It’s the best feature for most solver users because it allows for relevant, specific hand analysis based on the real situations you encounter regularly. And you can gain insight into how a solver goes about adjusting to take advantage of deviations from equilibria.GTO Solver Example #1 : Video
For example, take the passive opponent that rarely check raises us on the flop. Since we’ll get to realize our equity more often, we can cbet at a high frequency. Taking advantage of the fact we rarely get blown off our hand on the flop. Which was the situation a student asked me about recently, as discussed in the video below.Poker Combos Calculator SpeedGTO Solver Example #2: Check Raising
Or perhaps you’ve spent some time playing with an opponent and he seems to be cbetting 100% on the flop, poker solvers allow you to input this tendency and work out the best response.
Whilst it might be obvious to some that check-raising a player over cbetting is likely to be a good strategy, solvers provide more than just an ideal fold percentage, call percentage and raise percentage.
Additional insights such as; what parts of your range fit best as fold/call/raise, what raise sizing is best, your equity and EV for the situation, how you should proceed on various turn and river outcomes, and all the while what your opponent’s responses should be to your moves. In fact, the extensive amount of data presented can be a little overwhelming to a first time user.
Players modifying solvers to better represent their opponent’s behavior, frequently express overall improvements in their game from the knowledge they gain.
Seeing how a solver adjusts to different situations prepares players for the next time they encounter a similar situation.
Moreover, solver users tend to get a better handle on how they should be playing their range of hands as opposed to a specific hand. Which makes any player more savvy on the felt. As well as players expressing how they start to see the game more in depth, by being able to visualize a hands decision points as branches on a game tree.
This often assists with recognizing opponent leaks and identifying opportunities to exploit. And serves to place importance on strategy as a whole. Where ultimately, consistently making better decisions than your opponents over time, leads to winning results.Limitations Of Poker Solvers
Locking strategies requires a little more than the basic knowledge of using the solver and if not executed correctly, it could lead to unreliable results.
Use of this feature requires you to be able to fairly accurately gauge your opponent’s tendencies. And this is where a considerable ‘human element’ still remains. In fact, from the get go when you are selecting hands to include in your opponents range, and setting bet sizes, the more accurately you can set the parameters in the solver to reflect the game situation the more reliable the calculations will be.
Unfortunately, this often brings about another limitation solvers have, the time it can take to compute. Especially when setting multiple bet and raise sizes. As the game tree gets larger, so does processing time. Whilst simpler solutions might only take a minute or 2, having several betting and raising sizes, as well as the option to lead bet, might take the better part of an hour to process. And that’s presuming your PC is relatively up to date.Poker Combos Calculator Game
For extremely complex calculations, such as running scripts or doing heavy preflop work, people sometimes rent servers or use cloud computing. Or you could let the computer run over night.
To speed up regular hand calculations, compromises can be made. For small concessions in accuracy, considerable time can often be saved. With results still acceptably accurate.
So solvers can provide GTO solutions to the heads-up scenarios you encounter at the table. Calculations that are extremely accurate, and fast enough to be usable.So which GTO poker software is right f
https://diarynote-jp.indered.space
This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities
*Poker Combos Calculator Cheat
*Poker Combos Calculator Speed
*Poker Combos Calculator Game
Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.
___________________________________________________________________________Preliminary Calculation
Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.
Casino subtitles. No one stays at the top forever. Master director Martin Scorsese depicts the sloping depth of a casino mafia boss’ fall. Filmed in a semi-documentary fashion; about the life of the gambling paradise Las Vegas and its dark mafia underbelly. Watch casino 1995 online free.These are the same hand. Order is not important.
Poker Combinations Calculator table game is just as exciting to play online. Roulette requires no skill to play, although it is helpful to learn the best bets to make. Live dealer roulette is the most exciting game to play on online casinos, but bettors can find other roulette games to play online, too. The poker combinations calculator will help you calculate the poker hands of your opponents, sort the poker hand rankings by strength and tell you the exact chance of getting a royal flush. This software, like the turn tracker, is used by all advanced users to gain an advantage. A poker odds calculator is a piece of poker software that lets you run any scenario that you might see at a poker table. You can fill in your own hand and calculate the chances of you winning. A poker hand range calculator is a great tool to help make smarter decisions when playing for real money. Get in-depth knowledge of calculating hand ranges, equity, and combinations to improve poker strategies. This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog - multiplication principle, permutation.
The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.
The notation is called the binomial coefficient and is pronounced “n choose r”, which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.
Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is
This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.
The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.
If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.
Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.
Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of “3 diamond, 2 heart” hands is calculated as follows:
One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.
___________________________________________________________________________The Poker Hands
Here’s a ranking chart of the Poker hands.
The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.
Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.
The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.
Definitions of Poker HandsPoker HandDefinition1Royal FlushA, K, Q, J, 10, all in the same suit2Straight FlushFive consecutive cards,all in the same suit3Four of a KindFour cards of the same rank,one card of another rank4Full HouseThree of a kind with a pair5FlushFive cards of the same suit,not in consecutive order6StraightFive consecutive cards,not of the same suit7Three of a KindThree cards of the same rank,2 cards of two other ranks8Two PairTwo cards of the same rank,two cards of another rank,one card of a third rank9One PairThree cards of the same rank,3 cards of three other ranks10High CardIf no one has any of the above hands,the player with the highest card wins
___________________________________________________________________________Counting Poker Hands
Straight Flush
Counting from A-K-Q-J-10, K-Q-J-10-9, Q-J-10-9-8, …, 6-5-4-3-2 to 5-4-3-2-A, there are 10 hands that are in sequence in a given suit. So there are 40 straight flush hands all together.
Four of a Kind
There is only one way to have a four of a kind for a given rank. The fifth card can be any one of the remaining 48 cards. Thus there are 48 possibilities of a four of a kind in one rank. Thus there are 13 x 48 = 624 many four of a kind in total.
Full House
Let’s fix two ranks, say 2 and 8. How many ways can we have three of 2 and two of 8? We are choosing 3 cards out of the four 2’s and choosing 2 cards out of the four 8’s. That would be = 4 x 6 = 24. But the two ranks can be other ranks too. How many ways can we pick two ranks out of 13? That would be 13 x 12 = 156. So the total number of possibilities for Full House is
Note that the multiplication principle is at work here. When we pick two ranks, the number of ways is 13 x 12 = 156. Why did we not use = 78?
Flush
There are = 1,287 possible hands with all cards in the same suit. Recall that there are only 10 straight flush on a given suit. Thus of all the 5-card hands with all cards in a given suit, there are 1,287-10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108.
Straight
There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is . Then we need to subtract the number of straight flushes (40) from this number. Thus the number of straight is 10240 – 10 = 10,200.
Three of a Kind
There are 13 ranks (from A, K, …, to 2). We choose one of them to have 3 cards in that rank and two other ranks to have one card in each of those ranks. The following derivation reflects all the choosing in this process.
Two Pair and One Pair
These two are left as exercises.
High Card
The count is the complement that makes up 2,598,960.
The following table gives the counts of all the poker hands. The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960.
Probabilities of Poker HandsPoker HandCountProbability2Straight Flush400.00001543Four of a Kind6240.00024014Full House3,7440.00144065Flush5,1080.00196546Straight10,2000.00392467Three of a Kind54,9120.02112858Two Pair123,5520.04753909One Pair1,098,2400.422569010High Card1,302,5400.5011774Total2,598,9601.0000000
___________________________________________________________________________
2017 – Dan Ma
You might have heard of game theory optimal (GTO) or GTO poker solvers before. You might have also heard that you shouldn’t try to play GTO, that you should only play an ABC poker strategy - a simple yet effective that should beat your incompetent opponents. However you would be wrong.
GTO solvers are basically a super calculator for poker which allows players to set-up a hand scenario and find the optimal solution to that situation. You basically ask the solver a question and it gives you the GTO answer.Has poker been solved and turned into a game like Tic Tac Toe?
There are still limitations to what GTO solvers can do.
For example, they currently only solve for heads-up confrontations. But there’s a lot of benefits to using a GTO solver. They aren’t cheap. And often the learning curve deters people.
This article we’ll weigh up the benefits and pitfalls of using a GTO poker solver. And reveal how to get the most out of using a GTO solver.Is GTO the best poker strategy?
When it comes to beating poker, the term ‘GTO’ often gets thrown around like it’s the ultimate strategy. The idea of pure game theory optimal solutions (i.e. equilibria) works most effectively when players are playing perfect strategy. However, that isn’t often the case.
I HAVEN’T studied Tic Tac Toe, but I’m confident as the player going first, selecting the middle box as the first move would be optimal.
I HAVE studied poker for years, and sometimes I’m still not sure of the best play in a certain situation!
Poker is a complex game. As human players, we don’t consistently make optimal decisions. Some rarely do!
So what good is an equilibrium strategy when our opponent is deviating far from using an optimal game plan? After all, the importance of adjusting to your opponent and the mantra of ‘play the man’ has been at the crux of winning poker strategy since Cowboys on tilt were drawing pistols in saloons.
Here’s a short video that addresses the role GTO plays in the poker world.The power of GTO poker solvers
Well firstly, there are still certain takeaways from observing a GTO solver work its magic and plot an equilibrium solution. And secondly, solvers do allow you to set parameters so you can calculate an optimal strategy when playing a non-perfect player.Poker Combos Calculator CheatBenefits from eyeballing equilibrium play
Being able to eyeball a perfect strategy is a useful learning aid. It’s not always practical for the specific game type and opponents a player encounters in their regular games. But seeing a perfect strategy being modeled can be very thought provoking.
Especially when a players style of play differs in spots from the GTO mold. Players in a sense are forced to reflect on their own play and question why they exhibit certain tendencies.
Are they exploiting a certain opponent weakness or population tendency? Or is it a bad habit that’s developed that their opponents can capitalize on?GTO Poker Solver Example
Let’s take cbetting small pairs on the flop as an example. Solvers like to bet very small pairs in a lot of instances on the flop. These marginal holdings benefit greatly from taking the pot down on the early street. They have few outs to improve, and so the board texture usually develops unfavourably for them.
It makes sense to protect them in a lot of situations. But some players might frequently check back the flop rather than cbet figuring they just want to try to showdown with a weak hand.
Identifying these types of smart strategical patterns helps players modify and improve their own play. Here’ a few more examples;
*How is middle pair played?
*Should BB check-raise low boards a lot on the flop?
*What’s the role blockers play in spots?
*Backdoor flush draw play
*When do solvers over-bet the river?
*Should ace high cbet dry flops?
Some of which might be instantly beneficial if incorporated into a players gameFree MTT Poker Training:The Underused MTT Skills Essential For Success
*5 Day Email MTT Poker Training Course By Poker Pro Kelvin ’Acesup’ Beattie
*3 Key Skills That Will Take Your MTT Poker Game To A New Level
*1.5 Hours Of Professional Poker TrainingBenefits from locking opponent strategies
Frequently as we observe opponent play we notice tendencies they have. Additionally using a HUD or poker tracking software online will sometimes expose bad habits.
Once you’ve locked on to what you believe to be an opponent weakness, you can configure the poker solver to plot a new optimal strategy based on this information.
This approach of analyzing a GTO strategy for the specific opponent you’re playing against is a powerful tool solver’s offer and is usually referred to as ‘locking a strategy’ or ‘setting a strategy’.
It’s the best feature for most solver users because it allows for relevant, specific hand analysis based on the real situations you encounter regularly. And you can gain insight into how a solver goes about adjusting to take advantage of deviations from equilibria.GTO Solver Example #1 : Video
For example, take the passive opponent that rarely check raises us on the flop. Since we’ll get to realize our equity more often, we can cbet at a high frequency. Taking advantage of the fact we rarely get blown off our hand on the flop. Which was the situation a student asked me about recently, as discussed in the video below.Poker Combos Calculator SpeedGTO Solver Example #2: Check Raising
Or perhaps you’ve spent some time playing with an opponent and he seems to be cbetting 100% on the flop, poker solvers allow you to input this tendency and work out the best response.
Whilst it might be obvious to some that check-raising a player over cbetting is likely to be a good strategy, solvers provide more than just an ideal fold percentage, call percentage and raise percentage.
Additional insights such as; what parts of your range fit best as fold/call/raise, what raise sizing is best, your equity and EV for the situation, how you should proceed on various turn and river outcomes, and all the while what your opponent’s responses should be to your moves. In fact, the extensive amount of data presented can be a little overwhelming to a first time user.
Players modifying solvers to better represent their opponent’s behavior, frequently express overall improvements in their game from the knowledge they gain.
Seeing how a solver adjusts to different situations prepares players for the next time they encounter a similar situation.
Moreover, solver users tend to get a better handle on how they should be playing their range of hands as opposed to a specific hand. Which makes any player more savvy on the felt. As well as players expressing how they start to see the game more in depth, by being able to visualize a hands decision points as branches on a game tree.
This often assists with recognizing opponent leaks and identifying opportunities to exploit. And serves to place importance on strategy as a whole. Where ultimately, consistently making better decisions than your opponents over time, leads to winning results.Limitations Of Poker Solvers
Locking strategies requires a little more than the basic knowledge of using the solver and if not executed correctly, it could lead to unreliable results.
Use of this feature requires you to be able to fairly accurately gauge your opponent’s tendencies. And this is where a considerable ‘human element’ still remains. In fact, from the get go when you are selecting hands to include in your opponents range, and setting bet sizes, the more accurately you can set the parameters in the solver to reflect the game situation the more reliable the calculations will be.
Unfortunately, this often brings about another limitation solvers have, the time it can take to compute. Especially when setting multiple bet and raise sizes. As the game tree gets larger, so does processing time. Whilst simpler solutions might only take a minute or 2, having several betting and raising sizes, as well as the option to lead bet, might take the better part of an hour to process. And that’s presuming your PC is relatively up to date.Poker Combos Calculator Game
For extremely complex calculations, such as running scripts or doing heavy preflop work, people sometimes rent servers or use cloud computing. Or you could let the computer run over night.
To speed up regular hand calculations, compromises can be made. For small concessions in accuracy, considerable time can often be saved. With results still acceptably accurate.
So solvers can provide GTO solutions to the heads-up scenarios you encounter at the table. Calculations that are extremely accurate, and fast enough to be usable.So which GTO poker software is right f
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