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How-To: Calculating Hand Combinations, About Blockers, etc.

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  1. #1
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    Default How-To: Calculating Hand Combinations, About Blockers, etc.

    List of Topics:

    1. Introduction to Hand Combinations
    2. How to Calculate Possible Combinations of a Pocket Pair Hand
    3. How to Calculate Possible Combinations of a Non-Pocket Pair Hand
    4. Brief Discussion of Blockers
    5. Effect of Blockers on a Villain's Range with Example Calculations
    6. Some Additional Applications of Blockers

    1. Introduction to Hand Combinations

    There are 1326 possible pocket hands in hold'em if you assume that something like A A is the same hand as A A , which it is. We get this number by saying there are 52 ways to draw the first card, 51 ways to draw the second card, and divide that product of 52 and 51 by 2 since we're assuming A A is the same as A A . Statistically, it's more likely for you to be dealt AK than AA, and more likely for you to be dealt AA than AKs, and so quite obviously a study of the combinatorics of starting hands can be useful for developing a more accurate understanding of the development of ranges during a hand.

    In this post I'm going to cover what I consider to be the most important topics on the subject. First, I'm going to show you the fastest way to calculate how likely it is for someone to be dealt certain hands. Second, I'm going to show you how to put this into practical use with a discussion of blockers.

    I would like to note that this is a lot easier than most people make it, and with just a few minutes of practice, you will be able to tell me in about two seconds that it's equally as likely for someone to be dealt AA or KQ if the flop comes KQQ.


    2. How to Calculate Possible Combinations of a Pocket Pair Hand

    If you randomly choose two cards from a deck, there are six different ways to make a single pocket pair. If you examine the possible ways you can be dealt 55, for example, you come up with 5 5 , 5 5 , 5 5 , 5 5 , 5 5 , and 5 5 . For each pocket pair, there are the same combinations of suits.

    Intuitively we can figure out that on a flop of AK2, Villain having QQ is more likely than Villain having AA. Similarly, on a flop of 885, Villain having 55 is more likely than Villain having 88. The question that most people can't answer is: how much more likely is one hand than another? To answer this question, I'm going to ask you to remember a number, and it's the only thing I'm going to ask you to memorize in this entire post. The number I need you to remember is: 6310.

    Here is how you use this number to determine pocket pair combinations. If we are asking how many combos of AA there are, and we see no Aces in our hand or on the board, then there are 6 possible combinations of AA, just like we stated earlier. However, if there is 1 Ace in our hand or on the board, then there are 3 possible combinations of AA that a Villain can have. If there are 2 Aces in our hand or on the board, then (quite obviously) there is 1 possible combination of AA that a Villain can have. And finally, if there are 3 Aces in our hand or on the board, then (again, quite obviously) there are 0 possible combinations of AA that a Villain can have.

    So suppose we hold KT on a board of AAQJ7, and we want to know how many combinations Villain could have of AA, QQ, or 22. We can see two Aces exposed, so there is 1 possible combination of AA that Villain could have. We can see one Queen exposed, so there are 3 possible combinations of QQ that Villain could have. Finally, there are no Twos exposed, so there are 6 possible combinations of 22 that Villain could have.

    For another example, suppose we hold 44 on a flop of AJ4. There are 3 ways Villain could have AA, 3 ways Villain could have JJ, 6 ways Villain could have KK, and 0 ways Villain could have 44.

    For our final example, suppose we hold AK preflop. There are 3 ways Villain could have AA, 3 ways Villain could have KK, and 6 ways Villain could have QQ. (This ties in with our discussion of blockers later on, but note that it's because of this that AK is only a 40/60 dog against QQ+, AK).


    3. How to Calculate Possible Combinations of a Non-Pocket Pair Hand

    There are sixteen different ways to be dealt a non-pocket pair starting hand in hold'em because there are four possible suits for the first card and four possible suits for the second card, and we all know that four times four is sixteen. In light of this, it's not complicated to figure out how many possible combinations of a non-pocket pair starting hand there are.

    The first step is to figure out how many of each card is left in the deck. For example, if we want to know how many combinations of AK our opponent could have, then we want to know how many Aces and Kings are left in the deck. The second step is to simply multiply these two numbers together.

    For example, if I want to know how many combinations of QJ an opponent could have when we hold AJ on a flop of JT4, then I note that there are 4 Queens left in the deck and 2 Jacks left in the deck, so there are 8 possible combinations of left QJ that a Villain could have.

    For another example, if I want to know how many combinations of AK an opponent could have when we hold AQ on a board of AKQ53, then first I see that there are 2 Aces and 3 Kings left in the deck. Therefore, there are 2x3 = 6 possible combinations of AK that a Villain could have.


    4. Brief Discussion of Blockers

    When you hold a blocker, you hold a card that makes it less likely for an opponent to have a specific starting hand. For example, if in hold'em you hold A5s before the flop, it's half as likely that a specific opponent is dealt AA than if you held KQ or KK or 87s. There are other examples as well, such in 2-7 single draw if you are dealt 22277 then it's much less likely that an opponent was dealt a pat 7 (75432, 76432, 76532, or 76542).

    This is very intuitive, but the effects of blockers are often misrepresented and misunderstood, which is why I've added the following onto this post about starting hand combinations.


    5. Effect of Blockers on a Villain's Range with Example Calculations

    Suppose that in some preflop scenario, we hold A3s and Villain's range is {QQ+, AK}. That gives him 12 possible combinations of AK, 6 of QQ, 6 of KK and 3 of AA, for a total of 27, and 33.33% of that range is KK+. If instead, we held JJ, then Villain would have 16 possible combinations of AK, 6 of QQ, 6 of KK and 6 of AA, for a total of 34, and 35.3% of that range would be KK+. The point is that blockers have the potential to weaken our opponents' ranges significantly.

    For the fun part (an example calculation for understanding blockers) I'm going to look at a fun 3-bet bluffing scenario:

    Suppose with 100bb stacks, Villain 4x opens a range of {22+, AQ+} from early position. If we assume that Villain only continues against a 3-bet with {JJ+, AK}, then how often does Villain fold if we hold 87s? A4s?

    If we hold 87s, then there are 104 hands combinations that make up {22+, AQ+}. Villain continues with {JJ+, AK}, which is 40 combinations. This means that Villain continues 38.5% of the time, and that Villain folds 61.5% of the time.

    If we hold A4s, then there are now only 96 hand combinations that make up {22+, AQ+} since we're taking away 3 possibilities each for AA and 44, and 4 possibilities each for AQ and AK. Villain continues with {QQ+, AK}, which is now only 27 combinations. This means that when we hold A4s, Villain continues just 28.1% of the time, and folds 71.9% of the time.

    If we assume Villain opened for 4x in EP and we 3-bet to 12x in LP, we need Villain to fold 68.6% of the time to break even just from our fold equity. Against the exact same ranges from our Villain, A4s was a guaranteed +EV bluff while 87s was not because of the blocker.

    6. Some Additional Applications of Blockers
    Last edited by spoonitnow; 10-05-2010 at 12:25 PM.
  2. #2
    sarbox68's Avatar
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    This is vry helpful Spoon... esp the thought process around using this to inform EV of bet-sizing on bluffs / semi-bluffs. I put together the chart below a while ago based on something I read somewhere, and use it when playing 'cause my memory's for sh!t. The cumulative number was to help me get an idea of combined frequency, generally rank ordered (emph. generally, as I'm sure could have a whole thread on whether this ordering is correct...), that I could compare to a VPIP or PFR stat as a starting range. "Small blind cards" adds the "none of the above" random crap that is most likely to be completed with in the SB vs. limps.

    Thought it was relevant and might be helpful.


  3. #3
    wellrounded08's Avatar
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    ...Good Question........Where am I?
    I fully expected this thread to be filled with intelligent responses within a day. I hold off on the comment I was going to make, which would have consisted of one of the following-
    Nice, Very insightful
    So when/where is the sticky going up?
    etc.

    Yet, no. I come back to find that after 75 someodd views. A single reply(sars post, which is what I was talking about when I said Intelligent responses)

    One. That tells me one thing. People click, skim, gain nothing, move on. Probably moving on to a quicker shorter thread that they think will Plug whatever leak they happen to be focusing on today. Is it really so hard? Is there an honest belief that getting better consists of skiming the threads of FTR looking for quick fix solutions? How about take a little time to learn the fundamentals?

    BTW:
    NH Spoon. This is undoubtedly "sticky-worthy" material.
  4. #4

    Default wellrounded

    I totally agree with you. The one thing i was thinking when i read this post was damn i wish there was a way to save to a favorite box of your favorite posts so i could go back over this with out trying to search through all the other posts. I read the whole post and I pretty much understand everything that was said however it is going to take me some practice and several readings to be able to do this at the table. I have been looking for this answer to my question for about 6 months and even posted the question on here several times to only get advice on ev and pot odds and outs. I guesse not knowing the answer I did not know how to properly ask the question.

    SPOON THIS WAS WITH OUT A DOUBT A GREAT POST. THANKS

    Don
  5. #5
    spoonitnow's Avatar
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    Ship it lazy people holla imo.
  6. #6
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    Great post.
    I personally find it easier to think about the probability in percentage of the deck and not of all card combinations. For example AA would be 4/50x3/49 - and if you did a couple of those calculations, you can estimate the number pretty exactly. For practical purposes you would round it down - 4/50 is about 1 in 12 - 3/49 is about 1 in 15 - 15x12 is 10x15+2x15 is 180. So it's about 1 in 180. I'm sure most people can do that without pen and paper in a reasonable amount of time.

    So your example if the board is KKQ - say you hold 63.
    Then the possibility of a single person having AA is:
    4/47x3/46
    or or KQ is:
    ok now you got me... I mean there's nothing wrong with doing an approximation (5/47x2,5/46)... but the calculation isn't rocket science either.
    1-[(1-3/47x2/46)x(1-2/47x3/46)]
    This is first the probability of getting QK and then KQ, and the rest is the "or" part. Actually the probabilities are the same whether you draw the K or Q first, you can cut it short to
    1-(1-(3/47x2/46)²)
    It's only that complex when there's not an even chance for both of the cars. Explanation is on the first or second page of any elementary probability book of your choice. There's about a 60% chance I got something terribly wrong here... it's been a long time
  7. #7
    I missed this until now, hmmm. Great post. It may need to be one of those re-reads for some people after a bit. Like TOP or Gbucks, You may get more every time you read it.

    Spoon, you certainly have a way with the teachin'. 6310 is gold.
  8. #8
    nice post dude. Im not much of a math guy and feel sorta useless not having much to add, but I just wanted to say that this will probably boost my growth as a poker player to be able to think about ranges a little more deeply. Appreciate you sharing this.
  9. #9
    spoonitnow's Avatar
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    Quote Originally Posted by oskar
    Great post.
    I personally find it easier to think about the probability in percentage of the deck and not of all card combinations. For example AA would be 4/50x3/49 - and if you did a couple of those calculations, you can estimate the number pretty exactly. For practical purposes you would round it down - 4/50 is about 1 in 12 - 3/49 is about 1 in 15 - 15x12 is 10x15+2x15 is 180. So it's about 1 in 180. I'm sure most people can do that without pen and paper in a reasonable amount of time.

    So your example if the board is KKQ - say you hold 63.
    Then the possibility of a single person having AA is:
    4/47x3/46
    or or KQ is:
    ok now you got me... I mean there's nothing wrong with doing an approximation (5/47x2,5/46)... but the calculation isn't rocket science either.
    1-[(1-3/47x2/46)x(1-2/47x3/46)]
    This is first the probability of getting QK and then KQ, and the rest is the "or" part. Actually the probabilities are the same whether you draw the K or Q first, you can cut it short to
    1-(1-(3/47x2/46)²)
    It's only that complex when there's not an even chance for both of the cars. Explanation is on the first or second page of any elementary probability book of your choice. There's about a 60% chance I got something terribly wrong here... it's been a long time
    The only problem with this is that it's harder to be able to do at the table, but it most certainly is easier to be exact when you just figure the probability straight-up.
  10. #10

    Default Question for spoon

    Ok I have read this post about ten times now, so i think I am ready to ask a question. I understan how to calculate using the formula that spoon gives. He is right pretty easy, my question is how to use it.

    1. Does this just give you fold equity,
    2. How do you calculate how much fold equity you need to break even or gain positive ev
    3. How do you figure out that ak is 60/40 dog to qq.

    These are pretty much all the questions that come to mind after reading your post. I hope my questions don't sound too broad to be answered.

    Thanks for all the help anyone can give me on this.

    Don
  11. #11
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    Default Re: Question for spoon

    Quote Originally Posted by bigstock2001
    Ok I have read this post about ten times now, so i think I am ready to ask a question. I understan how to calculate using the formula that spoon gives. He is right pretty easy, my question is how to use it.

    1. Does this just give you fold equity,
    2. How do you calculate how much fold equity you need to break even or gain positive ev
    3. How do you figure out that ak is 60/40 dog to qq.

    These are pretty much all the questions that come to mind after reading your post. I hope my questions don't sound too broad to be answered.

    Thanks for all the help anyone can give me on this.

    Don
    To calculate fold equity what you do is:
    1. Put your opp on a range based on previous action(i.e: he called, he raised from UTG,etc.)
    If he is yet to act, this range is all possible hand combinations(1326)
    The result of this will be a number of hands. We will call this "A".
    2. Think of the range he would call your raise or shove with(dont forget blockers you have)
    We will call this number B.
    3. B/A=X -----> The percentage of time he will call
    So, (1-X) ------> The percentage of time he will FOLD

    That is how you calculate your fold equity. Then you can calculate the EV of your bluff(without considering value from post-flop action) like this:

    current pot * (1-X) - your raise(aditional $ you put in the pot by raising) * X= EV

    Replacing EV for 0 and finding X will answer question number 2.

    For question 3 i believe, but not 100% sure, the math is a little too complicated because you have to consider a lot of factors, and the probability calculations would be a little too long. The easiest way of doing this is using Pokerstove.

    Please correct me anyone if i messed up somewhere, hope not.[/i]
  12. #12
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    Default Re: Question for spoon

    Quote Originally Posted by bigstock2001
    3. How do you figure out that ak is 60/40 dog to qq.
    Your questions have really already been answered, you just need to apply the math to other situation.
    Let's say AKo against QQ.
    AK needs to catch an A or K to win.
    But won't win if QQ will make a straight, flush or a set. Flush and straight are so slim that I would just slap an additional 1% on there, and not bother with the math too much.

    Catching an A or K - there are 3 kings and 3 aces left you need to catch either of them with any card on the board - so the probability for each card is:
    6/48, 6/47, 6/46,... and so on to the river.
    Again - wikipedia or google will have an explanation that I will not bother with because it's rather long:
    1-((1-6/48)*(1-6/47)*...) gives you your chance of hitting either an A or a K.
    By now you should understand how you do that for QQ hitting a set after you made the best hand (approximately), and if you're ambitious take straights and flushes into account.
    Similarly you can see what the added bonus is of having two suited cards, or having 2 suited cards and share the suit with one of the Queens, and so on...

    If you think AK is a 3:2 dog, then I would recommend you do the math... might make you some moneyz in the future.
  13. #13
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    Default Re: Question for spoon

    Quote Originally Posted by oskar
    Quote Originally Posted by bigstock2001
    3. How do you figure out that ak is 60/40 dog to qq.
    You download PokerStove and use it.
    FYP
  14. #14
    oskar's Avatar
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    Final Year Project?
    For Your Pleasure?


    I know about Pokerstove, I just think it would be good for some people to actually understand what's going on. The math involved in poker is so ridiculously simple... its really something you should understand at some point.

    Also you might want to know what the odds are of an overcard hitting the board if you have JJ... what are the odds of an overcard hitting if your opponent has AK, and so on. There are quite a number of things you can't do with pokerstove.
  15. #15
    why isn't this a sticky?
  16. #16

    Default Re: How-To: Calculating Hand Combinations, About Blockers, e

    Quote Originally Posted by spoonitnow
    5. Effect of Blockers on a Villain's Range with Example Calculations

    Suppose that in some preflop scenario, we hold A3s and Villain's range is {QQ+, AK}. That gives him 12 possible combinations of AK, 6 of QQ, 6 of KK and 3 of AA, for a total of 27, and 33.33% of that range is KK+. If instead, we held JJ, then Villain would have 16 possible combinations of AK, 6 of QQ, 6 of KK and 6 of AA, for a total of 34, and 35.3% of that range would be KK+. The point is that blockers have the potential to weaken our opponents' ranges significantly.

    For the fun part (an example calculation for understanding blockers) I'm going to look at a fun 3-bet bluffing scenario:

    Suppose with 100bb stacks, Villain 4x opens a range of {22+, AQ+} from early position. If we assume that Villain only continues against a 3-bet with {JJ+, AK}, then how often does Villain fold if we hold 87s? A4s?

    If we hold 87s, then there are 104 hands combinations that make up {22+, AQ+}. Villain continues with {JJ+, AK}, which is 40 combinations. This means that Villain continues 38.5% of the time, and that Villain folds 61.5% of the time.

    If we hold A4s, then there are now only 96 hand combinations that make up {22+, AQ+} since we're taking away 3 possibilities each for AA and 44, and 4 possibilities each for AQ and AK. Villain continues with {QQ+, AK}, which is now only 27 combinations. This means that when we hold A5s, Villain continues just 28.1% of the time, and folds 71.9% of the time.

    If we assume Villain opened for 4x in EP and we 3-bet to 12x in LP, we need Villain to fold 68.6% of the time to break even just from our fold equity. Against the exact same ranges from our Villain, A4s was a guaranteed +EV bluff while 87s was not because of the blocker.
    Spoon, I'm writing notes for a math class (NGCSU's Prob-Stats 3350, a calculus-based prob-stats class for math majors). Can I use this example in my notes, which I publish online here?

    Link: Poker & Probability Notes

    If so, should I use your real name or online name for attribution? It's classic, and it will make a perfect EV question.

    Also, I would be interested to hear your opinion of the notes, which are a first-brush attempt to write a prob-stats books totally motivated by real poker problems and questions. They are a work in progress, but getting better with thought, time and effort.
  17. #17
    spoonitnow's Avatar
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    Quote Originally Posted by Massimo
    why isn't this a sticky?
    Because it's me.


    Robb, go for it. My real name is Jesse Eddleman, which might be more appropriate than spoonitnow.
  18. #18
    Quote Originally Posted by spoonitnow
    Quote Originally Posted by Massimo
    why isn't this a sticky?
    Because it's me.
    I know people here are impressed, but I'm awed. I have created hundreds of math example problems in my life, and copied down thousands. The effort Spoon has to invest to get these incredible precise and poignant examples tweaked perfectly is immense - it takes skill and time. This whole "Spoon math" series in the Beginner's Forum the past few weeks has been awesome, taught like a real professor who knows his subject inside-and-out and, additionally, has a flare for explaining well.

    vnh
  19. #19
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    Quote Originally Posted by Robb
    Quote Originally Posted by spoonitnow
    Quote Originally Posted by Massimo
    why isn't this a sticky?
    Because it's me.
    I know people here are impressed, but I'm awed. I have created hundreds of math example problems in my life, and copied down thousands. The effort Spoon has to invest to get these incredible precise and poignant examples tweaked perfectly is immense - it takes skill and time. This whole "Spoon math" series in the Beginner's Forum the past few weeks has been awesome, taught like a real professor who knows his subject inside-and-out and, additionally, has a flare for explaining well.

    vnh
    yep.. SPOON FOR MOD IMO!!!!
  20. #20
    I have to admit that I'm totally lost reading this. Which is a shame since all of you have put so much work into it. I have read it a couple of times.
  21. #21
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    Quote Originally Posted by jolub
    I have to admit that I'm totally lost reading this. Which is a shame since all of you have put so much work into it. I have read it a couple of times.
    E-mail me at jesseeddleman yahoo.com and I'll see what I can help you with.
  22. #22
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    this is brilliant stuff... now here's my question... what is this advanced concept doing in the beginners circle???
  23. #23
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    Quote Originally Posted by ChezJ
    this is brilliant stuff... now here's my question... what is this advanced concept doing in the beginners circle???
    Since when is this advanced concepts?? And sorry to go out on a little rant, seriously what is up with everyone being against introducing difficult concepts to beginners? They will need to learn it at some point, and tossing it there way in the early stages accomplishes alot of things imho. (1) they realize it isn't a cakewalk and that they will have to work at it, which (2) developes a better work ethic toward studying because they actually need to try in order to understand some things (3) it doesn't allow them to get into a mentality in which they feel what they have been/are doing is good enough (4) makes them begin to think in ways which are vital to becoming a better player. If we keep the content in the BC as "don't stack of with less than two pair" (btw this is a total blanket statement and I am by no means saying this is correct), etc. then how can we expect for the players to improve? We have to introduce them to concepts that they must work to understand, and for some this is one of them.
  24. #24
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    Quote Originally Posted by XxStacksxX
    Quote Originally Posted by ChezJ
    this is brilliant stuff... now here's my question... what is this advanced concept doing in the beginners circle???
    Since when is this advanced concepts?? And sorry to go out on a little rant, seriously what is up with everyone being against introducing difficult concepts to beginners? They will need to learn it at some point, and tossing it there way in the early stages accomplishes alot of things imho. (1) they realize it isn't a cakewalk and that they will have to work at it, which (2) developes a better work ethic toward studying because they actually need to try in order to understand some things (3) it doesn't allow them to get into a mentality in which they feel what they have been/are doing is good enough (4) makes them begin to think in ways which are vital to becoming a better player. If we keep the content in the BC as "don't stack of with less than two pair" (btw this is a total blanket statement and I am by no means saying this is correct), etc. then how can we expect for the players to improve? We have to introduce them to concepts that they must work to understand, and for some this is one of them.
    I agree with you completely...Information like this is VERY VERY important for us beginners, and it is not advanced concepts we wouldnt understand. If someone doesnt understand it, there are plenty of FTR regs willing to help(i think).
  25. #25
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    Quote Originally Posted by ChezJ
    this is brilliant stuff... now here's my question... what is this advanced concept doing in the beginners circle???
    This isn't advanced. At all.
  26. #26
    This is not tough math however it is hard for me to apply it at the table. I agree as a noob that i would miss out completely if no body took the time to tell us about it or took the patience to work with those who did not understand it. Spoon in no way has left any one out there with info that he is not willing to work with people on. By the way I am still reading this about twice a day until i can put it at the table. I now can sit there at the table and figure out the odds that they could have pocket pairs or ak or what ever the part I still can't figure out at the table is fold equity, however i am still practicing.

    I choose to be able to do this stuff in my head once i have it down than maybe poker stove or something to make it easier, But i choose to know how the concept works so i can explain it to my friends and others as well,.

    Great post spoon
  27. #27
    YOU GUY ROCK is all I can say. I can't believe I have found a site where so many people who are doing so well are SO DAMN HELPFUL!
    I'm reading and reading and reading. Then I cut, copy, paste and print. So much info and I want it all. It is very unfortionate I'm not anywhere near the skill level or education as are you the contributors. I doubt I'll be able to sit at a table and put this all to use but I am sure going to try and get my arms around it. I'll no doubt utilize some automated tools but atleast by reading and studying I'll better understand what it is pokerstove and that are telling me.

    THANKS AGAIN GUYS!

    Oh yeah Spoon you recommend "Apple picking and wall pushing?" Same guy I take it???
    "You start the game with a full pot o’ luck and an empty pot o’ experience...
    The object is to fill the pot of experience before you empty the pot of luck."

    Quote Originally Posted by XxStacksxX View Post
    Do you have testicles? If so, learn to bet like it
  28. #28
    Brilliance!
    Thanks for the great post.
    3 3 3 I'm only half evil.
  29. #29
    Great post.

    I was thinking about it today, and if you've ever played the guitar or snow skied, (those are two things that I do that I think relate to poker in what I'm about to say, but I'm sure there are more), you get started on a path that will take you from beginner to intermediate, but then you'll hit a wall.

    From what I can tell, there are really two paths on your way to becoming great at poker. The first path is from beginner to intermediate, and it's basically just repetition, learning the basics, and more or less just improving upon what you already know. But eventually, you stop improving.

    And that's when you need to approach the game from a different angle. You need to start thinking about your opponents cards, what your opponents thinks about your cards, etc.

    My point is, the path to being great isn't a straight line from beginner to pro with a stop in the middle at intermediate. It's two separate lines, and if you're not willing to essentially relearn the game from a different angle, then you can't expect to get anywhere significant in the game.
  30. #30
    This is another great post from spoon. The concepts in this post will improve my game to another level.
    Don't knock on deaths door... ring the bell and run! Death hates that LOL.
  31. #31
    Is spoony still around? Or still on a self ban?
    3 3 3 I'm only half evil.
  32. #32
    spoonitnow's Avatar
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    Quote Originally Posted by mrhappy333
    Is spoony still around? Or still on a self ban?
    Bump.

    I'm around. Sorta.
  33. #33
    Bumpage
  34. #34
    Can this please be a sticky already??
  35. #35
    I've just re-read this classic , It means more to me now than the last time i read it.
  36. #36
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    Spoonitnow,

    I just read this and I have 2 words for you:
    Awesome. awesome, awesome.

    6310 makes this seem even more basic than it already was!

    Am currently(still) at the micro level (5nl), mainly due to one of my major leaks...not being able to put opp's on a hand range.

    I see that it's been said many time already, but thnx for info.
    "The problem with Socialism is that you eventually run out of other people's money!".......M. Thatcher
  37. #37
    I wish there was someone around here who new how to press the sticky button.
  38. #38
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    Great post, this has really clarified a lot for me. Of course it will take a while to absorb it.
    I'm having a little trouble with this paragraph:
    If we hold A4s, then there are now only 96 hand combinations that make up {22+, AQ+} since we're taking away 3 possibilities each for AA and 44, and 4 possibilities each for AQ and AK. Villain continues with {QQ+, AK}, which is now only 27 combinations. This means that when we hold A5s, Villain continues just 28.1% of the time, and folds 71.9% of the time.
    Surely it is 104-14 = 90 combinations?
    Also, we are holding A4s not A5s or am I missing something

    I don't mean to nitpick but for a newbie I'm always worried I have misunderstood or missed something that I should be aware of.
    Also, you made an offer for people to send you an e-mail with specific questions. Is that still open and if so does it apply to any questions we may have?
  39. #39
    spoonitnow's Avatar
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    That should say A4s instead of A5s. Good catch.

    {22+, AQ+} before any blockers are accounted for is 110 combinations.

    110 - 3 (for AA) - 3 (for 44) - 4 (for AQ) - 4 (for AK) = 96.
  40. #40
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    22+ gives 13 paired hands, 6 combos in each = 78
    AQ+ gives two non-paired hands with 16 combos in each = 32

    78+32 = 110

    Okay, got it, thanks.
  41. #41
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    Bump. Someone e-mailed me asking the following:

    I read the article above and have a few questions. I understand the math. I did your exercises for hand combinations and was able to calculate all of the exercises correctly. I am not quite sure how to use this in my online game. With Poker Stove I can enter the range and run the situation. Doesn't that run using combinatorics? If so, is there really a reason to do it by hand? Or is all of this kind of just to know how the program is spitting out numbers? I'm sorry if this email is sloppy - long day and should get some sleep, but I wanted to send this because this question has really been bugging me. Thank you so much for your time!

    My reply was:

    PokerStove does deal with the combinatorics, so you're good there, and calculating equity by hand is kind of pointless. But part of the point of understanding this stuff is to be able to have an idea with how an opponent's range is weighted. For example, suppose you've got AK on a board of AKQ33 and your opponent's range for whatever reason is {AQ+, QQ+}. That's 1 combo of AA, 1 combo of KK, 3 combos of QQ, 4 combos of AK, and 6 combos of AQ, so we beat 6, lose to 5, and tie with 4, putting us slightly ahead. Someone who didn't understand this at all would just say we beat 1 hand (AQ), tie 1 hand (AK), and lose to 3 hands (AA, KK, QQ), giving them the idea that we're way behind here.

    Just thought that might be useful to someone.
  42. #42
    Quote Originally Posted by spoonitnow View Post
    Bump. Someone e-mailed me asking the following:

    I read the article above and have a few questions. I understand the math. I did your exercises for hand combinations and was able to calculate all of the exercises correctly. I am not quite sure how to use this in my online game. With Poker Stove I can enter the range and run the situation. Doesn't that run using combinatorics? If so, is there really a reason to do it by hand? Or is all of this kind of just to know how the program is spitting out numbers? I'm sorry if this email is sloppy - long day and should get some sleep, but I wanted to send this because this question has really been bugging me. Thank you so much for your time!

    My reply was:

    PokerStove does deal with the combinatorics, so you're good there, and calculating equity by hand is kind of pointless. But part of the point of understanding this stuff is to be able to have an idea with how an opponent's range is weighted. For example, suppose you've got AK on a board of AKQ33 and your opponent's range for whatever reason is {AQ+, QQ+}. That's 1 combo of AA, 1 combo of KK, 3 combos of QQ, 4 combos of AK, and 6 combos of AQ, so we beat 6, lose to 5, and tie with 4, putting us slightly ahead. Someone who didn't understand this at all would just say we beat 1 hand (AQ), tie 1 hand (AK), and lose to 3 hands (AA, KK, QQ), giving them the idea that we're way behind here.

    Just thought that might be useful to someone.
    BUMP

    I've read through this thread many times as is evident by a reply a few years back. I was reading through it again and was really glad I had when I came upon this addition!
    "You start the game with a full pot o’ luck and an empty pot o’ experience...
    The object is to fill the pot of experience before you empty the pot of luck."

    Quote Originally Posted by XxStacksxX View Post
    Do you have testicles? If so, learn to bet like it
  43. #43
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    Fun fact: the number of combinations of hole cards for pocket pairs is based off of triangles, while the number of combinations of hole cards for non-pocket pairs is based off of rectangles.

    There's a series of numbers called the Triangular Numbers, which is just based around stacking cans or something in pyramids like you would as a kid:



    T1 is the first triangular number, T2 is the second, and so on. If you notice, T1/T2/T3 are 1/3/6 which are the numbers that correspond to the number of possible pocket pair combinations if there are 2/1/0 of the respective card removed from the deck. What you can extrapolate is that if a deck of cards had 5 suits instead of 4, the pocket pair combinations would be based off of 10-6-3-1-0 instead of just 6-3-1-0. Similarly, if it had 6 suits, it would be 15-10-6-3-1-0, and so on.

    So for non-pocket pairs, imagine you have 3 Aces and 4 Kings available in the deck. Then you do 3x4 and get 12, which is a rectangle that's 3 by 4:

    ***
    ***
    ***
    ***

    or

    ****
    ****
    ****

    and so on. Same thing for the rest of the non-pocket pair combos. Like say you have 2 King and 3 Queens, then you'd have this rectangle:

    **
    **
    **

    or this one

    ***
    ***

    which both give you 6 combinations.
  44. #44
    Cool addendum.

    The one calc that used to make my brain hurt is figuring out non-paired offsuit combos. Pairs and suited == easy stuff. But then I finally figured out a shortcut: use spoon's rectangle math above for all combos of non-paired hands and then subtract out the number of suited combos left.

    Ex: How many AKo on AcKc9d board? 3 Aces * 3 Kings - 3 suited (d,s,h) = 6
    Ex: How many AKo on AcKdKs board? 3 Aces * 2 Kings - 1 suited (h) = 5
  45. #45
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    Bump. Been giving this thread to a lot of new players lately so that they can learn to calculate the combinations to figure out if their bluffs are profitable.
  46. #46
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    Bump. Still one of the most important threads.
  47. #47
    Nice post, read through it and understood most, bit late at night and my brain is sore from playing and reading all day lol! I shall re-read in the mornin when my mind is fresh and get practicing tomorrow, thanks!

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