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  1. #1
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    Default Hand Ranges, Odds and Pre-Flop Equity Tables

    I posted summary and detail SE% tables for all 169 hand combinations v 10 different opponent ranges in the Limit Holdem section - the link is here:

    http://www.dragthebar.com/poker-foru...=6649#post6649

    I thought it would be beneficial for new players to produce a simple Hand Range & Odds Chart (that you can build easily on Excel) to highlight the basics.

    THE BASICS

    There are 1326 hand combinations (if you include all the suits) and 169 hand combinations (if you do not).

    1/1326 = 0.075% and this is the value of 1 hand (if we include all the suits).

    There are 3 types of hands, each with a total number of possible combinations:

    6 hands = Pairs
    4 hands = Non Pairs (Suited)
    12 hands = Non Pairs (Unsuited)

    (There are 4 + 12 = 16 hands in total for each non-pair hand)

    Therefore any hand combination will have the following % of total hands:

    6 x 0.075% = 0.45% = Pairs
    4 x 0.075% = 0.30% = Non Pairs (Suited)
    12 x 0.075% = 0.90% = Non Pairs (Unsuited)

    (The total value for a non-pair hand is 0.30% + 0.90% = 1.20%)

    for example AA can be AsAh, AsAd, AsAc, AhAd, AhAc, AdAc = 6 combinations x 0.075% = 0.45%

    The split of the 169 total hands for each type, ignoring suits, is as follows:

    13 = Pairs
    78 = Non Pairs (Suited)
    78 = Non Pairs (Unsuited)

    It is possible to work out the total range % for various combinations:

    Pairs = 13 x 0.45% = 5.8% for 78 hands out of 1326

    Non Pairs (Suited) = 78 x 0.30% = 23.4% for 312 hands out of 1326

    Non Pairs (Unsuited) = 78 x 0.90% = 70.2% for 936 hands out of 1326

    (The balance of 0.6 is roundings as I only went to 2 decimal figure).

    CALCULATING RANGES

    A 'range' for an opponent is made up of a combination of possible hands and you can quickly work out the range %. For example:

    You put the opponent on 99+/AT+.

    There are 6 pair hands (AA/KK/QQ/JJ/TT/99) x 0.45% = 2.70%

    There are 4 non pair suited hands (AKs/AQs/AJs/ATs) x 0.30% = 1.20%

    There are 4 non pair unsuited hands (AKo/AQo/AJo/ATo) x 0.90% = 3.60%

    The total range for the opponent is = 2.70% + 1.20% + 3.60% = 7.50%

    Note:

    We could have used 1.20%, the value for a non pair hand, to work out the non pair range more quickly:

    There are 4 non pair hands (AK/AQ/AJ/AT) x 1.20% = 4.80%

    This is the same total as 1.20% + 3.60% for the suited + unsuited non-pair hands above.

    We are used to seeing players with tight (around 10%) to loose (25%) to maniac (50%+) vpip, but are there any standard ranges that apply?

    STANDARD RANGES

    There are 8 main hand categories:

    Pairs...................5.88%
    Axs.....................3.62%
    BWs....................3.01%
    SC.......................2.41%
    SC1 Gap..............2.11%
    Axo.....................10.9%
    BWo....................9.04%
    UnSC...................7.24%

    (BW = Broadway, any A/K/Q/J/T combination, SC = suited connectors)

    A 10% (approx) range could be made up of Pairs, BWs and SC (11.3%), or the upper half of Pairs, BW and SC (99+/AJ+/KJ+/T9s-76s) for 9.8% or other combinations - as a range % increases, the potential for different types of combinations increases as well.

    A player may also play different cards in different positions.

    It is very important to watch the cards people play and also make a note of how active they are from various positions. Do the play Axs or Ax, premium pairs or all pairs, all BW or just BW headed by A and K.

    There are only a certain number of combinations people can play - and showdowns provide a lot of information, so be alert at the table!

    The 8 main Range Categories above total over 43% of all available hands (if an opponent is playing ALL of these hands he is very loose indeed) and Hand Reading is a simple art based on structured range analysis - it should become second nature with experience.

    There are 169 possible hands (if you ignore suits) and you can use the Hands Ranges & Odds (or Table Monitor) Chart below as a guide to Hand Categories, use the 8 categories above or make up your own key groups - but preparation is important before you sit down at a table so that you know what to look for.

    A 10% VPIP is tight, over 25% is loose and between 10% and 25% fairly average. 40%+ is a very exploitable fish type player.

    When you sit down at the table, take you time and look at the hands people show, marking them off in your groups and you will start to build up a picture of their range and see how your picture compares to their VPIP. The picture you build will be very useful during hands you play against these opponents, because you will have a better idea if they have hit the board and can also use their betting patterns as an aid as well.

    The Chart also shows the odds you need to play the hands if YOU hold those cards - and the preflop SE% v 1 opponent.



    The chart highlights different types hands, made up of:

    Any pair/Browadway/Axs are 20% (in Orange) and:

    Suited Connectors, up to 3 Gap, are 10% (in Blue) and:

    Unsuited Connectors, up to 3 Gap, are 30% (in Yellow).

    The individual range for each group of hands is also shown.

    You may be unsure about the odds you need for a type of hand you have. The table shows you the expected Showdown Equity % (or chance of winning) v an opponent with a very tight 7.4% range - for every group of hands, via a minimum and maximum limit.

    For example, if you have 76s, your SE% is between 33% and 28%. The % falls from left to right for the hands listed, so you can make a better estimate of 30% because 76s is in the middle of the list. If you had 32s (at the end of the list), your SE% would be 28% and if you had T9s (at the start of the list) it would be 33%.

    The MINIMUM ODDS required to give the SE% against a 7.4% opponent's range is also shown - for the last hand in the list. For example:

    32s requires at least 2.5:1 odds to have a SE% of at least 28%.

    This rises to at least 2:1 odds for T9s at the start of the group.

    (You can quickly find the odds by looking at the same value in a higher group where it is the lowest. 33% is slightly better than the 32%/2.1:1 for the last hand in the Axo list).

    Therefore you have a quick and easy reference for any hand, giving SE% and the odds you need. These are ALSO the odds your opponent will be looking for if any of these hands are part of his range - useful information if you are in a hand against him.
    Last edited by sun137; 03-31-2010 at 10:46 AM.

  2. #2
    Coach Extroadinaire
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    Default Re: Hand Ranges, Odds and Pre-Flop Equity Tables

    Great job. Thanks for sharing all your hard work with everyone.
    Check out my books at qtippoker.com.
    DTB Rakeback/VIP signups at vip.dragthebar.com

  3. #3
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    Default Re: Hand Ranges, Odds and Pre-Flop Equity Tables

    TY QTip.

    The Rule of 13 is important as part of a quick and simple process for identifying total combos for any Hand Range and working out the call or fold decisions in pot equity v % share of villain's range required to be folded.

    It doesn't matter on the mix of hands in a range - the maximum number of combos is always very close to x 13.

    If you are facing (say) a 10% range, the maximum number of combos are roughly 130.

    If you have (say) 20% equity to call, are there more than 26 possible combos in his range that fit the board?

    If not, call. If there are, fold.

    (I am ignoring any other profiling factors).

    It is possible to use a simple table for all major equity decisions and this is something I will post in this thread after my next class.

  4. #4
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    Default Re: Hand Ranges, Odds and Pre-Flop Equity Tables

    Poker is always a balance between Investment and Risk.

    There are various ratios of BR to buyin used for different risk strategies and equity should be a key element in how you approach risk at the table. A detailed post session analysis is important for reviewing big decisions we made in the heat of battle, but tbh there is actually a narrow boundary for these type of decisions when you are facing one of the 15 profile types in the 'building a profile' thread.

    It is possible to build an 'attack' and 'defend' table to cover these types of opponents at all boards with the cards you normally play because the difference in equity is narrow for raise, shove or call decisions and large for fold decisions.

    If you look at the hand range chart (above) in this thread you can see the majority of equity against a 7.4% range is between 28% and 40% for all the hands we will normally play, except for the 99+/AQ+ where it is 44% - 84%. It is possible to identify the actions you will take against these players IN ADVANCE by working out the equity you will have in situations where you will actually PLAY the hand.

    There will be a lot of equity % that overlap and this allows you to condense the initial tables into an overall table for attack and defend in these shove/fold situations.

    This is one of the tables I will be using to develop the equity/combo/range analysis v a profiled opponent (see the profile building thread) when i get the time. I have touched on a few of the concepts in this thread.



    The table shows all the B/E Fold Equity % for investments or risk (bets) and reward (current pot), from 10bb - 200bb. A black line has been drawn at the the 100bb risk and reward figures, because we normally play with stacks 100bb deep.

    If, for example, you bet 40bb to win a 70bb current pot, the B/E Fold Equity is 36%.

    The bet of 40bb could be a cold bluff investment or a warm semi bluff where the average loss is 40bb.

    The table shows a large % of bluffs have a F/E within the 28% - 40% range, matching the all-in equity for the majority of hands we play against a 7.4% range. There is a strong link between aggressive bluffing and solid post flop hand/board reading skills, to identify the correct situation with the right opponent, because there is normally sufficent equity in the majority of hands we play to allow us to fall back on 'plan b' if called - our equity at showdown.

    Back TO BASICS

    If we go back to basics and the standard formula (or Cold Bluff) for the fold %:

    Pot : Cost of Bluff = Cost / (Cost + Pot)

    If we move to the Semi Bluff formula (or Warm Bluff) for the fold %, the 'Cost of Bluff' is replaced by 'Average Loss' (our 'True' bet cost or EV when called), but what is Average Loss?

    Average Loss is equal to our equity in the current pot and villain calling cost, less the losing equity of our bet cost:

    (Current Pot x Equity) + (Calling Cost x Equity) - [Bet Cost x (100% - Equity)]

    However the [Bet Cost x (100% - Equity)] can be expressed as:

    Bet Cost - (Bet Cost x Equity)

    Therefore the Semi (Warm) Bluff Formula can now be expressed as:

    (Current Pot x Equity) + (Calling Cost x Equity) - (Bet Cost - [Bet Cost x Equity])

    OR

    (Current Pot x Equity) + (Calling Cost x Equity) - Bet Cost + (Bet Cost x Equity)

    OR

    Equity(Current Pot + Calling Cost + Bet Cost) - Bet Cost

    This reduces the Average Loss formula to:

    (Final Pot x Equity) - Bet Cost

    Therefore our formula for Semi (Warm) Bluff for the villain fold % is:

    Pot : Average Loss = Average Loss / (Average Loss + Pot)

    Example:

    We have hero covered after calling a squeeze bet preflop - how often does villain need to fold on the flop to make a bluff profitable?:

    Hero Hand........................9d8d
    Villain Squeeze Range.......10%
    Flop..................................2d5h6h
    Effective Stacks.................$58.05
    Current Pot.......................$23.50
    Final Pot............................$139.60
    Bet Cost.............................$58.05
    Equity................................33%

    (The flop equity is from Poker Stove and increases by 1% if you ignore the flop cards).

    Average Loss......($139.60 x 33%) - $58.05 = $46.07 - $58.05 = - $11.98

    Fold %..............$23.50 : $11.98 = $11.98 / $35.48 = 33.76%

    Therefore the opponent needs to fold more than 33.76% to make the semi bluff profitable and the 'true' bet cost is $11.98 to win $23.50

    If you do not expect the opponent to call with all his range, the figures are as follows:

    98s v 5% range................29% equity..........$40.48 equity in Final Pot............- $17.57 Average Loss (true bet cost invested).......Villain needs to fold more than 42%

    98s v 3% range................25% equity..........$34.90 equity in Final Pot............- $23.15 Average Loss (true bet cost invested).......Villain needs to fold more than 50%

    3% range = 99+/AQs+

    B/E Formula

    The formula x*win + (1-x)*loss = 0, where x = B/E Fold Equity, can be expressed differently and converted to the Cold Bluff Formula:

    equals...............Win*x + Lose*x - Lose

    equals...............x(Win + Lose) - Lose

    equals...............x = Lose/(Win + Lose)

    equals...............F/E = Bet Cost/(Current Pot + Bet Cost) [This is the Cold Bluff Formula]

    equals...............F/E = Average Loss/(Current Pot + Average Loss) [This is the (warm) Semi Bluff Formula]

    where...............Average Loss = (Final Pot x Equity) - Bet Cost

    Therefore we can see it is possible to establish if a decision was correct in our post analysis review, but how do we make quick decisions in the heat of battle?

    We need to identify:

    The hands we will play by position to open the betting or respond to the betting
    The actions we will take v our 15 profiled opponents
    Our equity in all flops for the hands we play
    The size of the pot we want to play
    Our flop actions based on the betting, profile and board information
    Our turn action based on the possible cards we may see

    There are an infinite number of possibilities for all possible hole cards, but we are only interested in the hands we intend to play.

    The process is to take each playable hand in turn, identify the various actions and condense them into unique responses for attack and defence, using various equity tables to reach our goal.

    The tables in this thread are the starting point for the process.

  5. #5

    Default Re: Hand Ranges, Odds and Pre-Flop Equity Tables

    I really like these charts. Nice work.

  6. #6

    Default Re: Hand Ranges, Odds and Pre-Flop Equity Tables

    Can you post the excel version of that chart?

  7. #7

    Default Re: Hand Ranges, Odds and Pre-Flop Equity Tables

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