PokerCruncher Tutorial

What's Equity? Fully General Hand Ranges Deal-To-Flop Analysis, Many Flop Stats
Flop Texture Analysis Additional, Expert-Level Features
(Mac Version)
(New!)

Table Of Contents

Introduction

General Usage

Basic Features - Completely General

1) Internet Connection Not Needed
2) Up To 10 Players
3) Specific Or Random/Unknown Cards
4) Equity/Win/Tie %age's
5) Hand Type Stats
6) Equity
7) %age's Or n:1 Odds
8) Generate Random Player And Board Cards
9) Fold/Un-Fold Players
10) Dead Cards
11) Setting For Number Of Random Monte Carlo Simulation Trials
12) Shortcuts

Fully General Hand Ranges

* Hand Combos (Weights) In Hand Ranges
* Suits In Hand Ranges
* Top X% Of Hands Slider
* Hand Range %age/Odds Indicator
* Extensive Built-In Hand Ranges
* Range Equity Heat Maps And Hand Combo Stats

Deal-To-Flop Analysis, Many Flop Stats

* Hand Type Stats
* Flop Hit Stats
* Odds For Flopping Draws And Combination Draws
* OnePair Breakdown Stats

Flop Texture Analysis

Save/Load And Export/Import Scenarios (Hands) And Hand Ranges

Monte Carlo Simulation, Complete Enumeration

Answer Interesting And Challenging Odds Questions


Additional, Expert-Level Features (Mac Version) (New!)

Hand Ranges Features:
* Range Equity Distribution Graphs (Mac Version)
* Additional Hand Orderings For Top X% Of Hands Slider/TextField (Mac Version) (New!)
* View Hand Combo Counts In Hand Range Grid (Mac Version)

Stats Features:
* Mouse Over A Range's Stats When Doing Flop Texture Analysis (Mac Version)
* Full Stats And Features For Deal-To-Turn (Mac Version)
* Customizable "Total Hit" Stat (Mac Version)


Conclusion



Note:
This Tutorial's screenshots are from the iPhone version of PokerCruncher, except for the screenshots in the "Additional, Expert-Level Features" section which are from the Mac version of PokerCruncher. The Android version of PokerCruncher may have some small differences.




Introduction

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This Tutorial explains PokerCruncher's features and shows you how to use PokerCruncher to improve your game by:
  • Thinking in terms of hand ranges, not just specific hands or random hands.
  • Understanding flop odds, in addition to the usual river odds.
  • Using advanced techniques like flop texture analysis.
PokerCruncher is an advanced Texas Hold'em odds calculator that supports:
  • Fully General Hand Ranges
  • Deal-To-Flop and Flop Texture Analysis
  • Many Stats: hand type stats, flop hit stats, odds for flopping draws and combination draws, OnePair breakdown stats
  • Range Equity Heat Maps And Hand Combo Stats
  • Save/load and export/import scenarios (hands) and hand ranges (import feature: iOS and Mac versions)
Few, if any, odds calculators have these powerful features at the level of PokerCruncher (including PokerStove, the excellent Windows PC program). But with all of these powerful features it may be hard to see where to start to use PokerCruncher effectively; this is the goal of this Tutorial.




General Usage

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PokerCruncher is a powerful poker odds/equity study and analysis tool for improving your game. You can of course use it however you'd like, but it's not meant to be used in real-time in the middle of a live casino hand (no casino would allow you to).

Internet play is different; you should be able to use PokerCruncher effectively in internet hands, especially the Mac version of PokerCruncher. For example you can create a library of useful hand ranges for different styles of players and for different positions, and with PokerCruncher running side by side you can quickly put your opponents on hand ranges and calculate.

As a study and analysis tool, here's how you can use PokerCruncher to improve your odds knowledge and decision making process:
  1. Review key hands you've played to analyze the odds/equity each step of the way, to see if you made the right decisions and how you could have played better. Discuss your big hands and strategies with friends or on forums. PokerCruncher's save/load and export/import features let you save key hands (scenarios) for future review and share scenarios and hand ranges with friends (import feature: iOS and Mac versions).
  2. Set up and analyze realistic "what if" scenarios you're likely to encounter in the future.
  3. Analyze and test yourself on random scenarios (use the "Rnd" button to generate random player and board cards).
  4. Analyze specific hand vs. hand range scenarios. Poker is a game of incomplete information, you don't know your opponents' cards, so being able to estimate your equity against a range of hands is very important.
  5. Analyze flop odds/equity, in addition to the usual river odds/equity. PokerCruncher's Deal-To-Flop and Flop Texture Analysis features let you do this. These features also give you many stats - hand type stats, flop hit stats, odds for flopping draws and combination draws, OnePair breakdown stats.
The below sections explain how to use PokerCruncher's powerful features to do the above things, using real-life hand situations as motivating examples.




Basic Features - Completely General

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1) Internet Connection Not Needed

2) Up To 10 Players

3) Specific Or Random/Unknown Cards

4) Equity/Win/Tie %age's

5) Hand Type Stats

First note that PokerCruncher does all of its calculation locally on your device/machine so an internet connection is not needed.

You can enter up to 10 players. You can enter specific cards for the players and the board, or you can leave some cards blank, which means random/unknown cards. (You can also enter hand ranges, but that's an advanced feature that we'll cover later, below.) This is useful e.g. for reviewing hands you've played where in retrospect you know your opponents' cards, or for analyzing "what if" scenarios.

For example consider the below 3-player specific scenario. JTs has flopped an open end straight draw and a backdoor flush draw against overpairs AA and KK. As you can see, JT's Equity is about 38%, and the Stats view shows how often JTs will make a Straight, Flush, OnePair, TwoPair, etc. by the river.

Positive equities (10% or more above breakeven equity) are colored green; negative equities (10% or more below breakeven equity) are colored red (actually, orange); breakeven equities are colored yellow.

Also consider the below 10-player random scenario: AA vs. 9 random hands. AA's Equity is about 31%.

In addition to each player's hand type stats (tap/select the player to view the player's stats in the Stats view), PokerCruncher can also show the winning hand's hand type stats (tap/select the board). For example you can use the winning hand's stats feature to see what the expected best hand is for example if 3 players with random hands go to the river.


Example: Basic Calculation:
3 Players With Specific Cards,
And A Specific Flop:

PokerCruncher - Basic Calculation

Example: Basic Calculation:
AA vs. 9 Random Hands,
Preflop:

PokerCruncher - Up To 10 Players


6) Equity

Equity is a player's %age ownership of the pot (or of the situation/scenario). It's the sum of the player's Win %age and the fractional ownerships of the pot that the player has in ties with other players.

Equity's add up to 100% but Win %age's usually don't (because of ties). Most people usually think about Win %age, but Equity is really the more important stat.

Consider the below example: AA vs. AA. Win %age for both hands is only about 2.2% (when they make a flush using a single Ace). But the hands tie about 95.6% of the time and each hand's Equity is 50%. The 50% Equity %age describes the even nature of this matchup much better than the 2.2% Win %age. This example is extreme, but similarly in general, Equity is the better stat to think about.


Example: Equity: AA vs. AA:

PokerCruncher - Equity: AA vs. AA


7) %age's Or n:1 Odds

PokerCruncher can show all stats as %age's or as n:1 odds (against). "n:1F" means odds "in favor". The "n:1" ("%") button toggles between the two.


8) Generate Random Player And Board Cards

The "Rnd" button assigns random player and board cards.
  • If you tap/select a player card, the "Rnd" button assigns random cards to all players that you haven't assigned cards to. So for example you can enter specific cards for Player1 (you) and tap the "Rnd" button to generate random cards for the other players.
  • If you tap/select a flop/turn/river card, the "Rnd" button generates a random flop/turn/river. In addition, if you tap/select a flop card, a new submenu "Random Flop" appears in the Menu ("Menu" button), which you can use to generate more specific kinds of random flops like: broadway/medium/low flop, suited flop, paired flop.
You can use this feature to generate random what-if and test scenarios and test your odds estimates against PokerCruncher at each street: preflop, and after a random flop, turn, and river.


9) Fold/Un-Fold Players

You can use the "Fold Selected Player" button in the Menu to fold a player out of the hand, and the "Un-Fold Selected Player" button to put a player back into the hand.


10) Dead Cards

You can enter dead cards: tap Menu --> Dead Cards, Settings --> Set Deck Card Dead/Live button, then tap a deck card to mark it dead/live.


11) Setting For Number Of Random Monte Carlo Simulation Trials

PokerCruncher has a setting (Menu --> Dead Cards, Settings --> Number Of Sim Trials) for the number of random trials to do for Monte Carlo simulation.

"2 x Default" (or higher) is recommended for faster devices.

Note that there's an Infinite setting. You can stop/continue the calculation.


12) Shortcuts

  • Double-tap a player's card/range field to bring up the Hand Range Editor screen. (iPhone and Android versions)
  • Long-tap a player’s card/range field to bring up the player’s shortcut menu. This menu lets you do some important operations faster e.g. fold/un-fold a player, load a saved hand range onto a player (without having to open the hand range editor screen). (iPhone, iPad, and Android versions)



Fully General Hand Ranges

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Poker is a game of incomplete information; you don't know your opponents' cards. So you must put your opponents on ranges of hands given the information you've gotten so far in the hand, not just on specific cards. PokerCruncher's fully general hand ranges feature lets you do this, and this feature is where PokerCruncher starts to separate itself from many other odds calculators.


Real-Life Hand Situation: How to play QQ preflop when facing a re-raise?:

Let's look at a specific simple preflop situation that's very common - we call it the QQ dilemma. This example illustrates why QQ can be a difficult hand to play. You're in a 2/5 no-limit game and you have a 500 stack. You're in early position with QQ and you raise to 20. A solid tight-aggressive player on your left (also with a 500 stack) 3-bets you to 60. Everyone folds, and you 4-bet to 200, thinking your QQ is the best hand and since you're out of position (this may not be a smart play on your part, it may be better to call, or fold, but we'll say you 4-bet). Your opponent goes all-in for 500. It's 300 for you to call his all-in. Should you call his all-in?

It all depends on how this opponent plays of course. If he only makes this play with AA or KK, then you should fold, because it's 300 to you to win 707 (your opponent's 500 + your 200 + the blinds = 707), so you're getting about 7:3 pot odds for the call, but you're a 4:1 underdog (your QQ has about 20% Equity against AA or KK), so you don't have enough pot odds to make the call.

But let's say this opponent loves to make this play with AK too. Now the situation is more complicated. Here's how you can analyze this situation in PokerCruncher using hand ranges:
  1. Player1 (you): Enter specific cards QQ (suits don't matter in this example).
  2. Player2 (opponent): Enter hand range {KK+, AKs, AKo}. To enter a hand range select (tap) a player's field and tap the "Rng" button, or just double-tap a player's field. "KK+" means "KK or better" i.e. KK or AA. "AKs" means AK-suited. "AKo" means AK-offsuit.
  3. Calculate. You see that your Equity with QQ is about 40%.
This is pretty decent, not too much less than 50%. You may have thought your Equity would be lower than this because you're a big underdog against AA and KK (80:20 underdog), and you're only a 57:43 favorite against AK (only a little better than a coin flip). But there are 16 hand combos for AK (4 combos for AKs, 12 combos for AKo), and only 6 hand combos for AA and KK each, so your opponent will have AK more often (16 hand combos) than AA and KK combined (12 hand combos). Beware, not all odds calculators take this number of hand combos factor into account correctly.

Back to your decision - you're getting about 7:3 pot odds for the call (you need to call 300 to win 707), so you need more than about 30% Equity. You have about 40% Equity, so this is a profitable call. Best decision: call (if the hand range {KK+, AKs, AKo} for your opponent is accurate of course).


Example: QQ vs. Hand Range {KK+, AKs, AKo}, Preflop:

PokerCruncher - Hand Range Calculation: QQ vs. {KK+, AKs, AKo}               PokerCruncher - Hand Range: {KK+, AKs, AKo}




Hand Combos (Weights) In Hand Ranges

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In the QQ vs. {KK+, AKs, AKo} example above, we noted that there are 16 hand combos for AK (4 for AKs and 12 for AKo), and 12 hand combos for KK+ (6 for AA and 6 for KK). So in the hand range we constructed above, AK has more hand combos than KK+. This default/full hand weighting helps QQ's Equity (40%) in this example, because it's up against AK more often than it's up against KK+.

But what if our opponent doesn't always play AK this way. What if he plays it this way about half the time he gets this hand? We can use PokerCruncher's Suits view (hand combos) to model this custom hand weighting:
  1. Player2 (opponent): Enter hand range {KK+, AKs, AKo}, as in the above example.
  2. Tap the AKo grid cell to select it.
  3. Tap "Suits" button. Note that by default the full set of hand combos is turned on (12).
  4. Turn off half (6) of the hand combos by tapping on each of them. We'll remove the 6 hand combos in the top triangle. Unless flush draws are involved, the specific suits don't matter. If flush draws are involved (even backdoor flush draws), then suits most certainly matter.
  5. Tap the AKs grid cell to select it. Then as in the previous step turn off half (2 of the 4) of the hand combos; we'll remove the 2nd and 4th ones.
  6. Calculate. You see that QQ's Equity is now 33% (vs. 40% originally).
So cutting AK's weight in half reduced QQ's Equity from 40% to 33%. This is a significant change in Equity which may affect your decision.


Example: Custom Hand Combos (Weights) For AKo And AKs:

PokerCruncher - Hand Range Combinations (Weights): AKo               PokerCruncher - Hand Range Combinations (Weights): AKs


PokerCruncher - Hand Range Combinations (Weights) Calculation





Suits In Hand Ranges

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Here's another useful application of the "Suits" button mentioned in the Hand Combos (Weights) In Hand Ranges section above. You can use this button to control the suits of the hand combos you wish to add to the range.

For example you can enter the hand range Ahxh (h = Heart) instead of the more general suited range Axs (s = suited), for example if the flop has exactly two hearts and you want to put a player on the (Heart) nut flush draw. You can select any combination of suits. The below screenshot shows how you would select Ahxh (h = Heart).


Example: Select Suits In Hand Ranges (Ahxh (h = Heart)):

PokerCruncher - Select Suits In Hand Ranges




Top X% Of Hands Slider

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This slider selects the top x% of hands. PokerCruncher uses a standard hand ordering (PokerStove's): hands are ranked according to preflop all-in equity versus 3 random hands.




Hand Range %age/Odds Indicator

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This %age, shown in the top right part of the hand range editor screen, shows the %age of all possible hole-card hands that are in the hand range, taking assigned and dead (non-live) cards into account. This is also the odds of the player getting a hand in the hand range.

For example the range %age is 2.11% in the QQ vs. {KK+, AKs, AKo} example in the Fully General Hand Ranges section above.

However it's 1.51% in the Hand Combos (Weights) In Hand Ranges section above (lower than 2.11% because we removed some hand combos from the range).




Extensive Built-In Hand Ranges

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PokerCruncher has the following built-in hand ranges that you can use as building blocks:
  • Pairs: any pair, high, medium, low.
  • Broadway, medium, low cards.
  • Connectors, also 1-gap, 2-gap, 3-gap.
  • Ax, Kx, Qx, Jx, Tx.
  • Suited/offsuit subsets of the above hand ranges.
Also:
  • The 8 Sklansky Hand Groups.
  • Our own Group 1a (AA and KK).
For example the below screenshots show how you would select all suited connectors, and Sklansky Hand Groups 1..3.


Example: Select All Suited Connectors, Sklansky Hand Groups 1..3:

PokerCruncher - Built-In Hand Ranges: Select all suited connectors               PokerCruncher - Built-In Hand Ranges: Select Sklansky Hand Groups 1..3




Range Equity Heat Maps And Hand Combo Stats

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This feature lets you dig down into a range's overall equity and lets you see the equity of each hand in the range so you can understand the range's equity breakdown.

The equity breakdown is shown using a color-coded equity heat map. If you tap the "View Details" button you can see the specific equity and hand combo stats for each cell and also a %age value for each cell that tells you what %age of the range the cell comprises (taking dead and already assigned cards into account). You can also see the number of hand combos for each cell and for the entire range.


1) Note: Monte Carlo Simulation

Note that due to Monte Carlo (random sampling) simulation, each hand's (grid cell's) equity has a higher variance (margin of error) than the entire range's equity. You can set the Monte Carlo simulation "Number Of Random Trials" setting to 2x or higher (or even Infinite) to get a more accurate result.


2) Note: Complete Enumeration

If the scenario is simple enough, PokerCruncher computes the exact odds and stats by doing complete enumeration of the possible cases. For example it does this if all player and flop cards are specified (no random hands, no hand ranges).


Example: Top50%OfHands vs. Top25%OfHands:
Range Equity Heat Map And Hand Combo Stats For Player 1 (Top50%OfHands):

PokerCruncher - Range Equity Breakdown - Equity Heat Map: Top50%OfHands vs. Top25%OfHands               PokerCruncher - Range Equity Breakdown - Hand Combos Stats: Top50%OfHands vs. Top25%OfHands




Deal-To-Flop Analysis, Many Flop Stats

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* Hand Type Stats

* Flop Hit Stats

* Odds For Flopping Draws And Combination Draws

* OnePair Breakdown Stats

Most odds calculators (including PokerStove) can only deal to the river. But when we play e.g. speculative hands like 75s or JTs or even AK, especially for a preflop raise, we'd like to know how often these hands can flop big made hands and draws. We're not necessarily playing these hands for their river showdown value; we'd like to know how often they can flop big. PokerCruncher's Deal-To-Flop feature lets you do this. PokerCruncher also has Deal-To-Turn and Deal-To-HoleCards.

Set Deal-To = Flop, bring up the Stats view, then tap the "Hit" button to switch to flop hit stats (must hit hand strongly using the hole cards), from the default make hand stats. For example flop hit stats can tell you how often AK hits an Ace or King on the flop (OnePair), or hits TwoPair or 3OfAKind on the flop. The default make hand stats are weaker, but are true to the textbook definition of the stats. They include cases where the board's cards are solely or mostly responsible for making the hand, e.g. for OnePair, when the pair is on the board.

For Deal-To = Flop, the Stats view also shows odds for flopping draws and combination draws, and OnePair breakdown stats (TopPair, MiddlePair, BottomPair, OverPair). Swipe left/right in the Stats view to see these stats.


Real-Life Hand Situation: How much do you want to pay to see the flop with a speculative hand?:

You're in a 2/5 no-limit game and you have a 500 stack. A couple of early position players limp. Say you limp in middle position with a speculative hand like JTs (or 75s, etc., i.e. a suited/connected-type hand). A middle/late position player raises to 30, and the two early limpers call. Should you call with JTs to see the flop?

Actually we can't answer this question because we haven't given nearly enough information, for example:
  • What are the stack sizes of the other players?
  • What style of player is the preflop raiser?
  • What implied odds does the preflop raiser (and the other players) offer on his (their) entire stack? I.e. do these players lose entire entire stack easily (especially the preflop raiser)?
  • How likely is it that the early position players limped/called with monsters?
  • What's your table image?
  • What's the recent hand history and recent game flow at the table?
  • And much more ...
So currently you have limited information on your decision. But one factor in your decision should be how often your speculative hand can expect to flop a big made hand or a big draw. Knowing these odds will help you figure out if the additional chips you need to call to see the flop are worth it, especially in relation to your stack. The below screenshots show these odds for JTs (assuming random hands for your opponents; if you want to be more accurate, you can put your opponents on hand ranges).

You can see that on the flop, JTs hits OnePair about 27% of the time, and hits TopPair about 14% of the time. It hits TwoPair about 2% of the time, and hits 3OfAKind about 1.4% of the time. JTs flops a flush draw about 11% of the time and flops an open end straight draw about 9% of the time. Etc. Are these odds of flopping a strong hand or a strong draw good enough for you to call the preflop raise?, also taking all of the other considerations into account (stack sizes, player styles, etc.)?


Example: Deal-To-Flop Analysis For JTs, Many Flop Stats:

Hand Type Stats,
Flop Hit Stats:

PokerCruncher - JTs: Deal-To-Flop Analysis: Hand Type Stats, Flop Hit Stats






Odds For Flopping Draws,
OnePair Breakdown Stats:

PokerCruncher - JTs: Deal-To-Flop Analysis: Odds For Flopping Draws, OnePair Breakdown Stats





Odds For Flopping Combination Draws:

PokerCruncher - JTs: Deal-To-Flop Analysis: Odds For Flopping Combination Draws




Flop Texture Analysis

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Real-Life Hand Situation: How can you tell if a specific flop hits your opponent's range of hands hard?:

Any game, any player stacks. You have AJo, and say you put an opponent on a certain range of hands, e.g. top 10% of hands (use the range %age slider to assign this range). Then a specific flop is dealt, say it's 8s7s2d. You'd like to know if this flop hits your opponent's range of hands, and how hard it hits it, or if this flop misses your opponent's range of hands. Flop texture analysis lets you do this.

Set Deal-To = Flop. Assign a hand range (say top 10% of hands) to your opponent and assign your cards (say AJo). Assign a particular flop (say 8s7s2d). Bring up the Stats view, turn on flop hit stats, tap on your opponent's hand range field to select your opponent in the Stats view. Calculate. The Stats view shows how this flop hits your opponent's hand range (hand type stats, flop hit stats). Swipe left/right in the Stats view to see odds for flopping draws and combination draws, and OnePair breakdown stats.

The below screenshots show the above example. Note that on the flop, your opponent (top 10% of hands) hits OnePair about 29% of the time, hits 3OfAKind about 3% of the time, and hits a flush draw about 5% of the time. Note that since the top 10% of hands range consists mostly of high cards, when this range hits OnePair on this 8s7s2d flop, it will have an OverPair on the flop, as indicated by the healthy 29% OverPair stat.

Of course flop texture analysis also works if you assign specific cards to your opponent. But the more common use case is to see how a hand range hits a particular flop.


Example: Flop Texture Analysis: How Hand Range {Top 10% Of Hands} Hits Flop 8s7s2d:

Hand Type Stats,
Flop Hit Stats:

Odds For Flopping Draws,
OnePair Breakdown Stats:

PokerCruncher - Flop Texture Analysis: Hand Type Stats, Flop Hit Stats PokerCruncher - Flop Texture Analysis: Odds For Flopping Draws, OnePair Breakdown Stats




Save/Load And Export/Import Scenarios (Hands) And Hand Ranges

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You can save scenarios (hands) and load them back in, using Menu --> Save/Load Scenario --> ...

You can also export scenarios to email and import them back in, using Menu --> Export/Import & Share --> ... (import feature: iOS and Mac versions)

Similarly in the hand range editor screen you can save/load and export/import hand ranges (import feature: iOS and Mac versions).

These features let you save key hands (scenarios) for future review, share scenarios and hand ranges with friends, back up your hand range library, and transfer your saved hand ranges from one device to another.




Monte Carlo Simulation, Complete Enumeration

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PokerCruncher does Monte Carlo simulation: it generates hundreds of thousands or even millions of random hands (trials) to converge on accurate odds and stats within seconds. There's a setting for the number of random Monte Carlo simulation trials to do (Menu --> Dead Cards, Settings --> Number Of Sim Trials), and there's even an "Infinite" setting.

However if the scenario is simple enough, PokerCruncher computes the exact odds and stats by doing complete enumeration of the possible cases. For example it does this for postflop scenarios with specific players' cards, which is a common situation (for example the 3-player scenario in the first screenshot in the Basic Features section above). For such scenarios only the turn and river cards are unspecified, a small number of combinations (on the order of 1000), so PokerCruncher simply enumerates all possible cards for the turn and river to compute the exact answer, and it computes the answer very fast.




Answer Interesting And Challenging Odds Questions

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This section is more technical than the others, but it's because PokerCruncher is so powerful. Fasten your seat belts.


So far you've seen examples of some basic odds questions that PokerCruncher can answer:

Some Basic Odds Questions

  • Specific hands vs. specific hands preflop, e.g. AA vs. KK preflop.
  • Specific hands vs. specific hands on the flop, e.g. the 3-player scenario in the first screenshot in the Basic Features section above.
  • Specific hands vs. random hands, e.g. the AA vs. 9 random hands scenario in the second screenshot in the Basic Features section above.
  • How often specific hands make OnePair, TwoPair, etc. by the river (hand type stats). For example how often a flush draw on the flop makes a flush by the river, or how often an open end straight draw on the flop makes a straight by the river.

Let's go deeper and see examples of some more-challenging odds questions that PokerCruncher can answer, using
primarily its Deal-To-Flop and flop texture analysis and flop stats features. We won't even consider hand ranges here because the hand ranges feature adds an entirely new level of odds questions that can be answered.

Some More-Challenging Odds Questions

  • If you have a pocket pair then how often will you flop a set?
  • If you have a non-pocket-pair e.g. 72 then how often will you flop trips? Two-pair?
  • If you have suited cards then how often will you flop a flush? Make a flush by the river? How often will you flop a flush draw?
  • If you have a connector e.g. 76 then how often will you flop a straight? Make a straight by the river? How often will you flop an open end straight draw? What if you have a one-gap connector e.g. 75? Two-gap? Three-gap?
  • If you have a one-gap suited connector e.g. 86-suited then how often will you flop a strong draw, i.e. either a flush draw or an open end straight draw or a double gut straight draw? What if you have a two-gap suited connector? A zero-gap suited connector?
  • How often does AK flop top pair? Or other non-pairs like KQ, QJ, AT, etc.?
  • How often does KK run into an ace on the flop? How often does QQ, JJ, etc. run into an overcard on the flop?
  • How often does a suited connector like 76s overtake AA, KK, etc. on the flop?
  • If you have KK, QQ, JJ, etc. then what are the odds that someone has a higher pocket pair preflop? E.g. what are the odds that someone has AA if you have KK?, and what are the odds that someone has AA/KK if you have QQ?, say in a 10-handed game? What about in a 7-handed game? In a 5-handed game? The Deal-To-Hole-Cards feature lets you answer this.

Let's go even deeper. Here are some examples of more-advanced odds questions involving multiple hands that PokerCruncher can answer, again using primarily its Deal-To-Flop and flop texture analysis and flop stats features:

Some More-Advanced Odds Questions

  • If two players have suited cards of the same suit then what are the odds that they'll (both) flop a flush?
  • (Challenge) If say 5 players see the flop with you and the flop has a pair e.g. the flop is 772, then what are the odds that someone has flopped trips or better (assuming random cards for all of the players)? What if 7 players see the flop with you? 3 players?

A Challenge

Give your answer for the last question above before reading PokerCruncher's answer below ...

The last question is an example of conditional probability, which can lead to counter-intuitive results. To make the example more specific, say you raise preflop with AA and 5 opponents see the flop with you and the flop has a pair e.g. it's 772.

A hint: you may think, "it's really hard to flop trips or a full house, how lucky can these people be?, I have to be in the lead 90+% of the time here". The problem with this reasoning is, it's true that it's very hard to flop trips starting from scratch, but given the condition that the flop is paired, it becomes much easier to flop trips, especially if many players see the flop. Furthermore if there's significant betting action in the hand, the probability that someone has trips is conditioned even higher, but we won't even take betting action into account here.


Answering The Challenge Using PokerCruncher

Here's how you would model this in PokerCruncher: Set the number of players to 6. Give Player1 (you) AA; leave the other 5 players' cards blank (random). Enter 772 for the flop. Set DealTo = Flop. Calculate, and see how often your aces are in the lead. The below screenshot shows this example.

PokerCruncher's answer is you're in the lead on the flop with AA about 61% of the time. The other 39% of the time, one of your 5 opponents has flopped trips or a full house or quads (this is assuming random cards for your 5 opponents; if you want to be more accurate you can put your opponents on hand ranges). Is this answer of 39% higher or lower than you expected? If you nailed this question you have our congratulations! Actually it's probably not as hard as we made it out to be, maybe just counter-intuitive at first.

This example shows how PokerCruncher's powerful and general features complement each other to enable you to answer just about any odds question.


Example: Challenge: How Often Is AA In The Lead On The Flop Against 5 Random Opponents, When The Flop Is Paired?:

PokerCruncher - Challenge: AA Vs. 5 Opponents On A Paired Flop


Limitless Variety Of Interesting And Challenging Odds Questions

These examples just scratch the surface of what you can do with PokerCruncher. The powerful and general simulation and modeling features complement each other well and enable you to answer a limitless variety of interesting and challenging odds questions. The variety of scenarios and questions is limited only by your skill and experience and creativity. As you become more experienced and improve you'll find that you'll set up more interesting or complex scenarios to investigate new aspects of the game, or maybe even simpler and subtler but still important scenarios.


All of this powerful calculation and analysis is running locally on your device/machine (internet connection not needed) so you can think and study poker anywhere, any time.







Additional, Expert-Level Features (Mac Version) (New!)

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We've added the following additional, expert-level features to the Mac version of PokerCruncher:

Hand Ranges Features:


Stats Features:




Range Equity Distribution Graphs (Mac Version) (New!)

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A range equity distribution graph is a good way to see a range’s equity breakdown across all of its hand combos. The shape of this graph can tell you a lot about the range’s equity breakdown. The range equity heat map feature discussed earlier is another good (but slightly different) way to see this breakdown. Distribution graphs and heat maps each have their unique strengths and complement each other well, as we'll discuss later in this section.

In a range equity distribution graph, the X-axis shows the range's hand combos, sorted from highest equity (at the left) to lowest equity (at the right). The Y-axis shows each hand combo's equity.


Real-Life Hand Situation: You Flop TopPair With JTo On A Dry Flop, Villain Has Top25%OfHands:

This example is shown in the below screenshot. You (with JTo) have flopped TopPair on a dry flop against a Villain with range Top25%OfHands. We see that Villain has only 30% equity on the flop. To understand this 30% equity number better, we see the range's equity distribution graph and notice that most (about 80%) of the range's hand combos have low (< 30%) equity, but the bulk of the range's remaining hand combos (a little less than 20%) have very high equity (> 80%). This indicates a polarized range, i.e. either Villain is well ahead in this situation or is well behind; there are very few hand combos in his range that have breakeven (50%) equity.


Example: Range Equity Distribution Graph: Villain Has A Polarized Range:

PokerCruncher-Mac - Range Equity Distribution Graph

(View at full size)


Polarized And Non-Polarized Ranges

In the above example, even though Villain is behind overall in this scenario with only 30% equity, he has a good number of hand combos (a little less than 20%) that have you beat soundly. And he has a large number of hand combos (about 80%) that you beat soundly. This means he has a polarized range. This is a very different 30% equity situation than one where most of Villain's range's hand combos have around 30% equity, with very few hand combos that have significantly higher or significantly lower equity (i.e., a non-polarized range).

You can tell if a range is polarized or non-polarized by looking at the shape of the distribution graph.

A polarized range looks something like:

----------
           |
           |
           |
           ----------


(Most of the hand combos are at the top or bottom of the graph, with very few hand combos in the middle of the graph around the breakeven equity level.)

A non-polarized range looks something like:

-
 --
   --------------
                   --
                     -


(Most of the hand combos are in the middle of the graph around the breakeven equity level, with very few hand combos at the top or bottom of the graph.)

A polarized range is best suited for either value betting or bluffing. A non-polarized range is best suited for bluff catching (i.e., check/call).

This kind of further digging down into a range's equity breakdown can help you understand the situation much better than knowing just the range's overall equity number.


Additional Features Of Distribution Graphs

PokerCruncher-Mac's range equity distribution graphs have some additional features:
  • Click on a point on the graph (on a point that corresponds to a hand combo) to see that particular hand combo’s details.
  • “View Details” button shows all hand combos’ equities, in sorted order. This is a different ViewDetails output than for heat maps.
  • Your selection/preference for viewing Heat Map or Distribution Graph is saved in the app’s state.

Distribution Graphs And Heat Maps

Let's compare distribution graphs and heat maps. PokerCruncher-Mac has both, and each has its unique strengths.

Heat maps show hands e.g. AA, JTs, etc. clearly using cells and colors so you can easily see which hands (cells) have high equity, low equity, and breakeven equity. Distribution graphs don't show individual hand names (you'll have to click the "View Details" button for that).

However, distribution graphs show hand combo counts and weighting better than heat maps. In a distribution graph each hand combo is given an equal amount of space on the X-axis so each hand combo is treated equally. However in a heat map, you have to keep in mind yourself that a pair cell has 6 hand combos, a suited cell has 4 hand combos, and an offsuit cell has 12 hand combos. Distribution graphs also show the shape of the equity distribution better than the colors of a heat map.

But distribution graphs and heat maps have the same purpose, to show a range's equity breakdown, and have some similarities. For example, both can quickly indicate if the range is polarized or non-polarized. We saw above how the shape of a distribution graph indicates this. A heat map indicates this using color; a polarized range has mostly green-ish or red-ish cells, with very few yellow-ish (breakeven equity) cells. A non-polarized range would appear as mostly yellow-ish cells in the heat map.

But if an app has both distribution graphs and heat maps like PokerCruncher-Mac, that's the best of both worlds and you get a clear and full picture of a range's equity breakdown.




Additional Hand Orderings For Top X% Of Hands Slider/TextField (Mac Version) (New!)

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The “Ordering” popup selector under the top x% of hands slider lets you choose from 8 useful hand orderings:
  1. PokerStove (preflop all-in equity vs. 3 random hands)
    • This hand ordering balances the value of high cards with the value of drawing cards.
  2. Sklansky-Malmuth Hand Groups
    • This hand ordering, created by David Sklansky and Mason Malmuth, ranks playable starting hands at a full table.
  3. Sklansky-Karlson(Chubukov) All-In No-Limit Hold'em Rankings
    • This hand ordering is based on a heads-up preflop push/call/fold decision model.
  4. Heads-Up (preflop all-in equity vs. 1 random hand)
  5. ProPokerTools: 10-handed, evolution program
    • This hand ordering "evolves" its final hand ordering slowly over time, over each iteration the program runs. A given hand isn't pitted simply against random hands, but against a progressively-refined set of "good" hands that the program computes and improves on on each iteration.
  6. ProPokerTools: 6-handed, evolution program
  7. ProPokerTools: 3-handed, evolution program
  8. ProPokerTools: pre-flop all-in equity squared vs. 1 random hand
    • The key word in this hand ordering is "squared". Because a hand's equity (on each possible board, against the 1 random hand) is squared, drawing hands like JTs (which can make the nuts or nearly the nuts, i.e. 100% equity or nearly 100% equity) go up in value compared to non-drawing hands (like A8o) that make the nuts or nearly the nuts way less often. Non-drawing hands make mostly medium-strength hands, which have equity in the neighborhood of 50% on the vast majority of possible boards. Squaring these medium-strength equities isn't nearly as much of a benefit as squaring 100% or nearly 100% equities, so drawing hands go up in value in this hand ordering.
PokerStove’s hand ordering is the default.

These hand orderings are used by the top x% of hands slider/text-field, and also when you enter a range %age in a player's hand range text field.

These 8 established and well-known hand orderings each have their own strengths and weaknesses, and are best suited for different types of games (e.g., cash games vs. tournaments, no-limit vs. limit, heads-up vs. short-handed vs. full table).

We (PokerCruncher, LLC) didn't invent these hand orderings; explaining and discussing all of them fully here is out of the scope of this Tutorial; we couldn't easily do the topic justice. For further info. we suggest you google these hand orderings. And of course you can try out the different hand orderings in the app on some example ranges like Top5% or Top20% or Top50% to see what their differences are.




View Hand Combo Counts In Hand Range Grid (Mac Version) (New!)

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If you turn on the checkbox setting “View Hand Combo Counts” in the Range Editor view, each grid cell in the range shows its hand combo count.

Also note the related checkbox setting “View Card Removal Effect”. If you turn this setting on then card removal effect is shown in the Range Editor view, in the range %age (top right) and in the grid cells' hand combo counts. Note that the Heat Map and Distribution Graph views take both card and range removal effects into account, as do the calculation results of course (the calculation results must take all removal effects into account in order to be correct).

The below screenshot shows this feature using the Mouse Over A Range's Stats When Doing Flop Texture Analysis section's example scenario. In the below example both “View Hand Combo Counts” and “View Card Removal Effect” are turned on.


Example: View Hand Combo Counts In Hand Range Grid (And Also View Card Removal Effect):

PokerCruncher-Mac - View Hand Combo Counts In Hand Range Grid




Mouse Over A Range's Stats When Doing Flop Texture Analysis (Mac Version) (New!)

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When doing flop texture analysis for a hand range (Deal-To = Flop, with a specific flop), you can mouse over the range's stats' checkbox buttons (when you're in Range Editor view) to see which hands of the range hit a particular stat. The hands that hit the stat are shown in red color in the hand range grid.

Also, when you're mousing over a stat, the Range Editor view's range %age (top right) shows the %age of the range's hand combos that hit the stat (red color; includes card and range removal effects in numerator, only card removal effect in denominator). The hand combo counts in the hand range grid also adjust similarly.


Example: Mouse Over A Range's TopPair Deal-To-Flop Stat When Doing Flop Texture Analysis:

PokerCruncher-Mac - Mouse Over A Range's Stats

(View at full size)




Full Stats And Features For Deal-To-Turn (Mac Version) (New!)

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The full set of stats are calculated for Deal-To-Turn (as for Deal-To-Flop).

For this feature the MiddlePair stat has been changed to SecondPair, to give it a sensible meaning for Deal-To-Turn.

Also, the Mouse Over A Range's Stats When Doing Flop Texture Analysis feature is implemented for when you’re doing turn texture analysis (as for flop texture analysis). I.e., Deal-To = Turn, with a specific flop+turn.

Note that calculation runs slower for Deal-To-Turn than for Deal-To-Flop, because the full set of stats are much more expensive to calculate for Deal-To-Turn. However this shouldn’t be an issue because Mac’s are pretty fast in general.


Example: Full Stats And Features For Deal-To-Turn:

PokerCruncher-Mac - Full Stats And Features For Deal-To-Turn

(View at full size)




Customizable "Total Hit" Stat (Mac Version) (New!)

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The Stats view has a stat called "Total Hit" at the bottom of the view; this stat lets you see a hand's or hand range's total/cumulative hit (taking overlapping of stats into account). In the Stats view, turn on the checkmarks of the stats you want to include in the "Total Hit" stat.

The above screenshot in the Full Stats And Features For Deal-To-Turn section shows an example use of the "Total Hit" stat.







Conclusion

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Please write to us or post on our PokerCruncher-iOS TwoPlusTwo forum thread if you have questions or suggestions or ideas for future development, or on our PokerCruncher-Android thread or PokerCruncher-Mac thread.

We hope you enjoy PokerCruncher! Thank you.
-RJ