**RANGE DISTRIBUTION **is useful when doing range analysis. Anytime we want to know *how often* somebody has a particular sub range we can consider using RANGE DISTRIBUTION. This module does not return an expected value like many of the other modules. It's focus is to help us find frequencies of various sub ranges of a player's main range.

At the same time RANGE DISTRIBUTION is the only module that works *both* in Simulator and in Game Mode.

Before we dive into a specific example, let's go through some of the options we have in RANGE DISTRIBUTION.

**Cumulative ranges**

Cumulative ranges mean that the sub ranges are mutually exclusive. When this option is turned on (it is on by default) sub range A is automatically excluded from sub range B. Sub ranges A and B are automatically excluded from sub range C and so on:

A | =(A) |

B | =(B)!(A) |

C | =(C)!(B)!(A) |

D | =(D)!(C)!(B)!(A) |

E | =(E)!(D)!(C)!(B)!(A) |

F | =(F)!(E)!(D)!(C)!(B)!(A) |

G | =(G)!(F)!(E)!(D)!(C)!(B)!(A) |

H | =(H)!(G)!(F)!(E)!(D)!(C)!(B)!(A) |

When the option is turned off the frequency for each sub range is displayed without regard to what other sub ranges are entered. We will demonstrate Cumulative ranges in the examples below.

**Skip Equity Calculations**

Turns off equity calculations against each sub ranges. PokerJuice remembers this setting from session to session.

**Apply Card Removal Effect (CRE)**

As default PokerJuice calculates frequencies of sub ranges *in isolation *without taking other ranges into account. Let's demonstrate this by a quick example:

We have created a New Game using GAME BUILDER. Let's assign BB a range of 10%. We open RANGE DISTRIBUTION (RD) and enter sub range A = "AA". We check that CRE is off. We get 25.71%. We now click on SB and enter a preflop range of AA:

We click BB again and rerun RANGE DISTRIBUTION and we still get 25.71%. This is correct because as a default PokerJuice looks at ranges *in isolation*. Let's turn CRE on and run it again. We now get 7.37%. This time SB's range of AA affects the calculation and it is now less likely that BB has AA.

When CRE is turned on PokerJuice takes *all active player's ranges* into account.

Having CRE on is not more nor less correct than having CRE turned off. It depends on the situation and what kind of analysis we are doing. In PokerJuice we have the option to toggle it on and off as we wish.

**Set Number of Trials**

Let's us set the number of trials used when CRE is turned on. When CRE is off combinatorics is used and this setting will have no effect.

Let's do an example:

Example #1

In this first example we are opening from CO. BTN and SB both fold and we get called by BB. The flop comes:

We flop a queen high flush. We decide to cbet and we get called. Now is a good time to narrow Villain's range a bit:

We think that he defends about 60%and we exclude a reasonable 3bet range. On the flop we think he continues with:

- All flushes
- All two pairs or better
- All open-enders or better
- All sevens and fours without a pocket pair

We also think he will bluff raise us when he has a good blocker and raise the nut flush for value sometimes but not always. Let's utilize RD:

Notice that we have Cumulative Ranges turned on. This ensures that we have Ahh is subtracted from Ah etc.. We run RD to get a feel for the frequencies:

So given the flop and the fact we have **QhJs9d8h **in our hand we can expect Villain to have the nut flush 8.44% of the time. He has the nut blocker 4.23% of the time. He has the 2nd nut flush 6.52% of the time and finally the **Kh** blocker 3.24% of the time.

We expect this player to always bluff-raise with his **Ah** and **Kh** blockers and we expect him to raise the nut flush most of the time but not always. Let's find a good frequency for the nut flush:

We *turn off Cumulative Ranges*. Now we can compare different ranges to the main sub range of Ahh. Let's look at results:

He still has Ahh 8.44% of the time as expected. In range B we have tried adding a spade to find a proper sub range to use for raising. But it didn't work out that well. First of all it is small that we would like and second of all it is not very intuitive. Instead we examined how often he has the nut flush with and without the **Kh. **It turns out he has the nut flush without the **Kh **blocker 7.04% of the time (C). This was more like the frequency we were looking for and it makes sense that the times he would slowplay the nut flush are the time when he know we can't have the 2nd nut flush.

So, his combined check raise range (we think) looks like: Ahh!Kh,(Ah,Kh)!hh.

We update his flop range to reflect this. Since he check called we can exclude this sub range from his main range:

Let's go to the turn:

We bet again and he calls again. Let's plug in his turn range:

Now we think he is only calling with two pair or better and we don't think he will ever slowplay the nut flush more than one street so we exclude that.

We goto the river:

Before we (possibly) value bet we would like to know more about his range composition at this point. We open RD. We turn on Cumulative Ranges and enter some appropriate sub ranges:

We would like to see how often he has strong, medium and weak flushes, two pair and weaker. we run RD and get results:

As expected he never has the nut flush. We have assumed that he always raises that on flop or turn. He has the King high flush 14.63% of the time. A medium flush 19.61% of the time and a weak flush 10.88%. He has two pair or a set 54.87% of the time and as expected he never has weaker than two pair.

Ok, so we consider value betting our Queen high flush. We assume that if we bet he folds all two pairs but calls with all flushes. For a value bet to be good it has be called by worse 50% of the time or more assuming that we are never bluff raised. We assume that Villain never raises this river. So, in the cases where we get called we can update his main river range:

We have now established that he calls with all flushes. Let's see how often he calls with a better flush:

We enter Khh+ as the range of flushes better than our flush and then we enter hh as all worse flushes. We make sure Cumulative Ranges are turned on. We get:

About 2/3 of the time we can expect to get called by worse making our river bet a good value bet.

PJ Variables (Advanced)

We have now learned how to query ranges using sub ranges in RANGE DISTRIBUTION. But that's not all. We can also extract these sub ranges and use them anywhere in PokerJuice. This makes working with ranges easier and more intuitive than ever before. To learn more read our article on PJ Variables.

I hope this article was useful. Please do not hesitate to contact us. You can find me on Skype or in the PokerJuice Community.

**Morten**Skype: PokerJuice

PJC: morten.pokerjuice.com

Web: pokerjuice.com

Maseh Alhaeeخیلی خوب بود متشکرم