Wednesday, November 28, 2012

#5 Calling 4Bets and PQL Query

This is the moment it's getting a bit complex, and also the moment we're going to rely on the holy PLO tool. It's a tool maybe some of you are familiar with, with comparising equity's in NLH/PLO.  (PPT)

First an assumption: In all of the next Scenario's our opponent handrange = AA**

What we're going to do know is using the graph function to determine wether or not calling a 4bet is profitable or not. The reason we need to do this, is because there are lots of flops to be dealt, and we need to determine if we flop enough pieces with enough equity to get the money in. This is better known as the Flop Equity Distribution

The situation:

Eff stack = 100bb
Game = Rakefree

4Bet pot:
-Villain raises pot (3.5bb) we 3Bet (12bb), villain 4Bets (37.5bb) Hero call
-Pot OTF: 76.5bb
-Stack OTF: 62.5bb
-Effective pot-odds for commiting on the flop: 62.5 / (76.5 + 62.5 + 62.5)  * 100% = 31,0%
-Minimum equity threshold for calling/getting-it-in OTF= 31,0% (excluding rake)

This is the moment were PPT comes in, to calculate our Flop equity distribution.

Let's say we've got KK78ds. We fill AA** as the second hand and hit the graph button.

First we need to calculate the average equity on the top 31.0% of flops, we do that by calculating the surface  of everything that's on the left of the 31.0% border!

This is another part where PPT kicks in. It'll take ages to do it manually, and also you'll be adding quite some errors by doing it manually. 

In the menu border you'll find the tab "PQL" Which stands for Poker Query Language. From there go to the PQL runner. This is the PQL you'll need for calculating the surface:

select count(equity(hero, flop) >= 0.310) as threshold
from game="omahahi", hero="KxKy7x8y", player2="AA"

Where the bolded parts are respectively:

  1. Percentage of flops
  2. Hand Hero
  3. Hand Villain

2956614835 (50.18%)

Which gives us that we've got 31% equity on top 50.2% of flops.

Now we need to calculate our average equity on top 50.2% of flops, which we do with this PQL code:

select avg(equity(hero, river)) as rivereq
from game="omahahi", hero="KxKy7x8y", player2="AA"
where equity(hero, flop) >= 0.31

  1. Equity threshold on flop


Which allows us to fill in the following formula
Ev Calling 4bet:

-( 1 - top x% of flops = code 1 ) * Costs in bb calling 4bet
 top x % of flops = code 1 (Avg Equity = code 2 (Potsize) - Stacksize after 3bet))

- (1 - 0.50) * 25.5 + .50 (.58 (201.5) - 88) )
               -12.75     + 14.44 = + 1.69bb

Which would mean that the Expected Value of calling this 4bet is +1.69bb, in a rakefree game.

This is quite a calculation, but it needs to be done and understood if you want to win at PLO. One of those things you struggle to master, but once you master it, it'll pay of immediately.

With this part I'm about to end the Preflop part.

Any questions? Don't hesitate to ask them

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