Net Adjusted Winnings Graphs

PokerTracker 4 version 4.x.x
January 5, 2015
  • Overview

    Tournament players may wish to know the expectation of their all-in decisions at a final table as it relates to prize pool equity.  Net Adjusted Winnings is a calculation of this prize pool equity, adjusted by adding the expectation of the hand with the actual results; the "adjustment" is required to provide a result that can be used against a graph.  

    Net Adjusted Winnings can only be calculated when the following data is known by PokerTracker 4:

    1. The prize pool is accurately reported by the online poker room or manually entered by the user
    2. The payout structure for the tournament is included in a tournament summary saved by the online poker room, or PokerTracker 4's Tournament Detection Engine has a record of this tournament structure
    3. An All-In between two or more players must occur
    4. The hole cards of all players who have equity in the pot must be recorded in the hand history
    5. The All-In must occur at a final table
  • Measuring Prize Pool Expectation

    Before we begin, it should be clear that Net Adjusted Winnings does not calculate the EV (Expected Value) of your hand.  Net Adjusted Winnings is a calculation of the difference between the expectation of prize pool equity when an All-In action occurs at a final table, and the actual results.

    Net Adjusted Winnings is a measurement of the difference between reality and expectation, it is not a measurement of luck or skill. 

    This difference between reality and expectation is the reason why you can win a tournament, but have lower expectation results than the reality of your prize pool winnings.  Additionally, this is also the reason why you can lose a hand, but have higher expectation results than the reality of your prize pool winnings.

    • How Net Adjusted Winnings is Calculated

      Net Adjusted Winnings is calculated by correlating the ICM value of each chip, the size of the pot, and the all-in equity adjusted winnings in Chips. 

    • Independent Chip Model (ICM)

      Net Adjusted Winnings is calculated by correlating the ICM (Independent Chip Model) value of each chip, the size of the pot, and the All-In-Equity adjusted winnings in Chips.

      ICM is a mathematical model used to calculate a player's prize pool equity in a tournament final table using stack sizes. The probability of finishing is multiplied by the prize amount for each position, these numbers are added together to determine the players overall equity.

      The term ICM is sometimes misunderstood to mean a hand simulator which helps a player make decisions in a tournament, PokerTracker 4's replayer includes an ICM Simulator to review the your play in tournaments as well as a ICM Quiz available from the Tools menu which can be used to train you to learn the correct ICM Push or Fold situations.

      ICM Replayer

      ICM Simulator

       

      ICM Simulators use the Independent Chip Model to calculate the optimal Push or Fold decisions but they are not the same thing as ICM calculators, an ICM calculator determines the prize pool value of each chip by evaluating the remaining stack sizes, the payout structure, and the total prize pool. PokerTracker 4 has a built-in ICM Calculator which is available from the Tools menu.  PokerTracker 4 also has a built in ICM calculator that performs its functions quietly in the background thanks to it’s Tournament Detection Engine which predicts prize structures, buyins, and payouts. 

      ICM Calculator

       

      All ICM calculations that are necessary to perform All-In Net Adjusted Winnings calculations for a given hand will be automatically performed for you provided that PokerTracker 4 knows the payout structure and the prize pool. 

  • Net Adjusted Winnings Calculation Example

    To best explain how Net Adjusted Winnings are calculated, we will use this hand history from a $100 winner take all Heads Up Sit & Go:

    $98.12+$1.88|10/20 NL (2 max) - Holdem - 2 players


    SB: 620 (VPIP: 52.27, PFR: 39.76, 3Bet Preflop: 16.67, Hands: 99)


    HERO (BB): 380

    SB posts SB 10, HERO posts BB 20

    Pre Flop: (pot: 30) HERO has Qs Kd


    SB raises to 40, HERO raises to 100, SB calls 60

    Flop : (200, 2 players) Tc Ac 6h


    HERO bets 280 and is all-in, SB calls 280

    Turn : (760, 2 players) 3h

    River : (760, 2 players) Jh

    HERO shows Qs Kd (Straight, Ace High) (Pre 71%, Flop 54%, Turn 73%)

    SB shows 4c Qc (High Card, Ace) (Pre 29%, Flop 46%, Turn 27%)

    HERO wins 760

    From this hand history we know the following key facts that will be used to calculate ICM chip value, the All-In Equity expectation expressed in chips, and Net Adjusted Winnings prize pool expectation expressed in currency (both Game Currency and My Currency):

    • The Prize Pool is calculated by taking the $200 total in buyins and then subtract $3.76 in entry fees for a total prize pool of $196.24
    • The total number of Chips in play is 1,000 (T500 starting stacks)
    • The ICM value of each chip at the start of this hand is calculated by dividing the total prize pool by the total number of chips in play. $196.24/1000 =.19624, this means each chip is worth the equivalent of $.19624 in prize pool equity. 
    • The HERO has less than the Villain's stack, he can not win more than 760 chips at showdown.  Therefore this pot is worth 760 * $.19624 = $149.1424 in prize pool equity once the all-ins occur.
    • HERO’s equity on the flop is 52.63% wins / 45.15% losses / 2.22% ties
      • HERO's ICM outcome when he wins the hand will be $149.14, this will occur 52.63% of the time
      • HERO's ICM outcome when the HERO loses the hand will be $0 because this is a winner take all HUSNG, this will occur 45.15% of the time
      • HERO's ICM outcome when both players tie the hand will be $74.57, this will occur 2.22% of the time 

    When the HERO wins, he will get a pot that is worth $149.14 in prize pool equity, but it is important to note that the HERO will not earn his prize pool winnings because the tournament is not yet over - the earnings are considered "realized".

    When the HERO loses it costs $100 which was the price of the tournament entry, when HERO ties the expectation is split between the two players.  

     

    • Net Adjusted Winnings Formula

      Net Adjusted Winnings is calculated by adding the expectation of the hand with the actual results. Even when HERO wins the tournament, he loses the cost of the entry fee - this must be included in the calculation.

      Since this is such a complicated topic, we find it helpful to remember that this is NET Adjusted winnings, it is an adjusted expectation.  


      Net Adjusted Winnings Formula : (Outcome Wins * Probability) + (Outcome Loses * Probability) + (Outcome Ties * Probability)

    • The Hero wins the hand as shown in the Hand History

      First step is to calculate the Expected ICM by using the forumula above. 

      • ICM outcome when HERO Wins = $149.14, this will occur 52.63% of the time
      • ICM outcome when HERO Loses = $0, this will occur 45.15% of the time
      • ICM outcome when HERO Ties = $74.57, this will occur 2.22% of the time

      (Outcome Wins * Probability) + (Outcome Loses * Probability) + (Outcome Ties * Probability) = $80.14


      (149.14 * .5263) + (0 * .4515) + (74.57*.0222)

 = $78.49 + $0 + $1.65 = $80.14

      The ICM Expectation is therefore $80.14

      In the actual hand the HERO won, which means his Realized ICM is $149.14 which we get from the ICM outcome when the HERO wins.

      Now that we know the ICM Expectation and the Realized ICM we can calculate the Net Adjusted Winnings using the formula Expectation - Realized ICM 


      $80.14 - $149.14 = $69 BELOW the actual results on the graph. 

      Net Adjusted Winnings = -$69

    • What if the HERO lost the hand?

      What if the distribution of cards was different and the HERO instead lost the hand?  

      The Net Adjusted Winning calculation process remains the same, the Expected ICM remains $80.14, but the Realized ICM becomes $0.00 because the tournament is over when the hand is lost and there is no prize pool winnings when this occurs.  

      Now that we know the ICM Expectation and the Realized ICM we can calculate the Net Adjusted Winnings using the formula Expectation - Realized ICM 


      $80.14 - $0 = $80.14 ABOVE the Actual Results

      Net Adjusted Winnings = $80.14

      Yes, you read this correctly.... the HERO lost the hand, yet the Net Adjusted Winning result shows a positive value.  Why?  Because Net Adjusted Winnings is a measurement of prize pool expectation, we expected to win in the majority of all situations, but in this case the card distribution was not in our favor. 

       

       

       

  • Is Net Adjusted Winnings Calculated Correctly?

    The calculation of Net Adjusted Winnings is a very complicated mathematical process to display expectation measured in prize pool equity.  It is import to note that adjusted expectation and reality will never meet, Net Adjusted Winnings has a highly specific statistical value in the use of probability theory. Many tournament players attempt to turn to Net Adjusted Winnings as a measurement of luck or skill; unfortunately luck and skill cannot be measured and Net Adjusted Winnings is not a good substitute for the lack of skill or luck measurement.  

    Net Adjusted Winnings is only a measurement of prize pool expectation and nothing more.

    With that said, the staff at PokerTracker frequently receive questions about the accuracy of Net Adjusted Winnings.  The truth is the calculation of Net Adjusted Winnings is as accurate as the data that PokerTracker 4 has been given by the online poker room you play at.   If you belive the calculation may be in error, we suggest that you first manually perform the calculations described within this guide and then compare the Net Adjusted Winnings results with your own calculations. The vast majority of time that PokerTracker's support team receives complaints about the accuracy of Net Adjusted Winnings we find that the calculations are in fact correct; instead the problem is in the misunderstanding of how Net Adjusted Winnings is calculated or what this calculation stands for.  On rare occasion we do find a calculation error, usually this is caused by either an improperly formatted hand history or a bug in the PokerTracker 4 Tournament Detection Engine which keeps track of all payout structures.  

    If you find an error in the calculation of Net Adjusted Winnings that you can prove by manually calculating the result, then please create a Support Ticket to notify our developers of the problem.  Kindly include all necessary evidence to support your claim including the hand history and the relevant tournament summary (if available).  When there is no tournament summary available, please note the following in the support ticket:

    • The total prize pool 
    • Confirm that you are at the final table
    • Please verify that the hand history contains the hole cards for all hands that have equity in the pot.  Net Adjusted Winnings cannot be calculated when a player had equity in the pot but then folded before showdown of the all-in hands.
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