All-In Equity Graphs

PokerTracker 4 version 4.0.x
October 25, 2013
  • Overview

    Poker players who are active in online forums often discuss the EV or Expected Value of a decision. Expected Value is a forward projection of winnings which incorporates the range of hands that your opponent may hold. At this time, software cannot accurately determine an opponents range of possible hands, therefore EV calculation could only be performed in scenarios where all players are effectively all-in; the terminology All-In EV was born from this adjustment.

    With the advent of PokerTracker 4, we have moved away from using the terms "EV" and "All-in EV" because the terminology for these phrases are misleading, they do not truly represent Expected Value because these are results oriented stats rather than forward projecting stats. To replace All-In EV in PokerTracker 4, we have introduced a new concepts called "All-in Equity" and "All-In Equity Adjusted Winnings" which better represents the functionality of the stat while improving accuracy. This guide will discuss the differences between the terms, why the change was made, and how to interpret graphs which use these stats.

  • All-in Equity vs. All-in EV

    Before we start, we have to understand the difference between both of these terms.  Both terms describe the calculation of what the result would be if no more cards were to be dealt and instead each player was returned their equity in the pot in all-in situations.  It is calculated by subtracting the total amount you bet from your equity in the pot.

    However, the term All-in EV is technically incorrect because EV (Expected Value) is calculated by using at the equity of our hand versus our opponent's range of hands; as opposed to the exact hand they had in this situation.  Using the range of hands allows the player to properly project the expected value of a decision, when we are using the actual hand that an opponent holds then this projection turns into a measurement of  the luck of the draw of cards to come.  All-in Equity is a more appropriate title as it looks at the equities of the all-in hands and calculates the equity shares at that point, All-In Equity can only be calculated in scenarios where all active opponent's cards are provided in the hand history.  To increase accuracy of calculation, All-in Equity ignores certain situations that PokerTracker 3 included in All-in EV calculations, this makes All-in Equity a more precise measurement of luck. 

    For more reading on the subject, here is an article written by Jeff Hwang on the topic of All-in EV which originally appeared in Card Player Magazine, re-hosted by permission of the author in the PokerTracker Blog.

    • What is Equity in the Pot?

      Equity in the pot is the percentage of times you expect to win the pot multiplied by the size of the pot.  This will tell you how much of the pot you would get if the cards were run an infinite number of times. Note that if players are all-in on the river or one player is guaranteed to win, the players' equity and actual results are the same.

      Let us consider the following example. Hero has AA and Villain has KK, and Hero has Villain's suits dominated. Hero and Villain are both all-in before the flop for $100 each, so the total pot is $200 (we will assume the blinds account for the rake in this example to keep the math simple). In this case, Hero will win 82.6% of the time. Thus Hero's equity in the pot is $200 times 82.6% or $165.20 and Villain's equity in the pot is $34.80 ($200 * 17.4%).

    • What Does the Graph Show?

      In the above example, Hero and Villain both put $100 into the pot. Thus Hero's All-in Equity is +$65.20 ($165.20 - $100), and Villain's All-in Equity is -$65.20 ($34.80 - $100). If Hero wins the hand (Figure 1), his Amount Won for the hand will increase by $100, but his All-in Equity line will only increase by $65.20. If Hero loses the hand (Figure 2), his Amount Won will decrease by $100, but his All-in Equity line will not change.

      Figure 1 Figure 2

      The All-in Equity graph shows your normal results for hands that were not all-in but for all-in hands it shows your All-in Equity instead of your actual results.

      All in Equity Graph

    • When in the Hand Are These Calculations Performed?

      These calculations are performed at the point of the all-in. If, in our above example, the all-in did not occur until the flop and the flop was K72, Hero would then expect to win 8.6% of the time instead of 82.6%, changing the results drastically.

    • What About Multi-Way All-in Pots?

      If all players have the same stack size, it is calculated as above for each player.

      If the players have differing stack sizes, All-in Equity actually ignores this situation.  To understand why PT4 does this, let's look at a simple example.  

      Hero ($100)

      Player A ($900)

      Player B ($1000)

      Hero open shoves for $100 with QQ and both Player A and Player B call.  The flop is KQ3, Player A bets $150 and Player B calls.  The turn is a J, Player A bets $500 and Player B folds.  Player A shows AK, the river is a T and Player A wins.

      At what point would we calculate the All-in Equity?  Do we do it preflop?  We don't know what Player B has and thus the calculation would be incorrect.  Do we do it on the turn once Player B folds?  We shouldn't do that as we got our money all-in preflop and not on the turn with influenced action.  Starting to see the issue?

      This is why PokerTracker 4 does not include hands like this in the All-in Equity results.  There is simply no correct/complete way to do so, and we'd rather not give you incorrect information.

    • What About Unknown Cards?

      PokerTracker 4 does not include hands with unknown hole cards in the All-in Equity calculation.  This includes the multi-way situation we reviewed above (where we were all-in preflop v two other players, and one of those players later folded) and also on sites with no mucked hole cards.  These types of situations would make the All-in Equity result incorrect and create skewed graphs.

highfalutin