Quick Studies: Poker Math Fundamentals Lesson B: What Is EV?

Solve For Why -

Expected Value, or ‘EV’ for short, is the driving force behind all poker decisions. It tells us how much we expect to gain or lose in the long term with every decision we make. What makes EV difficult to understand and apply is that we must overlook the results of each individual hand, and instead, imagine that each hand of poker is playing out an infinite number of times. Our EV is a function of all possible outcomes on the infinite spectrum, as opposed to one specific outcome we’ve observed.

EV is connected to equity, but it's not the same. Equity is a measurement of how often our hand, or range, is likely to win at showdown - it’s measured in percentage. EV is measured in dollars, big blinds, Euros, yen, dogecoin - anything with monetary value. While equity is a major variable in our EV, it doesn’t act alone - the current pot size, stack sizes, positions, and betting options all contribute to our EV in a variety of ways.

Let’s examine a simple scenario. Imagine we’re on the river with a hand like middle pair, and we expect our hand to be the best 50% of the time against our opponent’s range of hands. Since there are no more cards to come, this means our hand has 50% equity. There is $100 in the pot, and our opponent bets $100. Should we call?

Let’s calculate the answer.

First, we list the two potential outcomes if we call:

  • We call and win
  • Or we call and lose

… and then we establish the probability of each outcome:

  • We win 50% of the time
  • And we lose 50% of the time

Next, we establish the value of each outcome:

  • If we call and win, we get the $100 in the pot, plus the $100 bet
  • If we call and our opponent wins, we have lost that $100

Now multiply those values by their likelihood to occur:

  • If we win, it’s $200 50% of the time, or +$100
  • If we lose, it’s $100 50% of the time, or -$50

Finally, add the two together to create the average outcome. This is the value we expect, and we get an EV of +$50. Clearly, we should make this call on the river, as it's profitable on average.

Note that in this particular spot, the maximum EV from this call is $200. Without raising and increasing the pot size, the best possible scenario is that we always win that $200 in the pot.

On earlier streets, calculations like these are more complicated because there are so many different possible events on the remaining streets. As a result, EV on earlier streets becomes much more of an estimation, as opposed to a certainty..

In addition, EVs run extremely close together on earlier streets because the pot is smaller, and only the strongest possible hands can guarantee making a lot of money on the remaining streets. Preflop, for example, is often full of hands which possess EV extremely close to zero, one way or the other. Since folding is always zero EV, meaning we can’t win or lose money by folding, we are faced with marginal raises or calls.

On early streets, EV is still the driving force behind our decisions, but given these narrow margins, the route it is taking us is less clear. We can use technology such as solvers to calculate the EV of complex strategies with multiple streets left, but even the solvers require input from us in order to perform the calculations.

Determining where our EV gains and losses are coming from is the essence of getting better at poker. It’s a learning process that never ends, no matter how long you’ve been playing. The more you understand EV and how it works, the easier it will be to identify strategic edges over your opponents. Do that, and you’ll be well on your way to the ultimate goal in poker:  maximizing the expected value of your decisions.