Take this spot where we decide to bluff the river with a missed draw:. We have enough information to start filling in parts the EV formula. So the formula is now:. In spots like this you make an assumption of how often the button would fold when you bluff.
Now we can solve everything:. These kinds of situations are very common in poker and by using EV we can proof the validity of our plays. If you are interested in calculating the EV automatically, grab my poker EV spreadsheets today. These sheets are incredibly useful for doing these calculations quickly rather than by hand!
My spreadsheets pack includes a basic EV calculator, a complex EV calculator, and the ability to compare EVs quickly such as comparing the value of betting vs. Thus when making decisions about whether to call a bet it is crucial to take into account both the stack sizes of yourself and your opponents and how willing they are likely to be to call big bets if you make your hand. To make it easier to understand why this move is correct even though it usually loses, suppose you have a six-sided die.
You will be wrong five times out of six, but you stand to gain a lot over the long run! The payoff odds are called pot odds in a poker game. Comparing the odds of winning to the pot odds is how you can estimate your expected value.
Ideally, you want to avoid all situations where you have a negative expectation. Even slightly negative situations can pile up and bleed away your bankroll. However, you will often have a draw which, if you hit, you will very likely win the pot. The exact arithmetic involved varies from game to game. In Texas hold'em and Omaha , once you see the flop, the percent chance of making your hand within one card is generally your number of outs cards that will make your hand multiplied by two, and the odds of making your hand within two cards is your number of outs multiplied by four.
For example, if you have four hearts and you need one more for a flush, you have nine outs, because there are thirteen hearts in the deck, and subtracting the four hearts you already have gives nine. You hesitate. Steph Curry is, of course, an incredible free throw shooter. By looking at the two outcomes and their likelihoods, your can probably tell intuitively that this is a losing bet for you. But exactly how much is it losing? To calculate the EV of this bet, we simply multiply the probability of each outcome as a decimal by its respective result, and add them together for a less hands-on approach, you can use an expected value calculator :.
Your intuition was correct. With very exceptional cases set aside certain rare bubble and pay jump scenarios in tournaments , would you ever have considered folding those aces in hindsight?
Of course not. Because you know that getting your money in before the flop with pocket aces is a hugely profitable play in the long term. Both blinds elect to fold, leaving you heads up. On the other hand, if Villain calls, you will need to hit your combo draw to win the pot. Villain Calls and You Lose: 0. So I played around in Equilab and got the following:. Oh fun. This range has combos. Of those combos, 32 include a K. To find out if at least one of them holds a K, we calculate the probability that neither of them holds a K.
A more accurate result would require using the initial ranges and running a Monte Carlo simulation which assigns CO and BTN a specific hand drawn randomly from that range for 10, iterations or so. Board is , rainbow. Villain has JJ. Hero has KK. River is J. Board is A-J, rainbow.
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