# Can a decision be both + and - EV?

Is there ever a situation that in a short-term a certain decision might be + or - EV but in the long-term the EV actually change?

My interpretation is that mathematically, the expectation in EV is taken across the probability distribution of poker cards that are yet to be dealt in a particular hand as well as the randomness in opponents' play, and it is assumed that every other piece of information (including situation, position, etc) you can have is already taken into account when you calculate your EV in a hand. Under this definition, there is only one EV for each decision you make, as Lee says.

More generally, what you should really care about is not only your EV for one particular hand, but the EV of your future decisions. e.g. Calling the river with a moderate hand against a hyper-aggressive player will discourage bluffs in the future, and may be +EV even if you lose the pot. This is called investing in a reputation. Conversely, occasionally bluffing may also affect your future hands' EV positively if it reduces the image that you're tight and balances out your real hands. If you include these considerations in your EV calculation, then you might well make a distinction between "short EV" and "long EV", but this reduces the clarity and thus helpfulness of the term. I prefer to use "EV" simply to judge correct play in a hand (taking into consideration the table history and current situation, but not the future), and use additional terms to describe other considerations, like being in a bubble or when you're building an image.

In this case "short term" implies that you may have specific situational context that might be relevant to this narrow class of decisions. Say you're in a NLHE game and you have aces pre-flop and you know that you're sitting immediately to the right of a a big-stacked aggressive opponent who will very often punish your limp with a big raise. Since he's been drinking a lot, he's less likely to interpret your limp as a trap, so you might be more likely to limp here so you can reraise him when it comes back to you. In this case, the +EV play might be to limp, given your situational awareness of your relative position, his tendencies, and his lack of sobriety that you're extremely likely to get him to risk his stack. In the bigger picture, though, with more player types and more possible scenarios, pre-flop limping with aces is usually a bad idea. So, I'd say that this is one place where a certain "decision" -- limping aces pre-flop in holdem -- might be -EV in some cases but +EV in others.

Another example might be in a tournament where there are 10 players remaining and the last 9 players get equal prize money, while the 10th gets nothing. You're the short stack and have aces pre-flop. There is action ahead of you among the smaller stacks. What's the right move? Of course you need to fold here. In this case, folding aces pre-flop is the +EV decision.

Of course, you could also certainly argue that these examples are really distinct types of decision because the context is different in each.

No, the EV is the EV. But probability is a function of knowledge. Your estimate of the likelihood of the various events that go into your calculation of EV will change over time with new information, so that what may seem like the "same situation" to you at different times might actually be a very different situation when you take into account your added knowledge.

EV is pure math and is based on cards. Although there are cases as @Chris Farmer said where the EV may be positive but even the slight chance that you have to lose should ignore the EV. Such case are the `satellite` tournaments where a number of players get exact prize and another number of players get exact nothing.

In such cases a `80+%` winning chance (or say a sky high EV or easier, aces) doesn't mean much if there are, say, tiny stacks out there to take the risk as they're closer to elimination than you. EV situations are good when you actually win something in return `than nothing`.

If, for example, a big stack got all-in and you have aces and a similar stack (big) and call, while there are tiny stacks out there and 1 place before actually win something, then you're doing it wrong. In such cases, big stacks should only play the tiny stacks and ignore the EV of their cards and the other big stacks as well.

Another example is `single table tournaments` or `STT` as @Chris said. You have 10 players, 3 are getting a prize. The catch here is that the prizes have not so big of a difference as MTT top places but like `20%` to 3rd, `30%` to second and `50%` to first (or something like that). The 4th player does get a honorary nothing while the 3rd player gets quite big prize. In such case, where the prize of `3rd player` doesn't really have a colossal difference from 2nd and the 1st prize is really a double prize, your EV situation as well change. You now have to play mostly `AA, KK and the likes`, regardless the fact you are huge favorite in most hands, although one step from the `honorary 4th position and the nothing prize`. All this provided if there is at least one smaller stack out there and not you.

EV is a mathematical term that only makes sense on the long run.

In probability theory, the expected value of a random variable is intuitively the long-run average value of repetitions of the experiment it represents

Thus there's just one value of EV which more or less translate to "the expected total value if we were to repeat this draw an infinite (or in practice very big) number of times.

Statistically a sample size of one hand means nothing (you can't extract a value from one coin flip), as you increase the sample size you can draw more conclusions. With a big enough sample size you can express statistical truths with a given confidence interval.

That level of confidence is important. When we talk about EV in poker we simplify part of the information to be able to use math to make a decision. Thus, you can compare the odds of getting there against the pot size and calculate what we normally call EV.

In reality, even though we don't say it, what your are calculating is "if I was to repeat this exact same situation 10000 times with this cards and this flops I'm 98% confident I would make around 100\$"

This is just a simpification as, obviously you're not going to be on the same exact situation that many times but the simplification lousy translate to "if I play this kind of situation (I.e. Flush draw) all in every time, in the long run given enough times I'd expect to gain this much value" that is the EV, is always in the long run.

Going by probabilities where the expected value is the average of the sums of all possible outcomes in the set, the standard application of EV in poker is for hand analysis, meaning did I make the right decision based on the current pot, cards, and previous play. In this sense we are dealing with constant values and your best estimation of the opponent and the EV is exactly one value which you can only guess based on your evaluation of the possible range of hands your opponent might have.

In reality, the future is variable, so when we look at the possibility of repeating this exact situation against the exact same opponent, the next time will likely not have the same set of outcomes for the sample set of possible plays, which means your EV will likely be different next time. In this case it seems reasonable that maximizing your EV this time might make your play more obvious if you use the same reasoning, and hurt your long turn profits. This is one of the reasons that Mason Malmuth and David Sklansky make a distinction between "perfect poker" and "excellent poker." To truly maximize your EV, both situations might have to be played differently, and you're definitely going to have to think about more than just the combinatorics.

Think about the information you give someone when you make a bet sizing decision. Maybe a tiny sucker bet on the river will get you a call when you lose only a little now, but might induce a bluff raise where you can gain alot next time. There is a specific case where you can go -EV immediately to go +EV in the long run.

Note that EV is usually not a precise value, but an estimate. Because it is an estimate, the true expected value of an action can span a range which includes both positive and negative values. For example, calling might have an estimated EV of 0.05 bets, but the standard deviation for that estimate might be 0.15 bets, leading to a 95% confidence interval of [-0.10, 0.20] bets.

• I disagree. Expectation is, by definition, a weighted average. The realized value might have a range and variance, but there is only one EV ex-ante (conditional on your information and beliefs). en.wikipedia.org/wiki/Expected_value – Yang Jun 1 '15 at 1:54
• You are confusing the standard deviation of the outcome with the standard deviation of the EV estimate. Any construction of EV (in poker) can only be an estimate. As such, that estimate has an associated standard error (the standard deviation of the estimate). – Andrew P. Jun 1 '15 at 2:31
• Your point is technically true; for every estimate, we can always incorporate uncertainty about that estimate, up to infinite order. So if you want to estimate the "population" mean of EV, there is indeed variance from not having enough information about a player. However, I fail to see how this additional qualification is in any way useful to your decision-making, since you'll still play the action that has the best EV estimate with as little estimated variance in the action as possible, while variance in the mean estimate doesn't affect your choice at all, unlike actual variance. – Yang Jun 1 '15 at 22:30
• Of course it will affect your decision making process. For example, you have two choices, with EV intervals of [0.1,0.2] and [-100,101]. The EV estimate of the second is higher than the first, but you might choose to take the more certain action over the higher EV action. – Andrew P. Jun 1 '15 at 23:00
• Again, you're conflating estimated variance [of an action] vs variance in the mean estimate. Expected value is useful, variance in useful, variance in estimated EV isn't. – Yang Jun 1 '15 at 23:04