Implied odds, fold equity and EV estimation

I have not introduced the EV, expected value, concept formally in the previous articles, and will not end up doing it now either (but you'll find the Wikipedia definition of expected value linked, if interested), as I promised to not spend time defining basic statistics. That being said, I'll present to you some poker-specific nuances of how to calculate EV.

Maybe you noticed how the pot odds samples I gave you were all from the river facing a bet? This means there were no more actions to come (unless you raised, which we excluded from the game rules here by manipulating the stacks) - and since you knew what the opponent could hold, at least with a certain frequency, the EV estimation of a call had a final answer.

In our first example on the basic probabilities, there was more cards to come, though. To recap:

Hero: J♠T♠
Board: K♦Q♥2♠3♣

Here, when facing a 1/2 pot bet, we know from the pot odds that we need 25% equity for it to be profitable to call as such. But since there is potential for more action on the river, we might win more than the current pot if we make the call. This is called implied odds. In this specific example, we need at least an additional 8% or so implied odds to make the call - as we calculated before that the pot odds were 17% or so. Since this is based on the turn pot size, even a small river bet paid off - the exact % of a pot-sized-bet would in fact be the same as the "missing" pot odds on the turn - will make this a call.

When calculating implied odds, do not assume you can always get the opponent's stack if you hit your hand. Think practically about if some of the outs are likely to give your opponent an even better hand - often called dirty outs. This can for instance be outs that also complete a flush, when you have a straight draw. Furthermore be careful counting on implied odds for outs that make it very unlikely that you will get paid. Four to a flush or four to a straight on the board are prime examples of the latter. That being said, implied odds helps us quantify exactly how much extra you need to get compared to the raw pot odds. So while it is still a judgement to make, we can quantify what the result of that judgement needs to be to make a call profitable.