Hi,

A few years ago when equity realization was less of a "thing" you could easily construct ranges for say big blind vs a utg open because you simply added hands that had the required pot odds necessary. But nowadays, at least for me, I'm confused to how I should defend because I don't know how much equity I will realize.

Let's create a scenario. Full ring 100big blinds deep, utg raises 9%(of hands) to 2.5big blinds, folds to the big blind who needs rouqhly 27% equity, what should our defending frequency be?

I know how much equity we need to realize but not how much equity we will realize. For instance JTs have rouqhly 36% equity, the pot odds we are given are 27%, so we need to realize 27/36=0.75 75% of our JTs for it to be profitable to defend.

To summarize. I know how much equity I need to realize but now how much I'm going to realize. I also know that OOP we will realize less equity and IP more equity, off suit hands realize less and suited hands more. Is there any math based way of going about equity realization?

Thanks

You could search this forum for the old threads about "capture factor", which I think was an attempt to put a numerical value on each hand's ability to realize its equity, but it's a bit of an academic exercise. I'd just look at some pre-flop defending charts (e.g. from Snowie, or from training courses) and go with them. That is to say, I don't personally know exactly how much equity 64s realizes in BB vs UTG, but I believe it's a more profitable call than A8o or KTo, which are hands that don't do well in that situation (due to domination, lack of suitedness etc).

Thanks, will for sure look in to it. Are those charts ur talking about free?

Equity realization is a function of these factors:

a) the effective stack

b) the number of betting rounds left

c) the opponents betting frequency

d) the opponents bet sizing

e) the probability that the opponent will bet the next street

Larger values for these factors will lead to less equity realization.

Smaller values will lead to more equity realization.

I’m not sure how all of the above would combine mathematically to give us something useful.

The following is extracted from a blog I’ve drafted. It attempts to define realized equity and suggests a way to estimate it from your playing history if you have poker tracking.

Realized Equity Group (REG) – A set of game situations for which realized equity (see next definition) is approximately equal for each element of the set. Includes hands/ hand types /ranges plus other relevant factors such as position and stack sizes. As an initial cut for hand types, such groups may consist of Pocket Pairs: Low, Medium, High; Ace-X. Low, Medium, High; Two Broadway Excluding Aces; Suited Connectors: Low, Medium, High; Other: User Selected.

Realized Equity (RE) – The equity a REG actually achieves for a player determined from his playing history. RE includes wins at showdown and those hands won through villain folds.

Note that if all hands in a REG went to showdown, then RE should, in the long run, equal the theoretical (showdown) equity provided by an equity calculator. The only reasons that will not be true are that hero mistakenly folds hands that would have won or villain mistakenly folds hands he would have won. Note RE can be either less or greater than the theoretical showdown equity and is player dependent. Small pairs generally have very poor realized equity for if you don’t hit a set on the flop and if one or more opponents show some aggression, a small-pair fold will usually occur. That suggests that one way to account for future actions is to use realized equity in the EV analysis rather than showdown equity.

Quantifying realized equity is doable but it is not always easy. You need a large database of played hands. You then filter for hands that match the particular play situation- the REG. You don’t have to be exact. For example, for evaluating a pair of threes, you can filter for small pairs. say 22-55, and other relevant factors. You then calculate the percent of hands that you won and that will be your realized equity. The more detail you include in the filtering that matches the game situation, the better the estimate will be, but sample size becomes a constraining factor. A sample in the low hundreds, or possibly less, will usually be adequate unlike the need for a sample size of tens of thousands you often see for other poker statistics.

How does piosolver calculate equity realization?

The Snowie pre-flop advisor for 100bb deep 200NL is: https://www.pokersnowie.com/preflop-advisor.html
e.g. If UTG opens 3x and everyone else folds, KJo is a fold, but 53s is a call. I don't know exactly how much raw equity 53s has vs UTG's range, but I know it plays a lot better than offsuit Broadways in that spot.

On the flop, should both players equity realization always add up to 100%? If OOP is only realizing 70% of his equity due to having the weaker range, his position etc, then IP will always over realize by 30% if he plays optimally?

It depends on your definition of equity realization. I use the upswing definition where equity realization is ev/eq. In that case eqr (A) * eqr (B) = 100. If you go with the definition about getting to see the 5 cards, then I warn you that's not a very important or practical concept. In that case eqr doesn't add up to 200%