Poker Math That Matters

Equity Versus a Range
We've already learned how to estimate our equity postflop verses
certain hands. We went over the 4/2 rule for that. Let's do a
quick review with an example.
Hero: A♦A♠
Villain: 3♦4♣
Board: 5♥6♠J♣.
We get all-in on the flop. Our opponent has eight outs with two
cards to come. He has about 32% equity. This means we have
the remaining equity, which is 68%. However, we didn’t talk
about how we got all-in.
81
Let’s say the pot was $25. We bet $25 on the flop, and the
opponent shoved all-in for $100. We have to call $75 more.
Now what do we do? We’ve learned to look at our pot odds
first. The pot is $150, and we have to call $75. We’re getting
2:1 and need to be good 33% of the time. When we know he has
3♦4♣, this is an easy call. However, again, poker doesn’t work
like this in real life. We don’t know what he’s holding. Since
we don’t know his cards, we have to work with assumptions
concerning what range of hands we believe he can hold given the
certain actions he’s taken. So, without talking about why we’re
assuming this range, let’s give him an assumed range of 78, 55
and 66. 7 This is a very narrow range. A narrow range is always
easier to work with, so we’re going to start here. We still know
for sure we’re getting 2:1. What we do not know is our equity
against his assumed range. That’s what we’re working on in this
7 Notice our assumed range does not include his actual hand. Welcome
to real poker. Sometimes we run into the strongest part of villain’s
range; other times we run into the weakest part of it. Sometimes we’re
not even in the ballpark.