Poker Math That Matters

Also, do not forget about backdoor outs. Remember these are
worth one out on the flop. So, if you were going to see the turn
and river, they’re worth about 4% equity.
It’s not necessary that you understand the math involved in
getting these percentages; however, I’m going to include it here
for those who like to know the whys in life. Let’s start with the
turn in our J7 hand. We had four outs. We already estimated
our equity at 8% and found out it was actually 9%. Where does
this number come from? Well, we know there are four 8s in the
deck. How many unknown cards are left? Well, we know there
are 52 cards in a deck. We also know our two cards, our
opponent’s two cards and the three cards on the flop. This is a
total of seven cards that we know.
52 – 7 = 45
There are 45 unknown cards. There are four 8s in there
somewhere. The chances of an 8 coming next are 4
. We
45
divide 4 by 45 to get our percentage. When we do that, we get
9%.
Going from the flop is a bit more complicated than that. We
need to find out how often we hit an 8 on either the turn or the
river. The method I use is to find out the times we do not hit our
8 and subtract that from one. What are the chances we do not hit
our 8 on the turn? Again, we have 45 unknown cards and four
8s. So, there are 41 cards that aren’t 8s. The probability of not
hitting our 8 on the turn is 41
45 . Now, let’s move on to the river
after we miss the turn. We now know another card, so we now
have 44 unknown cards. There are still four 8s in the deck, so
there are 40 cards that are not 8s. The probability of not hitting
our 8 on the river is 40
44 .
55