
An Explanation of Texas Hold em Odds 


Probability is a huge
factor in texas hold 'em. Players use odds
to determine their actions. The chances of
finishing a flush or a straight, the
probablity of getting an overcard, the
percentage of times you're going to flop a
set to match your pocket pair are all
important factors in poker. Knowledge of
these statistics is key to winning. In
online games especially with very few (if
any) tells, statistical knowledge becomes
the main factor when choosing whether to
bet, call, or fold.


Here are some terms that you'll hear
whenever you're talking about poker odds...


Outs 
The number of cards left in the
deck that will improve your hand.
"I had four hearts on the
turn, so I had only 9 outs left to
finish that flush."

Pot Odds 
The odds you get when analyzing the
current size of the pot vs. your next
call.
"There's $200 already in the
pot, and only another $10 bet coming
at me, so my pot odds are good if I
hit that flush."

Bet Odds 
The odds you get as a result of
evaluating the number of callers to a
raise. "With a 1 in 5 chance
of hitting it, and knowing all six of
these guys are gonna call my bet, my
bet odds are good too."

Implied Odds 
The odds you are getting after the
assumed result of betting for the
remainder of the hand. "Since
I think these guys are going to call
on the turn and river, my implied odds
are excellent." 

In Texas Hold 'Em, you
commonly use outs and pot odds the most.
This is also the starting point for those
who want to learn about poker odds. To those
out there who "ain't good at countin'
much", you better get good because that
is how it's done. At this point it's only
simple division The numerator will be the
number of outs you have. The denominator is
the number of cards left that we haven't
seen. The result will be the percentage
chance of making one of those outs.
Therefore, the most math you'll be doing
will be dividing small numbers by 50
(preflop), 47 (after the flop), or 46
(after the turn).
Before we move on, I must clarify one thing.
A lot of you might wonder why we never
factor the opponents' cards or the burn
cards when figuring out how many cards are
left. The reason is that we only consider
"unseen cards". If you saw what
the burn cards were, or an opponent showed
you his hand, you would know that those
cards are not going to be drawn and could
use that. We typically do not know what they
have, so we don't even think about it when
talking about odds. For instance, take a
standard deck of 52 cards, remove 2 Aces and
burn 25 of them. If you drew the next card,
what are the chances of it being an Ace? It
would be 2/50 (2 Aces left out of 50 unseen
cards). It would NOT be 2/25 just because
you burned half the deck. Okay, do the same
thing again, but this time you get to look
at the burn cards. Let's say that of all the
cards you burned, none were an ace. Now your
odds are 2/25 because there are still 2 Aces
and now only 25 "unseen cards".

By that same reasoning,
let's play a game of draw poker where you
get 5 cards as usual, but your opponent gets
40. Say you got Ace, King, Queen, Jack all
of Spades!, and a Four of Clubs. You get to
ditch the Four and draw one from the
remaining pile of 7 cards. What are your
chances of getting that Ten of Spades?
Assuming you don't get to see your opponents
hand, your chances of drawing that card
would be 1 in 47 (1 Ten of Spades in the
deck, 47 "unseen cards"). It would
NOT be 1 in 7. Let's say your opponent goes
to the bathroom, and you cheat and look at
his hand while he's on the crapper. If he
doesn't have that Ten of Spades, that would
be 1 in 7. If he did, well...it'd be 0 in 7.


Pot odds are as easy as computing outs. You
compare your outs or your chance of winning
to the size of the pot. If your chance of
winning is significantly better than the
ratio of the pot size to a bet, then you
have good pot odds. If it's lower, then you
have bad pot odds. For example, say you are
in a $5/$10 holdem game with JackTen facing
one opponent on the turn. You have an
outside straight draw with a board of
259Q, and only the river card left to
make it. Any 8 or any King will finish this
straight for you, so you have 8 outs (four
8's and 4 K's left in the deck) and 46
unseen cards left. 8/46 is almost the same
as a 1 in 6 chance of making it. Your sole
opponent bets $10. You if you take a $10 bet
you could win $200. $200/$10 is 20, so you
stand to make 20x more if you call. 1/6
higher than 1/20, so pot odds say that
calling wouldn't be a bad idea on this occasion.


Another clarification...a lot of players
want to somehow factor in money they wagered
on previous rounds. With the last example,
you probably had already invested a
significant portion of that $200 pot. Let's
say $50. Does that mean you should play or
fold because of that money you already have
in there? $50/$200? That's a big no. That's
not your money anymore! It's in a pool of
money to be given to the winner. You have no
"stake" in that pot. The only
stake you might have is totally mental and
has no bearing on hard statistics.


The next step is to use bet odds and implied
odds. That's tougher, because it involves
predicting reactions of other players. With
bet odds, you try to factor in how many
people are going to call a raise. With
implied odds, you're thinking about
reactions for the rest of the game. One last
example on implied odds...
Say it's another $5/$10 holdem game and you
have a four flush on the flop. Your neighbor
bets, and everyone else folds. The pot is
$50 at this point. First you figure out your
chance of hitting your flush on the turn,
and it comes out to about 19.1% (about 1 in
5). You have to call this $5 bet vs a $50
pot, so that's a 10x payout. 1/5 is higher
than 1/10, so bet odds are okay, but you
must consider that this guy's going to bet
into you on the turn and river also. That's
the $5 plus two more $10 bets. So now your
facing $25 more till the end of the hand. So
you have to consider your chances of hitting
that flush on the turn or river, which makes
it about 35% (better than 1 in 3 now), but
you have to invest $25 for a finishing pot
of $100. $100/$25 is 1 in 4. That's pretty
close. But there's more!... if you don't
make it on the turn, it'll change your outs
and odds! You'll have a 19.6% chance of
hitting the flush (little worse than 1 in
5), but a $20 investment for a finishing pot
of $100! $100/$20 is 1 in 5. So the chances
would take a nasty turn if you didn't hit
it! What's makes it more complicated is that
if you did hit it on the turn, you could
raise him back, and get an extra $20 or
maybe even $40 in the pot.


I'll let it go at that,
as once you've mastered simple outs and pot
odds, bet and implied odds are just a longer
extension of these equations. If you sit and
think about these things while you play,
it'll come to you eventually without any
tutoring. Good luck!


