Shortcuts For Calculating Odds

OK, so now you know the details of “poker math” and how to calculate pot odds… while
also taking implied odds and appropriate adjustments into consideration.
Up until this point we’ve been using the CHARTS as our source of data. Now I want to
teach you how to use the odds WITHOUT charts… and without complicated
calculations. This will give you the power to understand in-depth poker math IN YOUR
HEAD… without being a math genius.
OK, let’s get started.
First off, let me show you a neat shortcut, based on the percentage charts. Here is the
chart again:





As you know, it’s not really necessary to know the EXACT percentage. For instance,
2.13% can be considered 2%, 6.38% can be considered 6%, 27.66% can be considered
28%, etc. for all practical purposes.
With that being said, you’ll notice that you can find the percentage by DOUBLING THE
OUTS and adding ONE. The “formula” looks like this:
(OUTS X 2) + 1 = % of getting a card you need
That formula works anytime you have between three and eleven outs. If you have
FEWER than three outs, it doesn’t really matter… since you should fold anyway. And if
you have MORE than eleven outs, you’ve got great odds and will probably call (or raise).
To be exact, here are the formulas to cover the possibilities…
1-3 Outs: Outs x 2 = % of hitting
3-11 Outs: (Outs x 2) + 1 = % of hitting
12+ Outs: (Outs X 2) + 2 = % of hitting
For instance, let’s say you pick up an open-ended straight draw and have eight outs.
Instead of using the chart to find the percentage chance of hitting on the turn (17.02%),
you can simply do it in your head. All you do is multiply eight by two and add one, which
equals seventeen.
(8 outs x 2) + 1 = 17%
Simple huh?
This is a very powerful strategy. For most real-life poker situations, you will have
between three and eleven outs. And in most real-life poker situations you definitely
won’t have access to any charts. This makes the simple “double the outs and add one”
technique easy-to-remember and quite efficient.
Of course, now the question becomes: How can this be used for POT ODDS?
As we discussed earlier, pot odds are found by comparing the hand odds in X:X format
versus the betting odds in X:X format. If you’re getting lots of money for a little
investment, then a call is justified. To be exact… if the betting odds number is BIGGER
(when in X:1 format), you should call. If it’s smaller, you should fold.
For example…
If you’re getting 4:1 on your money and 2:1 on your hand, a call is JUSTIFIED.
If you’re getting 4:1 on your money and 8:1 on your hand, a call is UNJUSTIFIED.
OK, but now we have a problem. Before, we were using the charts for the X:X number…
under the “odds against” column. How can we do the odds IN OUR HEAD and still use
the SHORTCUT method we just discussed?
The solution is to CONVERT THE BETTING ODDS TO A PERCENTAGE. There are a
few different solutions actually, but this is fastest and easiest.
What I mean is… instead of comparing everything in X:X format, we’ll start comparing
everything in terms of percentages.
All right, let’s look at how to calculate the “betting percentage”…
We need the same two numbers as before: pot size and bet size. Before, we compared
the numbers like this:
Pot Size: Bet Size
So if there was $100 in the pot and the action was to you to call a $20 bet, the figure
would be 100:20, or 5:1.
Now all we want to do is CONVERT THAT into a PERCENTAGE. It’s actually very easy.
All we do is DIVIDE THE BET SIZE by the POT SIZE ADDED TO THE BET SIZE. The
formula looks like this:
Bet Size / (Pot Size + Bet Size)
In our example before, the bet size was $20 and the pot size was $100. Plugging that
into our formula…
20 / (100 + 20)
Which equals…
20/120
Which equals
1/6
You’ll notice that 5:1 can be converted to 1/6 fairly easily. All you have to do is add five
and one and make it the bottom part of the fraction. This is just another way to say the
same thing as what we just did.
Then, your job is to know what 1/6 equals. This is the “hardest” part. If you’re terrible at
math, you can brush up on basic fraction percentages here:
1/2 = 50%
1/3 = 33%
1/4 = 25%
1/5 = 20%
1/6 = 16.5%
1/7 = 14%
1/8 = 12.5%
1/9 = 11%
1/10 = 10%
1/11 = 9%
1/12 = 8%
So for our example, we can see that 1/6 equals 16.5%.
The next step is to simply compare the BETTING PERCENTAGE with our HAND ODDS
percentage. The hand odds are figured using the shortcut we just learned.
If the hand odds percentage is bigger than the betting percentage, a call is justified. If
not, a call is unjustified.
Hand % > Betting % Call is justified.
Hand % < Betting % Call is unjustified.
All right, you’re ready for a real-life example…





That means you have the nut flush draw with your four hearts.
You’re on the button. There’s $80 in the pot from before the flop. Sally bets $40 after
the flop and three players call. The action is to you.
First, you calculate the pot size. It equals $240. You need to decide whether a call is
justified or not. You have nine outs (since there are thirteen hearts in the deck and you
already see four of them).
Plugging the nine outs into our formula…
(9 x 2) + 1 = 19%
If we were using the chart we’d see the actual percentage is 19.15%.
Now you must find the betting percentage. Since the pot size is $240 and the bet size is
$40, we plug these numbers into our formula…
40 / (240+40) = 40/280 = 1/7
Now we just need to decide is 1/7 is bigger or smaller than 19%. Well, 19% is about 20%.
So is 1/7 bigger or smaller than 20%? The answer is smaller.
That means that a call IS justified.
Of course… we haven’t considered other factors in our example here. Since there were so
many players in the hand, we would have DISCOUNTED a couple of the outs, since
someone else was probably on the flush draw. BUT, we would have also considered the
IMPLIED ODDS of busting someone else’s flush with our “nuts”.
So all in all, a call is a good decision to make either way you look at it.
Let’s do another example:





You’ve got an inside straight draw (you need a two).
Let’s say the pot size is $100 and the betting amount is $20. Should you call or fold?
Well, since there are four twos in the deck, you know that you have four outs. After
doubling that and adding one you have a 9% chance of making your straight on the turn.
Now you just need to decide if the betting percentage is larger or smaller. Divide 20 by
(100 + 20). The answer is 20/120, or 1/6. You know that equals about 16.5%... so it’s
LARGER than 9%. That means your hand percentage is SMALLER.
Remember…
Hand % > Betting % Call is justified.
Hand % < Betting % Call is unjustified.
So in this case, you should FOLD.
A lot of this will become instinctual and “second nature” very soon. As you become
familiar with these types of calculations, you’ll understand that inside straights are
hardly EVER worth chasing. It’s the same way with staying in a hand just because you
have one overcard… it’s just not worth it.
Let’s summarize the pot odds calculations one more time in this easy three-step process:
1. Double your outs and add 1. This equals your approximate percentage of making your
hand. (Your “hand odds percentage”.)
2. Divide the bet size by the pot size added to the bet size. (This equals your “betting
percentage”.)
Bet Size / (Pot Size + Bet Size)
3. Compare the "hand odds percentage" to the "betting percentage". If the hand odds are
higher, a call is justified. If the hand odds are smaller, a call isn’t justified.
All that’s left is to consider your implied odds, discounted odds, and make adjustments
according to the players you’re up against. If anything extreme sticks out (i.e. drawing
for the nuts, up against a rare playing style, etc.), then you should factor that into your
decision.

Miscalculating Odds

There are three main MISTAKES players make when it comes to odds for no limit Texas
Holdem. The first is simply miscalculating the OUTS.
For example, let’s say you’ve got an open-ended straight draw and you’re certain your
opponent has a flush draw. You’re holding:



Normally here you would have eight outs, since you have an open-ended straight draw.
But since you put your opponent on the flush, you discount the two of diamonds and the
seven of diamonds. That means you have six outs:



Discounted cards:



Now here’s what’s surprising. Just discounting those TWO outs can amount to saving
THOUSANDS of dollars when making your poker decisions…
For a normal open-ended straight draw, you’d have a 31.45% chance of getting an out.
However, with the flush draw on the table, you only have a 24.14% chance.
Let’s say you run into this situation three times per game, about four times per week.
That’s twelve times per week. Say you lose an average of $10 per missed draw, and win
$25 profit from every completed draw.
After about two months, you would have seen this situation 100 times. Without
discounting your outs (making a bad calculation), you would expect to win about 32
times (since your odds are 31.45%... rounded up for runner-runner situations).
If you calculate the fact that you’ll win $25 profit per win, that equals $800. If you lose
68 times (for the missed draws), you’d lose $680. That means you expect to make a
profit of $120 in the two months. It’s worth it, right?
Now if you calculate the REAL odds, however, you will find a much different story. Let’s
crunch some numbers…
With six outs (instead of eight), you’d have a 24.14% chance of winning. After 100
hands, you’d win 25 times, which equals $625 in profit. But you’d lose 75 times, which is
a loss of $750.
That means you’d LOSE $125 total… rather than MAKE $120 total… after two months of
play. That’s a BIG DIFFERENCE, considering we’re talking about very low stakes. And
we’re only talking about ONE specific situation.
Think about all the OTHER outs miscalculations that can happen… and the implication
of all those mistakes COMBINED. It’s really no wonder so many guys go broke at the
poker tables.
Remember, if you’re going to make informed poker math decisions, you must be sharp.
You must remember to discount outs when possible, not count the same card twice, and
look for all “outs” possibilities within a given situation.
OK, now let’s take a look at the second mistake I often see players make. It is comparing
betting odds of ONE round of betting with the TURN PLUS RIVER odds of the hand.
Remember, when calculating pot odds you must pay attention to the probability of
getting an “out” on the NEXT card… NOT on the next two cards.
Every round of betting is INDEPENDENT of the other rounds. That’s why I said earlier
in this report that the column on our chart that says “Turn And River” isn’t used to
calculate pot odds.
If the action were to you to call a $20 bet with a $100 pot size, you’d need to be getting
better than 5:1 on your hand.
Let’s say you have six outs. That means the odds of making your hand on the turn is
6.83:1 and the odds on the river is 6.67:1. The odds of making your hand on EITHER the
turn or river is 3.14:1.
3.14:1 is better than 5:1. So does that mean you should call the bet?
NO! Absolutely not.
Here’s why: Because the $20 bet is JUST for the turn card… not the turn and river. The
number to pay attention to is 6.83:1, which isn’t good enough to justify a call. So you
should fold.
Think about it… after the turn hits, your opponent is going to bet AGAIN. And this time
the bet will probably be HIGHER. If he bets $40 into a $140 pot, you’re forced to make
another decision in order to see the river card. And if you call that, then you’ve just
spent a total of $60 to see both the turn and river… rather than $20. And that’s why the
3.14:1 stat is irrelevant.
So now the question becomes… Can you EVER use the odds figure of making your hand
on EITHER the turn or river?
The answer is yes. The number can be used when making an ALL-IN decision after the
flop.
For example, if you have a lot of draws after the flop and someone goes all-in, you can
use the odds of making your outs on EITHER the turn or river in order to make a
decision to call.
But besides those cases, you should focus only on the odds of making your hand for one
specific round of betting. Period.
The third big mistake I’ve seen regarding odds is USING THEM AT THE WRONG
TIME.
This is critical.
You see, a lot of amateurs and “fish” out there make DUMB decisions at the poker table.
When you encounter one of these players, you’ll want to make YOUR decisions based on
your read of the situation more than the “odds” of winning.
For example, if someone has played extremely tight the entire game and comes out
betting aggressively after the flop, you can put that player on a monster. Even if “odds”
dictate a call in your position, you should probably just fold the hand and live to see
another day.
It’s the same way with overly-aggressive players. Even though the pot odds might dictate
folding, sometimes a call will be a better play.
It all depends on the players you’re up against. I’ve said it a million times: poker math is
a TOOL, nothing more. Odds are not meant for every situation… and you can’t rely on
them too much, especially in no limit Texas Holdem.

Calculating Discounted Odds

Calculating the number of outs in order to make a hand is rather easy. But a problem
arises when one of YOUR outs is also one of your OPPONENT’S outs. This changes the
calculation considerably.
For example, let’s say you’re holding:



You have an open-ended straight draw. Normally, that means you have eight outs.
However, let’s say you put your OPPONENT on a club flush draw. Let’s say he’s holding:



That means if an eight of clubs or a King of clubs hits the board, your opponent will have
the FLUSH and you’ll have the straight. Since OUTS refers to cards that can give you the
WINNING HAND, the eight and King of clubs are no longer “outs” for you… since they
give you a losing hand.
This information brings the number of outs down to six.
This concept is called “discounted odds”, because you’re DISCOUNTING cards that will
help someone else’s hand.
Now, of course, you don’t necessarily KNOW if someone has the club draw in our
example, but based on a player’s betting patterns and history of play you might be able
to INFER that he does. This type of decision making is where the ability to READ
players meets with the ability to do poker math.
One of the important parts of discounting relates to how many players are at the table.
Let’s say you’re sitting at a 10-man table and five players see the flop. Well, this
unusually high number of players would suggest that at least one or two… quite possibly
more… of the Aces are in other players’ hands.
If you need an Ace as one of your “outs”, it would be smart to DISCOUNT a couple of
them from your calculation. Instead of saying you have four outs (for all four aces),
you’d calculate the number with one or two outs… since “common sense” tells you that
other players have some Aces.
Once again, there’s no science to this. You’ve got to combine your feel for the players
and the table with your odds calculations in order to use discounted odds.

Calculating Implied Odds

Put simply, implied odds has to do with the “extra” amount of money you stand to win if
you complete your hand (make your outs).
We’ll start with an example. Let’s say you’re on the flush draw after the turn and have a
20% of making a winning hand (4:1). Your opponent has two pair. The action is to you
to call a $20 bet. There’s a pot size of $70.
In terms of “explicit odds” (what we’ve been doing so far), you know that in order make
a justified call there needs to be at least $80 in the pot… but there’s only $70.
But in this situation, your opponent has been betting aggressively the entire hand.
You’re confident that he’ll bet again after the river no matter what hits… and that you’ll
be able to even RAISE him for more money.
You figure you can get at least another $30 from your opponent if you hit your flush. So
you add this “implied value” to the current pot size… and see that it’s worth calling now.
That’s how implied odds work. There’s no “math” to them, because they’re based on
your intuition. They aren’t present in every hand situation—just the ones where you
have a “hidden” hand or your opponent is too pot-committed, etc. Considering implied
odds requires that you have a read on your opponents and can roughly deduce what
they’re holding.
The implied value of an out is up to you. The great thing about no limit Holdem is that
often the implied value is DOUBLING UP. If you hit a hidden hand on the river, you can
get your opponent to call an all-in bet and take every single last one of his chips.
For instance, here’s a cool scenario. Let’s say you’ve got pocket Aces:





That means your opponent has the flush and you have trip aces. There’s just one river
card left to go. Your opponent (who is chip leader) bets $2,800 into a $800 pot.
You have lots of outs here. There’s:
1 ace + 3 fours + 3 eights + 3 nines + 7 clubs left = 20 outs
The fours, eights, and nines give you a full house. The other club would give you the nut
flush. With twenty outs, the explicit odds STILL don’t quite justify a call. But you know
that if you DO get your full house or nut flush, you’ll be able to move the REST of your
chips into the middle and double up.
You’d factor a lot of different things into this type of decision, including the implications
of LOSING all your money (Is it a tournament or cash game? Are there re-buys?), how
big your chip stack is, how many players are at the table, and so on.
This is an extreme example, but it shows the importance of implied odds. Most all-in
decisions are made according to implied odds, which is part of the reason why the
behavior from one card player to the next is so different.
All right, let’s move on to “discounted odds”.

Calculating Pot Odds

Now it’s time to use the RIGHT side of the probability charts we saw earlier. This time
we’ll be dealing with the “odds against” something happening, which will help you know
whether a decision is “justified” according to the odds or not.
Here’s the main chart again:



For our purposes here, we’ll only be looking at the RIGHT side this time, under the
heading “Odds Against”.
The chart works the same way as before. First you figure out how many OUTS you have.
Then you compare that to the corresponding column… whether the turn card is about to
come or the river card is about to come (or if you want to see BOTH the turn and river
cards together).
For example, if you have 14 outs after the flop, it means the odds against you are 2.36 to
1 on the turn and 2.29 to 1 on the river.
Let’s look at what “odds against” really MEANS. If the odds against you are 4 to 1 (also
written 4:1), that means you will NOT get your card for every four times that you DO get
it. It means you’ll win one out of five times… or 20% of the time.
A lot of people misconstrue 4:1 to mean ¼, but that’s NOT the case. 4:1 equals 1/5. Four
times you lose, one time you win. That means you won ONCE out of FIVE times. It’s
really critical that you “get” this, because it’s a fundamental aspect of poker math.
OK, now when you hear the phrase “pot odds”, it means the odds you have of making
your hand compared with the odds of the betting. The goal is to always be able to
“justify” a call according to the odds… assuming all other things are equal.
For example… let’s say the odds against you are 4:1 and you must decide whether to call
a $5 bet. That means the POT SIZE compared to the BET SIZE should be BIGGER than
4:1. In this case, the bet size is $5, so the pot size would have to be MORE THAN $20 in
order to justify a call.
I just covered a lot of ground there, so let me explain.
If the odds are 4:1, and the hand plays out five times, here’s what would happen (in
terms of probability):
- Lose
- Lose
- Lose
- Win
- Lose
That’s in no particular order, of course. Now, if you lost $5 every time that situation
occurred, that means you’d lose $20 total for the four losses. Still with me?
With that being said, you want to WIN MORE THAN $20 the one time you win… that
way you make a PROFIT. If you win exactly $20, the odds come out even. If you win $21
or more, then the odds are in your favor. If you win $19 or less, the odds are against you.
In poker, you’ll encounter situations dozens of times per hour where you’ll either get the
card or you won’t. Over time, everyone’s odds come back out to “equal”. So that means if
you play the odds in your favor consistently, over the long term you’ll come out on top.
OK, back to the calculations. With odds against you of 4:1, the “1” represents the time
you win, and the “4” represents the times you lose. The “1” represents the BET SIZE that
you must make a decision about. In our scenario it’s $5. The “4” represents the pot size.
Let’s look at a different scenario. Let’s say the odds against you winning are 7:1. You’ve
figured the pot size to be $150. Someone made a $20 bet and the action is to you. Are
the odds in your favor to call or fold?
The answer is to compare 150:20 to 7:1. Which is bigger? 150:20 is equal to 7.5:1, which
is bigger than 7:1. So that means if you played the hand eight times, you’d win once and
lose seven times. That means you’d lose $140 ($20 x 7) but win $150 (the pot size). So
you’d come out on top with a net profit of $10. So yes, you should call.
You’ll know this QUICKLY by simply figuring out if the BETTING ODDS are bigger or
smaller than the HAND ODDS. If the betting odds are bigger, a call is justified. If the
betting odds are smaller, the call is not justified.
All right… let’s do a quick quiz to test your skills. Here’s the “odds against” chart. The
questions come right after it with the answers at the end.



Circle “J” for a justified call, or “U” for an unjustified call. (Ignore “implied odds” if
you’re familiar with them.)
1. A $2 bet on the turn (river card is left) with a $12 pot when you have 7 outs:
J U
2. A $4 bet with an $8 pot after the flop when you have 8 outs:
J U
3. An opponent moves all-in after the flop for 275 chips making the pot 500 while you
have an inside straight draw and the nut flush draw.
J U
(Hint: You have 12 outs.)
4. A $10 bet after the flop with a $65 pot when you have an inside straight draw.
J U
…
…
…
…
…
…
…
…
…
…
Here are the ANSWERS…
(1. J 2. U 3. J 4. U)
How’d you do?
If you had trouble with these, just email me at roy @ royrounder dot com and I’ll email you
an explanation of each. But I’ll assume you aced them all for now.
OK, so now you understand how to use “odds against” to calculate pot odds. We’re going
to get back to pot odds soon. But now it’s time to talk about implied odds, discounting
odds, and other related factors to consider in a hand…

Calculating Pot Size

Pot size is pretty simple. There are three main considerations:
1. How much money is already in the middle.
2. How much is bet in the current round of betting.
3. How much WILL be bet in the current round.
Let me explain.
Let’s say four players (including you) call the big blind of $10 in a game. That puts $40
in the middle.
The flop hits. You’re on the button. Drew bets $25 into the pot. Shelly calls. Rick folds.
Now the action is to you. What’s the current pot size?
The answer is $40 (from the before the flop) added to $25 (from Drew) added to $25
(from Shelly). That equals $90 as the current pot size.
OK, now what if you weren’t on the button. Let’s say you were second to act…
Four players called the big blind, which puts $40 in the middle. Drew bets $25 and then
the action is to you… with two more players BEHIND you left to act. What’s the pot size?
The answer is $40 + $25 + UNKNOWN.
Notice these are congruent with the three “considerations” we outlined earlier. So what
exactly is “unknown”?
Unknown refers to the two players BEHIND you… who will act AFTER you make your
decision. Put simply, you just don’t know if those two players will call, raise, or fold. So
you really don’t know the exact pot size.
This is another fundamental “problem” with odds. Because you don’t know the exact pot
size, you must “guess” or “infer” what the players behind you will do.
And like I mentioned earlier in the report, this is what makes the game of no limit
Holdem fun and exciting... the fact that you CAN’T just base the game on math. The
advantage ultimately goes to the most well-rounded players.
OK, so in this situation, you would do your best to get a read on the other players in
order to determine pot size.
Now, there’s one more tricky part about how to calculate pot size…
A lot of players get confused about whether to count THEIR OWN MONEY in the actual
pot size figure. The answer is to include money that’s already in there… but not money
you’re about to wager. In the example above, you had already called the big blind of
$10… so that $10 gets counted.
You were trying to make a DECISION about calling a $25 bet. YOUR $25 bet doesn’t get
included in the total pot size, because it’s not in there yet.
Let’s say in our example that you called and the other players behind you folded. So it’s
just you and Drew heads-up. Now let’s say the turn card comes, and Drew bets $50.
What’s the pot size then?
The answer is $40 (pre-flop) + $50 (after the flop) + $50 (bet on turn from Drew). This
time, the $25 you called with after the flop IS included, since now it’s officially in the
pot. But the $50 you may or may not call with is NOT included… because it’s still yours
for now.
All right… so that’s how to calculate pot size. Now that you know pot size and outs,
you’re ready to learn “pot odds” and how to APPLY the information you’ve learned to
real-life poker situations.

Calculating Pot Size

Pot size is pretty simple. There are three main considerations:
1. How much money is already in the middle.
2. How much is bet in the current round of betting.
3. How much WILL be bet in the current round.
Let me explain.
Let’s say four players (including you) call the big blind of $10 in a game. That puts $40
in the middle.
The flop hits. You’re on the button. Drew bets $25 into the pot. Shelly calls. Rick folds.
Now the action is to you. What’s the current pot size?
The answer is $40 (from the before the flop) added to $25 (from Drew) added to $25
(from Shelly). That equals $90 as the current pot size.
OK, now what if you weren’t on the button. Let’s say you were second to act…
Four players called the big blind, which puts $40 in the middle. Drew bets $25 and then
the action is to you… with two more players BEHIND you left to act. What’s the pot size?
The answer is $40 + $25 + UNKNOWN.
Notice these are congruent with the three “considerations” we outlined earlier. So what
exactly is “unknown”?
Unknown refers to the two players BEHIND you… who will act AFTER you make your
decision. Put simply, you just don’t know if those two players will call, raise, or fold. So
you really don’t know the exact pot size.
This is another fundamental “problem” with odds. Because you don’t know the exact pot
size, you must “guess” or “infer” what the players behind you will do.
And like I mentioned earlier in the report, this is what makes the game of no limit
Holdem fun and exciting... the fact that you CAN’T just base the game on math. The
advantage ultimately goes to the most well-rounded players.
OK, so in this situation, you would do your best to get a read on the other players in
order to determine pot size.
Now, there’s one more tricky part about how to calculate pot size…
A lot of players get confused about whether to count THEIR OWN MONEY in the actual
pot size figure. The answer is to include money that’s already in there… but not money
you’re about to wager. In the example above, you had already called the big blind of
$10… so that $10 gets counted.
You were trying to make a DECISION about calling a $25 bet. YOUR $25 bet doesn’t get
included in the total pot size, because it’s not in there yet.
Let’s say in our example that you called and the other players behind you folded. So it’s
just you and Drew heads-up. Now let’s say the turn card comes, and Drew bets $50.
What’s the pot size then?
The answer is $40 (pre-flop) + $50 (after the flop) + $50 (bet on turn from Drew). This
time, the $25 you called with after the flop IS included, since now it’s officially in the
pot. But the $50 you may or may not call with is NOT included… because it’s still yours
for now.
All right… so that’s how to calculate pot size. Now that you know pot size and outs,
you’re ready to learn “pot odds” and how to APPLY the information you’ve learned to
real-life poker situations.