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Pot Odds, Calculating Outs and the Rule of 2 and 4 Pot Odds, Calculating Outs and the Rule of 2 and 4

03-27-2009 , 05:47 AM
I'm going to be working with Rob 1on1 teaching him. Hopefully he'll be able to report back in a couple months on the progression he has had. Already worked with him tonight on pot odds and figuring out how to implement the 2/4 rule.
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
03-27-2009 , 05:58 PM
Quote:
Originally Posted by Shick
Pot Odds, Calculating Outs and the Rule of 2 and 4:

This question is asked quite a bit on this forum so I thought it would be useful to have the oft repeated information in one post.

The most sited example is the 4 to a flush, so I will be lazy and use it here as well. You have two cards of one suit, and there are 2 cards of your suit on the board. Another card of that suit would give you the nut flush and the winning hand. What are your odds to draw to the flush? Furthermore, should you draw to the flush (are you getting proper odds)? You have:

K 8

and the board is:

Q A 2

There is $80 in the pot. The bet to you is $20.

The first part, determining the pot odds, is easy. There is $100 in the pot ($80 pot + Villain's $20 bet) and it will cost you $20 to make the call. Dividing the total pot by the price to call ($100 / $20) gives you pot odds of 5 - 1.

Now what about our card odds? Assuming only the flush will give you the winning had (in this example let's say your opponent has at least a pair of aces so we cannot count the three Kings as outs), you have 9 outs to improve, since there are 13 spades in the deck, 13 minus 2 on the board minus 2 in your hand = 9. How do we determine what our odds are of making the nut flush on the flop? Here is the equation:



P is the percentage, UC is the number of unseen cards, which in this case is 47. (52 total cards minus 2 cards in our hand minus 3 cards on the board). Our chances of making the nut flush on the turn are therefore:

1 - (47-9)/47 = 19.15%

Then we turn this into a ratio to compare it to pot odds with:

R = (1/19.15)*100-1 = 4.22 – 1 dog

So, we’re getting 5-1 on our money by calling the bet to us, and we only need 4.22-1 to make the call profitable, so we call.

But what if we’re facing an all in bet on the flop? Villain bets $20, we raise to $60, and Villain shoves in his remaining $140. The pot is now $300 and it costs us $80 to call. So the pot is giving us an immediate 3.75-1 odds ($300/$80). But what are our odds of making the flush? We will see two cards, the turn and the river. So we need to multiply our turn and river odds together using the following equation:



Chug away at that and we get a 34.97% chance to make our flush, or 1.86-1 odds. Our pot odds are 3.75-1 so we call.

Ok, ok. Wait! How do I possibly do all this complex math in my head, you ask? This is where the Rule of 2 and 4 comes in. The Rule of 2 and 4 will give us a good estimate (but not exact) of the percentage chance of making our hand. Keep that last point in mind. These are the odds for making your hand, not winning the pot!

So, to use the Rule of 2 and 4, we multiply our outs by 4 on the flop, or by 2 on the turn and we will get a rough estimate of the percentage of making our hand. On the flop, we had 9 outs. 9 x 4 = 36%, which is roughly the same as the actual percantage of 34.97%. On the turn, we multiply our outs by 2 and get 18%, which is roughly the same as the actual 19.57%. Keep in mind that you can misapply this rule if you are not in an all in situation on the flop but still use the rule of 4 to determine your odds. This is because you will most likely be facing another bet on the turn and, therefore, will not be using the correct pot odds to make your flop decision. Also, the rule of 2 and 4 is not very accurate in situations where you have lots of outs. As you can see, if we had 18 outs on the flop, 18*4 = 72%, where actually you only have 62.44%. But with so many outs, all that really matters is you're a huge favorite in the hand.

Another way to keep these odds straight is to just print out a list like the one below and keep it next to your computer for a handy reference:



Hope this helps. Good luck at the tables!

How would one do all of this in his head at the tables?
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
03-27-2009 , 06:01 PM
Quote:
Originally Posted by MasterAsylum
I'm going to be working with Rob 1on1 teaching him. Hopefully he'll be able to report back in a couple months on the progression he has had. Already worked with him tonight on pot odds and figuring out how to implement the 2/4 rule.
Yes you did Chris!!! Glad to have met you on here man and hopefully we can build a long lasting poker friendship on here!! Cause I like to make money in poker ... makes me feel successful but I am really just looking for new friends to communicate and game with too!! Thank you for your help Chris and everyone else on this thread for that matter!!

Rob-
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
03-27-2009 , 06:10 PM
Chris can you do all of that math in your head at the tables?? or do you need a calculator too?? like for example how do you divide 9 by 47 in your head to get 15%?
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
03-28-2009 , 03:06 PM
or 19% rather sorry!
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
03-28-2009 , 10:31 PM
I have heard the pros say that I am a 2-1 dogg or I am a 3-1 favorite .... How can I know this when I am playing in a hand?
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
03-29-2009 , 12:39 AM
Quote:
Originally Posted by ROBSCOTT5385
How would one do all of this in his head at the tables?
You don't need to do it all in your head. After you have figured the same odds over and over for all the common situations that come up, you'll just know how many outs you have in certain situations and know your odds. For those situations you don't, getting close is fine, hence the 2 - 4 rule--you really don't need an exact calculation at the table.

Figuring pot odds is pretty easy, but one of the benefits of playing online is you can have a calculator and a printout of the chart beside you while you play and no one will look at you funny.
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
03-29-2009 , 10:07 AM
Schick on the odds chart you posted for me what does the "odds to 1 against" section mean!?!? I dont understand this area I almost got everything down but I still am not catching on to everything completely!
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-07-2009 , 09:34 PM
very nice
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-07-2009 , 11:29 PM
Quote:
Originally Posted by ROBSCOTT5385
Schick on the odds chart you posted for me what does the "odds to 1 against" section mean!?!? I dont understand this area I almost got everything down but I still am not catching on to everything completely!
Say your odds are 20:1, this means the odds are 20 to 1 against you making your hand. In other words, for every 21 times you'll only win once.
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-18-2009 , 12:48 PM
Bumpage because I link this thread to people rather than try explaining it to them.
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
06-10-2009 , 05:14 PM
I came by this thread, not sure if this is the right place to ask as the thread is dated a bit so sorry if it isn't:

This calculation compares the odds that your hand improve with the call/pot ratio.

But when I read these kind of explanations about pot odds I always wonder: shouldn't we take in account the odds the opponent has? You can't put an exact calculation on it as it's unknown how many outs he has that would make his hand even better than your improved hand. But for example when the board is 99T rainbow, you're holding JQo. Your guess is that opponent has KK/AA. So you think you have 8 outs to improve on the next 2 streets, so 31.45% or 2.18 to 1. He puts you allin, which amounts to 28% of the total pot. It seems +EV to call while I think it isn't cause even if turn or river gives you a straight... either turn or river can also give him a FH with a likelyhood of 16.47%.

Is there a quick rule of thumb to take into consideration that opponent always has atleast like 2 outs or something and how it effects EV?

I know software like PokerStove does this, based on possible ranges opp. holds, but I'd prefer a quick handy rule of thumb calculation you can make in your head instead of having to fill in everything in PokerStove while time to decide runs out.

Also, I assume improvement odds should atleast be 1% higher than the call/pot ratio to take rake into consideration?
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
09-23-2009 , 09:27 PM
Quote:
Originally Posted by Soopafly_NL
I came by this thread, not sure if this is the right place to ask as the thread is dated a bit so sorry if it isn't:

This calculation compares the odds that your hand improve with the call/pot ratio.

But when I read these kind of explanations about pot odds I always wonder: shouldn't we take in account the odds the opponent has? You can't put an exact calculation on it as it's unknown how many outs he has that would make his hand even better than your improved hand. But for example when the board is 99T rainbow, you're holding JQo. Your guess is that opponent has KK/AA. So you think you have 8 outs to improve on the next 2 streets, so 31.45% or 2.18 to 1. He puts you allin, which amounts to 28% of the total pot. It seems +EV to call while I think it isn't cause even if turn or river gives you a straight... either turn or river can also give him a FH with a likelyhood of 16.47%.

Is there a quick rule of thumb to take into consideration that opponent always has atleast like 2 outs or something and how it effects EV?

I know software like PokerStove does this, based on possible ranges opp. holds, but I'd prefer a quick handy rule of thumb calculation you can make in your head instead of having to fill in everything in PokerStove while time to decide runs out.

Also, I assume improvement odds should atleast be 1% higher than the call/pot ratio to take rake into consideration?
Yeah, there is a simple way to do what you're talking about. It's called discounting your outs. Say you have an open ended straight draw giving you 8 outs, but there's a flush on the board so it's possible 2 of your outs are tainted. So, when you do the equity calculation, you don't give yourself the full 8 outs. You could use 6, but say it's also not 100% that Villain has a flush draw here every time, so you can use 7 outs when you do your calculation. Basically, whatever makes sense to you.

Also, the rake does make a difference, but this is meant to be something easy to do in your head at the table during the hand, so trying to figure in all the numbers exactly is just going to make it too complicated. You can just fudge a bit off the pot equity to account for rake if you want. That's going to be good enough.

Hope this helps!
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
09-24-2009 , 11:10 AM
Someone asked about odds and I pointed them here when I found this thread - one thing that has wroked for me is a simple concept that the card odds + outs = 13 if your outs are between 5 and 9. Rounded. I play limit and this is a quick way to see if the pot is offering me the right price.

13 - outs = needed pot odds (size of pot/call amount)
13 - 5 = 8-1 (8.40)
13 - 6 = 7-1 (6.83)
13 - 7 = 6-1 (5.71)
13 - 8 = 5-1 (4.88)
13 - 9 = 4-1 (4.22)

works for me as does the rule of 2 with one card to come.
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-14-2011 , 03:13 PM
Quote:
Originally Posted by Shick
Pot Odds, Calculating Outs and the Rule of 2 and 4:

This question is asked quite a bit on this forum so I thought it would be useful to have the oft repeated information in one post.

The most sited example is the 4 to a flush, so I will be lazy and use it here as well. You have two cards of one suit, and there are 2 cards of your suit on the board. Another card of that suit would give you the nut flush and the winning hand. What are your odds to draw to the flush? Furthermore, should you draw to the flush (are you getting proper odds)? You have:

K 8

and the board is:

Q A 2

There is $80 in the pot. The bet to you is $20.

The first part, determining the pot odds, is easy. There is $100 in the pot ($80 pot + Villain's $20 bet) and it will cost you $20 to make the call. Dividing the total pot by the price to call ($100 / $20) gives you pot odds of 5 - 1.

Now what about our card odds? Assuming only the flush will give you the winning had (in this example let's say your opponent has at least a pair of aces so we cannot count the three Kings as outs), you have 9 outs to improve, since there are 13 spades in the deck, 13 minus 2 on the board minus 2 in your hand = 9. How do we determine what our odds are of making the nut flush on the flop? Here is the equation:



P is the percentage, UC is the number of unseen cards, which in this case is 47. (52 total cards minus 2 cards in our hand minus 3 cards on the board). Our chances of making the nut flush on the turn are therefore:

1 - (47-9)/47 = 19.15%

Then we turn this into a ratio to compare it to pot odds with:

R = (1/19.15)*100-1 = 4.22 – 1 dog

So, we’re getting 5-1 on our money by calling the bet to us, and we only need 4.22-1 to make the call profitable, so we call.

But what if we’re facing an all in bet on the flop? Villain bets $20, we raise to $60, and Villain shoves in his remaining $140. The pot is now $300 and it costs us $80 to call. So the pot is giving us an immediate 3.75-1 odds ($300/$80). But what are our odds of making the flush? We will see two cards, the turn and the river. So we need to multiply our turn and river odds together using the following equation:



Chug away at that and we get a 34.97% chance to make our flush, or 1.86-1 odds. Our pot odds are 3.75-1 so we call.

Ok, ok. Wait! How do I possibly do all this complex math in my head, you ask? This is where the Rule of 2 and 4 comes in. The Rule of 2 and 4 will give us a good estimate (but not exact) of the percentage chance of making our hand. Keep that last point in mind. These are the odds for making your hand, not winning the pot!

So, to use the Rule of 2 and 4, we multiply our outs by 4 on the flop, or by 2 on the turn and we will get a rough estimate of the percentage of making our hand. On the flop, we had 9 outs. 9 x 4 = 36%, which is roughly the same as the actual percantage of 34.97%. On the turn, we multiply our outs by 2 and get 18%, which is roughly the same as the actual 19.57%. Keep in mind that you can misapply this rule if you are not in an all in situation on the flop but still use the rule of 4 to determine your odds. This is because you will most likely be facing another bet on the turn and, therefore, will not be using the correct pot odds to make your flop decision. Also, the rule of 2 and 4 is not very accurate in situations where you have lots of outs. As you can see, if we had 18 outs on the flop, 18*4 = 72%, where actually you only have 62.44%. But with so many outs, all that really matters is you're a huge favorite in the hand.

Another way to keep these odds straight is to just print out a list like the one below and keep it next to your computer for a handy reference:



Hope this helps. Good luck at the tables!
So once I get my percentage by multiplying my number of outs, how do i figure out if it is proper to call or not with that percentage? Sorry if this is newb question, I am just trying to get a handle on this.
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-14-2011 , 03:46 PM
If your percentage of the pot is less than your percentage to hit your hand, you have the right "price" to call.

Keep in mind if you're using percentage, you use the percent you are calling of the total pot (i.e., pot in middle of table, plus your opponent's bet, plus the amount you have to call).

For example, if there is $50 in the middle of the table, and your opponent bets $25, your price to call is 25% of the pot. This means any hand with a 25% or BETTER chance of hitting in one card to come is a profitable call (assuming the hand is the winner).

If you were doing it by odds, then you do NOT include your call - you are comparing your call to the size of the pot plus your opponent's bet.

For example, if there is $50 in the pot, and your opponent bets $25, then you are getting "3-to-1" on your call of $25. So in terms of odds, you need 1-in-3 odds or better to call. (better being 1-2.5, 1-1, etc. - not good enough would be 1-4)
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-14-2011 , 08:12 PM
Quote:
Originally Posted by ClubKid
If your percentage of the pot is less than your percentage to hit your hand, you have the right "price" to call.

Keep in mind if you're using percentage, you use the percent you are calling of the total pot (i.e., pot in middle of table, plus your opponent's bet, plus the amount you have to call).

For example, if there is $50 in the middle of the table, and your opponent bets $25, your price to call is 25% of the pot. This means any hand with a 25% or BETTER chance of hitting in one card to come is a profitable call (assuming the hand is the winner).

If you were doing it by odds, then you do NOT include your call - you are comparing your call to the size of the pot plus your opponent's bet.

For example, if there is $50 in the pot, and your opponent bets $25, then you are getting "3-to-1" on your call of $25. So in terms of odds, you need 1-in-3 odds or better to call. (better being 1-2.5, 1-1, etc. - not good enough would be 1-4)
nice thx man, i appreciate the help. i think i pretty much got the hang of it now, so the 2 and 4 rule is a good start for beginner math player?
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-14-2011 , 08:13 PM
hmmm what if they over bet the pot? how do i figure that out?
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-14-2011 , 09:34 PM
It's always the same. Whether they bet less or more than the pot, you are calculating your percentage of the TOTAL pot.

So if the pot is $50, and they bet $100, you have to call $100 into a pot that will be $250 (including your call). So your pot odds as a percentage are 40%.

In fact, no matter how much they over bet, you will never have pot odds over 50% (or 1 to 1). Consider this example - you are playing in a game with no blinds, no antes, head's up. Your opponent goes all in for $1,000. Your $1,000 is exactly 50% of the total, $2,000 pot.

Since there are always some blinds/antes (i.e., an existing pot in the middle), you will always be less than 50%. This is because your money is always matched at least evenly in poker.

I remember you asked some questions before, though.

To be honest, do not hang yourself up too much on the math. Most decisions are automatic, you just have to learn to recognize what hand fits what scenario. If someone bets the pot, you're never going to have odds to call with pretty much any draw in holdem, unless you have a 21 outer (open ended straight flush draw plus two live overcards). This is why normally, with big draws like an open end straight flush draw, it probably makes more sense to just move all in (on the flop), because you'd rather see TWO cards, even though it means risking your whole stack on the draw. With lesser draws, the same applies, except your bluff equity also starts to factor in (i.e., does raising opponent all in also potentially get him to fold the better hand enough times that it makes the play a winner over many trials).

The only time you really need to calculate at the table is if you play limit poker, or if you have odd scenarios in NL holdem (like if you're on the turn, but many opponents in, and someone bets half the pot - if enough people call, you might still have pot odds to chase a open end straight draw; or if you're on the flop, and someone bets very small, like 1/3 pot or less).

I hope this helps. It would be more useful (I think) if you post any hands you have trouble with specifically. That is better too because you will remember the decision making process you made in reviewing the hand, and you will be able to make the (correct) decision very quickly whenever it comes up again!

Let me give you an example. When I first started playing, in limit holdem, I wasn't so sure calling the flop with just two overcards was a good idea. I'd find myself calculating too much, and not thinking about other things, like, who is in the hand, am I drawing live most of the time against them, what is the board texture, etc. So I simply reviewed some hands after they were played, and memorized how may bets had to be in the pot at a MINIMUM to make calling with two overcards (a six outer) the right play. So now I just think of it in terms of, was it raised with three players in plus the blinds - if so (7.5 small bets), and one person bets, and I am not afraid of a raise (due to my position or reads), I know I have odds to call with overcards (or with a better draw, of course).
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-17-2011 , 02:07 AM
Quote:
Originally Posted by ClubKid
It's always the same. Whether they bet less or more than the pot, you are calculating your percentage of the TOTAL pot.

So if the pot is $50, and they bet $100, you have to call $100 into a pot that will be $250 (including your call). So your pot odds as a percentage are 40%.

In fact, no matter how much they over bet, you will never have pot odds over 50% (or 1 to 1). Consider this example - you are playing in a game with no blinds, no antes, head's up. Your opponent goes all in for $1,000. Your $1,000 is exactly 50% of the total, $2,000 pot.

Since there are always some blinds/antes (i.e., an existing pot in the middle), you will always be less than 50%. This is because your money is always matched at least evenly in poker.

I remember you asked some questions before, though.

To be honest, do not hang yourself up too much on the math. Most decisions are automatic, you just have to learn to recognize what hand fits what scenario. If someone bets the pot, you're never going to have odds to call with pretty much any draw in holdem, unless you have a 21 outer (open ended straight flush draw plus two live overcards). This is why normally, with big draws like an open end straight flush draw, it probably makes more sense to just move all in (on the flop), because you'd rather see TWO cards, even though it means risking your whole stack on the draw. With lesser draws, the same applies, except your bluff equity also starts to factor in (i.e., does raising opponent all in also potentially get him to fold the better hand enough times that it makes the play a winner over many trials).

The only time you really need to calculate at the table is if you play limit poker, or if you have odd scenarios in NL holdem (like if you're on the turn, but many opponents in, and someone bets half the pot - if enough people call, you might still have pot odds to chase a open end straight draw; or if you're on the flop, and someone bets very small, like 1/3 pot or less).

I hope this helps. It would be more useful (I think) if you post any hands you have trouble with specifically. That is better too because you will remember the decision making process you made in reviewing the hand, and you will be able to make the (correct) decision very quickly whenever it comes up again!

Let me give you an example. When I first started playing, in limit holdem, I wasn't so sure calling the flop with just two overcards was a good idea. I'd find myself calculating too much, and not thinking about other things, like, who is in the hand, am I drawing live most of the time against them, what is the board texture, etc. So I simply reviewed some hands after they were played, and memorized how may bets had to be in the pot at a MINIMUM to make calling with two overcards (a six outer) the right play. So now I just think of it in terms of, was it raised with three players in plus the blinds - if so (7.5 small bets), and one person bets, and I am not afraid of a raise (due to my position or reads), I know I have odds to call with overcards (or with a better draw, of course).
Thanks bro, this helped very much. I am not specifically have any problems on certain hands, it's more that I just want to have a math foundation and understand why some scenarios are mathematically correct and some are not. But what you said makes a lot of sense, about how I should just shove with a monster draw hand to get more fold equity.
I have been reviewing my hands in a universal hand replayer and it tells your pot odds and stuff, so I can actually see situations where I was stuck on whether or not I should call. It is helping me a lot reviewing them. Thank you for your post, and yea I was just looking back through this thread and seen some of my old posts lol, seems crazy that is 2years ago and I still have not learned any math at all in the game.
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-17-2011 , 02:16 AM
You're welcome, man. I'm glad I could help!
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-17-2011 , 02:58 AM
Quote:
Originally Posted by ClubKid
You're welcome, man. I'm glad I could help!
also, reading back over this helps a ton too ... man some of the questions I was asking 2 years ago .... lol! =) it is crazy because i am a winning player now and never really learned math lol. i just kind of use common sense i guess, if i have 77 and i think that there is a good chance villain has tt+ i am not going to call off 30% of my stack to his 3bet to set mine him. But say is utg min raises and gets 3 flat callers and I wake up to 22 on the button which only costs me 3% of my stack to call ..... i will make the call to hopefully set mine and get them all to the felt.
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-17-2011 , 03:33 AM
Absolutely - a lot of the "math" is pretty correct by feel, as long as you review hands to see if your "feel" was right. Plus a lot of times the exact math isn't so important, because there might be implied odds, or you might have more outs (or simply the best hand without realizing it, like an ace high draw against a lower draw), or you might get a free card on the turn just because you called a flop bet (because opponent is scared that you called his flop bet with a monster).

In fact, if anything, I think reviewing the "math" helped me realized that a lot of times, I should be calling when I might not naturally.

Anyway, it's good to see you're still in the game and have been improving since two years ago! That's always a plus!
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
04-17-2011 , 01:35 PM
Quote:
Originally Posted by ClubKid
Absolutely - a lot of the "math" is pretty correct by feel, as long as you review hands to see if your "feel" was right. Plus a lot of times the exact math isn't so important, because there might be implied odds, or you might have more outs (or simply the best hand without realizing it, like an ace high draw against a lower draw), or you might get a free card on the turn just because you called a flop bet (because opponent is scared that you called his flop bet with a monster).

In fact, if anything, I think reviewing the "math" helped me realized that a lot of times, I should be calling when I might not naturally.

Anyway, it's good to see you're still in the game and have been improving since two years ago! That's always a plus!

haha, yea thx a ton bro ... but not sure if i will be around to much more with the whole doj thing. =( however i will play live at this casino they just built here if worse comes to worse.
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote
08-23-2011 , 01:53 PM
Hi all,

My first post here.... please be gentle!

I think I understand how to calculate pot odds and how to calculate my outs e.g. I have a gut shot straight draw which if I hit will win me the pot. The pot stands at 1100 and villain has bet 250 so I need to call 250 into a pot of 1350. That gives me odds of 5.5/1.

I have 4 outs to help me and there are 47 unknown cards so the odds are 43/4 or just under 11/1 meaning I shouldn't call.

I'm not sure however how to calculate the odds if villain had bet 250 and he was all in so there is the turn and river to come. Could anyone help show me how to calculate this at the table. The odds I have shown above are what I would do at the table and therefore not precise.

Many thanks in anticipation!
Pot Odds, Calculating Outs and the Rule of 2 and 4 Quote

      
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