T
Tublecain
Rock Star
Silver Level
Hey Wildcard, welcome! First of all, don't take it personally; sometimes people will take a peek and won't answer for whatever reason. It happens.
In this case though, I think maybe it has to do with the fact that your question is a bit broad and lacking in detail, so people aren't quite sure how to answer. The reason being that there's a great deal that goes into calculating odds (pot odds, implied odds, outs, etc.), possibly much more than you are expecting, and more than could ever be covered in a single post. I highly suggest you take a look at some of the great sections in Cardschat's Strategy Articles. I'm sure you'll find what you're looking for right away.
To get you started though, a quick and easy formula I learned recently is the x2+1 rule. I can't quite remember where I saw it, but it gives you a rough (off by a couple of percentage points depending on the number) estimate of your chances of catching your outs (or the cards that would improve your hand). You just take the number of outs, multiply by 2, and add 1.
For example, lets say you have AhKh and you're looking at a board of 3h10s8h. There are at least four hearts out there (the two in your hand and the two on the board) and just need one more to give you the nut flush. If there are 13 hearts in a deck, that means that there are 9 hearts left in the deck; in other words 9 outs. In addition, we could also assume that any Ace or King would also improve your hand. If you have one of each, then there's 3 of each left; another 6 outs. Meaning you have a total of 15 outs. (Yes, your opponents might have any one of them, or it might have been a burncard; but there's no way for you to know that, so when you're calculating outs you just go by what you know for certain).
So if you have 15 outs, just multiply by 2 and add 1=31. Meaning you have approximately a 31% (or 3:1) chance of getting a card that would improve your hand on the turn. Basically double that for the river.
The real question however, is how does this help you? That's where pot odds comes in. Pot odds is basically a comparison of the amount of money you have to put into a pot in order to win it. If the pot is currently $100, and you have to call $30 in order to see the next card, then your pot odds are roughly 30% (or around 3:1). If your pot odds are equal or less than your odds of hitting an out, then it is "mathematically correct" for you to make the call.
What does mathematically correct mean? It means that if you were to play the exact same hand a million times the exact same way, over THE LONG RUN, you would end up a winner. Of course, in this game or the other you might get sucked out on (after all, you are 3:1 to hit your card, not 100%), but in the long run you will win. And the no. lesson in poker is that it is the long run that counts, not the short term.
Of course, in practice there's SO MUCH more to take into consideration than just these two factors, that I will outright say DO NOT take what I'm saying here as "everything you need." So many others have a much deeper and complete understanding of other factors that come into play, such as implied odds in NL games, reverse odds, anti-outs and blockers, that I won't even try to go into all of that here. I just wanted to give you a general idea on where you could get started in "learning the math". So hit that Strategy Page and get to reading. Every hour you invest in CAREFUL study of these concepts will immensely improve your game, guaranteed.
Hope that helps,
T.
In this case though, I think maybe it has to do with the fact that your question is a bit broad and lacking in detail, so people aren't quite sure how to answer. The reason being that there's a great deal that goes into calculating odds (pot odds, implied odds, outs, etc.), possibly much more than you are expecting, and more than could ever be covered in a single post. I highly suggest you take a look at some of the great sections in Cardschat's Strategy Articles. I'm sure you'll find what you're looking for right away.
To get you started though, a quick and easy formula I learned recently is the x2+1 rule. I can't quite remember where I saw it, but it gives you a rough (off by a couple of percentage points depending on the number) estimate of your chances of catching your outs (or the cards that would improve your hand). You just take the number of outs, multiply by 2, and add 1.
For example, lets say you have AhKh and you're looking at a board of 3h10s8h. There are at least four hearts out there (the two in your hand and the two on the board) and just need one more to give you the nut flush. If there are 13 hearts in a deck, that means that there are 9 hearts left in the deck; in other words 9 outs. In addition, we could also assume that any Ace or King would also improve your hand. If you have one of each, then there's 3 of each left; another 6 outs. Meaning you have a total of 15 outs. (Yes, your opponents might have any one of them, or it might have been a burncard; but there's no way for you to know that, so when you're calculating outs you just go by what you know for certain).
So if you have 15 outs, just multiply by 2 and add 1=31. Meaning you have approximately a 31% (or 3:1) chance of getting a card that would improve your hand on the turn. Basically double that for the river.
The real question however, is how does this help you? That's where pot odds comes in. Pot odds is basically a comparison of the amount of money you have to put into a pot in order to win it. If the pot is currently $100, and you have to call $30 in order to see the next card, then your pot odds are roughly 30% (or around 3:1). If your pot odds are equal or less than your odds of hitting an out, then it is "mathematically correct" for you to make the call.
What does mathematically correct mean? It means that if you were to play the exact same hand a million times the exact same way, over THE LONG RUN, you would end up a winner. Of course, in this game or the other you might get sucked out on (after all, you are 3:1 to hit your card, not 100%), but in the long run you will win. And the no. lesson in poker is that it is the long run that counts, not the short term.
Of course, in practice there's SO MUCH more to take into consideration than just these two factors, that I will outright say DO NOT take what I'm saying here as "everything you need." So many others have a much deeper and complete understanding of other factors that come into play, such as implied odds in NL games, reverse odds, anti-outs and blockers, that I won't even try to go into all of that here. I just wanted to give you a general idea on where you could get started in "learning the math". So hit that Strategy Page and get to reading. Every hour you invest in CAREFUL study of these concepts will immensely improve your game, guaranteed.
Hope that helps,
T.
D
Daleyboy1234
Rock Star
Silver Level
I read a poker guide and it had a quick table of rough of draw odds so here they are
If you hit a Flush Draw on the flop you are roughly 4/1 to hit the flush
If you have an O/E Straight Draw on the flop you are rought 5/1 to hit the straight
If you have a SET on the flop you are roughly 6/1 to hit the Full House
If you have a Gutshot Straight Draw on the flop you are roughly 11/1 to hit the straight
If you Have 2 Pair on the flop you are roughly 11/1 to hit a Full house.
These are all based on Two cards t come.
* A double gutshot Straight Draw has the same odds as a O/E straight Draw
You have to compare this with the pot odds to see whether you are getting a good deal for you your money.
This isnt set in stone and there may like said above be other outs that can help you out. Mine is very basic but it always helps to have some numbers in your head to simplify your situations
Hope this helps
If you hit a Flush Draw on the flop you are roughly 4/1 to hit the flush
If you have an O/E Straight Draw on the flop you are rought 5/1 to hit the straight
If you have a SET on the flop you are roughly 6/1 to hit the Full House
If you have a Gutshot Straight Draw on the flop you are roughly 11/1 to hit the straight
If you Have 2 Pair on the flop you are roughly 11/1 to hit a Full house.
These are all based on Two cards t come.
* A double gutshot Straight Draw has the same odds as a O/E straight Draw
You have to compare this with the pot odds to see whether you are getting a good deal for you your money.
This isnt set in stone and there may like said above be other outs that can help you out. Mine is very basic but it always helps to have some numbers in your head to simplify your situations
Hope this helps
WildCard_QQ
Enthusiast
Silver Level
the multiply by 2 +1 example is what i saw on learn from the pro's its quite useful, i didnt understand the pot odds before but i think i do now, correct me if im wrong
i limp into a pot (for interest sake)
pot is 3000 with 3 players
i have Jh 8h
flop come 9s 10h 3h
i have 9 hearts a jack a 8 a queen or a 7 to give me a hand which means
i have 21 outs
so i have a 43 percent chance of hitting (a card) on the turn
a 19 percent chance of hitting (a flush) on the turn
and a 13 percent chance of hitting (a straight) on the turn
doubling that for the river ofcourse..
Now, in a pot of 3000 and having a raise of 1500 into that pot.. means im getting 2:1 on my money, so a 50 percent chance, while my odds of hitting are 43 percent...
seems fair...
also, to keep in mind is how low the flop was, does that affect the percentages, at all?
also, if it was a pot size raise, so if someone bet 3000 into that put, im getting 1:1 on my money...
or how does that work
i limp into a pot (for interest sake)
pot is 3000 with 3 players
i have Jh 8h
flop come 9s 10h 3h
i have 9 hearts a jack a 8 a queen or a 7 to give me a hand which means
i have 21 outs
so i have a 43 percent chance of hitting (a card) on the turn
a 19 percent chance of hitting (a flush) on the turn
and a 13 percent chance of hitting (a straight) on the turn
doubling that for the river ofcourse..
Now, in a pot of 3000 and having a raise of 1500 into that pot.. means im getting 2:1 on my money, so a 50 percent chance, while my odds of hitting are 43 percent...
seems fair...
also, to keep in mind is how low the flop was, does that affect the percentages, at all?
also, if it was a pot size raise, so if someone bet 3000 into that put, im getting 1:1 on my money...
or how does that work
T
Tublecain
Rock Star
Silver Level
Your calculations are a little off: i.e. if there's already a pot of 3000, and someone bets 1500 (half the pot into it), then you have to pay 1500 in order to win 4500 (the 3000 already in the pot, plus the 1500 bet going into it); in other words, you're getting 3:1 odds which is really good! You only need a 30% chance of hitting a hand to mathematically justify calling this bet. If someone bet 3000 into a 3000 pot (also known as a 'pot sized bet') then your odds are a little worse (paying 3000 to win 6000, or about 2:1), meaning you need at least a 50% to hit your hand in order to call. Remember when calculating pot odds to calculate everything in the pot, including what was in before and what has just been bet.
When it starts to become REALLY useful is when you can begin to put your opponents on a range of hands. For example, lets say that in your example, given your opponents betting patterns and any tells (if it's a live game), you think your opponent has a monster hand (i.e. JJ+ or AQ+). If that's the case, then your number of outs changes (namely, a J is no longer an out, but is instead an anti-out, because it could be giving him his set). Or lets say you can tell your opponent is on a flush draw, and because of the preflop action you think he has at least K or A high. In that case, it eliminates all your heart draws because he may have the nut flush, and so on and so forth.
In other words, if you can combine sound pot-odds theory, with skillfull reads and assessments of your opponents hands, then you are already on your way to becoming a long-term successful player. That's why new-breed players like Durrr and Phil Ivey are so hard to play against: they pretty much bet and act the same whether they have pocket AA or 84o, so its very hard to get a read on them, which makes it very hard to play effectively against them no matter how good your pot odds are.
This is also a tool you can use against your opponents when you begin to think about what THEY think that YOU have, and whey THEY think YOU think THEY have. To make this a little clearer... lets say that you decided to play 8s6s from middle position to shake up your game, and raised 3xBB, and the BTN (a very tight player) decides to call you.
The flop miraculously falls 9s7sAh. You have an open ended straight flush draw, and there's also an A on the board, which means that your opponent (playing very tight) may have hit top-pair top-kicker, or even a set if he's slowplaying AA. You decide to fire a c-bet (or continuation bet, following through on your preflop raise), and again, your opponent (a typical Nit) cold-calls you. The turn then comes 5s: you just hit your straight flush. More importantly, your opponent possibly just made the high-flush (if we can also assume he's could playing a top hand like AKs). He however probably thinks you have something like pocket pairs, or at the most a straight, but he will probably not suspect you have the straight flush. Using this knowledge, you can size your bets to draw him into the pot, knowing he doesn't suspect your straight flush, including check-raising.
If you suspect that your opponent is drawing dead (for example in this case he has something like AsKh, drawing one more card to a flush that still loses to your straight flush), you can use pot odds to make it mathematically correct for him to call your bet, even though he can't win. Conversely, if the tables were reversed, if by putting your opponent on a range of hands you know that even though calling to your draw is mathematically correct, your opponent has you beat, knowing pot odds AND being able to read opponents is a lethal combination.
Hope that makes sense... I'm a little bit drunk!
When it starts to become REALLY useful is when you can begin to put your opponents on a range of hands. For example, lets say that in your example, given your opponents betting patterns and any tells (if it's a live game), you think your opponent has a monster hand (i.e. JJ+ or AQ+). If that's the case, then your number of outs changes (namely, a J is no longer an out, but is instead an anti-out, because it could be giving him his set). Or lets say you can tell your opponent is on a flush draw, and because of the preflop action you think he has at least K or A high. In that case, it eliminates all your heart draws because he may have the nut flush, and so on and so forth.
In other words, if you can combine sound pot-odds theory, with skillfull reads and assessments of your opponents hands, then you are already on your way to becoming a long-term successful player. That's why new-breed players like Durrr and Phil Ivey are so hard to play against: they pretty much bet and act the same whether they have pocket AA or 84o, so its very hard to get a read on them, which makes it very hard to play effectively against them no matter how good your pot odds are.
This is also a tool you can use against your opponents when you begin to think about what THEY think that YOU have, and whey THEY think YOU think THEY have. To make this a little clearer... lets say that you decided to play 8s6s from middle position to shake up your game, and raised 3xBB, and the BTN (a very tight player) decides to call you.
The flop miraculously falls 9s7sAh. You have an open ended straight flush draw, and there's also an A on the board, which means that your opponent (playing very tight) may have hit top-pair top-kicker, or even a set if he's slowplaying AA. You decide to fire a c-bet (or continuation bet, following through on your preflop raise), and again, your opponent (a typical Nit) cold-calls you. The turn then comes 5s: you just hit your straight flush. More importantly, your opponent possibly just made the high-flush (if we can also assume he's could playing a top hand like AKs). He however probably thinks you have something like pocket pairs, or at the most a straight, but he will probably not suspect you have the straight flush. Using this knowledge, you can size your bets to draw him into the pot, knowing he doesn't suspect your straight flush, including check-raising.
If you suspect that your opponent is drawing dead (for example in this case he has something like AsKh, drawing one more card to a flush that still loses to your straight flush), you can use pot odds to make it mathematically correct for him to call your bet, even though he can't win. Conversely, if the tables were reversed, if by putting your opponent on a range of hands you know that even though calling to your draw is mathematically correct, your opponent has you beat, knowing pot odds AND being able to read opponents is a lethal combination.
Hope that makes sense... I'm a little bit drunk!
O
only_bridge
Legend
Silver Level
Ok, this maths is a little off, if you have 3:1 you only need 25% to have the pot odds, and 2:1 (pot bet) you only need 33% chance to hit.
Of course by hitting you can only count the cards you can hit that would actually beat your opponent, no use drawing for a hand that turns out to be 2:nd best.
Another thing is the implied odds, and this is really tricky to calculate. Implied odds mean that you dont have the direct pot odds to make the call, but if you call and hit you will get payed off more than whats in the pot at the moment.
Always try to put your opponent on a range rather than a specific hand, as that will help you to make a more correct decision when you try to count out your pot odds. I mean how often do you know exactly what hand your opponent has?
T
Tublecain
Rock Star
Silver Level
Thanks for the corrections! I thought I would be a little off; 5 beers will do that to me sometimes... 
Either way, the most important point I wanted to get across was precisely that putting your opponent on a range, in addition to being able to 'do the math' is of paramount importance. Neither the math alone, nor 'reads' alone will cut it in the long run.
Peace!
Either way, the most important point I wanted to get across was precisely that putting your opponent on a range, in addition to being able to 'do the math' is of paramount importance. Neither the math alone, nor 'reads' alone will cut it in the long run. Peace!