The Theory of No-Limit Poker
Big title, eh? Sounds like I have a great deal to live up to in this post. I actually think I can. Everybody who is anybody knows all about Sklansky's Fundamental Theorem of Poker:
But here, I suggest the Theory of No-Limit Poker: In addition to the above, I submit this:
To apply this theory, we need to consider each action in the hand individually. Take for example (no, please--take it) this hand I played yesterday:
Seat 1: Donkey ($20.15)
Seat 2: Button ($23.30)
Seat 3: SB ($9.75)
Seat 4: BB ($17.80)
Seat 5: UTG ($22.15)
Seat 6: UTG+1 ($35.80)
Seat 7: MP1 ($10.20)
Seat 8: MP2 ($9.65)
Seat 9: Hero ($46.35)
*** HOLE CARDS ***
Dealt to Hero: (Ah Ac)
2 folds,MP1 raises to $0.50, 1 fold, Hero raises to $1.25, Donkey calls $1.25,3 folds, MP1 calls $0.75
*** FLOP *** (8s 2h Js) ($4.10)
MP1 checks, Hero bets $2.60, Donkey calls $2.60, MP1 folds
*** TURN *** (8s 2h Js) (3h) ($9.30)
Hero bets $9, Donkey calls $9
*** RIVER *** (8s 2h Js 3h) (9s) ($27.30)
Hero bets $7.30, Donkey calls $7.30, and is all in
*** SHOW DOWN ***
Hero shows (Ah Ac) (a pair of Aces)
Donkey shows (Qs 7s) (a flush, Queen high)
Donkey wins the pot ($39.85) with a flush, Queen high
I'm not using this as a bad beat post, but as a description of where I went wrong here:
PRE-FLOP: (Ah Ac)
Hero raises to $1.25
What am I doing?
Re-raising.
Why?
I want to tell the table that a) I have a strong hand. b) I want to make anyone with a weaker hand pay to see any flop that can beat me. c) I want to build a pot for me to win if/when people DO call.
Why that amount?
The original raise was a wimpy min-raise, so I raised to 5BB, 2.5x the original raise.
FLOP: (8s 2h Js)
Hero bets $2.60
What am I doing?
Betting $2.60.
Why?
To show strength and to eliminate any flush draw from calling.
Why that amount (about 2/3 pot)?
This is where I made a mistake. Part of me wants the call, therefore the sub-pot-sized bet. The other part wants to price out draws, but do I bet enough here? Anyone with a flush draw has 9 outs, not including any overcards or pairs they may have. We'll assign 10.5 outs, and assume that the player has (As 2s), the hand least likely to fold here. The opponent has about 3.5-to-1 odds to hit with 10.5 outs, or 4.2-to-1 odds to hit with a naked flush draw. My bet gives him only 2.57-to-1 on his money, which means he would need >18 outs to correctly call, so my bet was technically and mathematically correct, but the question is--would he have called given a full-pot bet? We'll never know.
TURN: (8s 2h Js) (3h)
Hero bets $9
What am I doing?
Betting a full-pot sized bet--$9.00
Why?
To build a potential pot, and to price out the now two flush draws that are out there on the board.
Why that amount (Full pot)?
Again, I'm trying to price out any potential drawing players. With two draws out there, I need to bet large. I need to protect my hand, which is quite vulnerable, not only to the flush draw, but also to any potential two pair hand. I bet $9 into a $9.30 pot, meaning that the caller is getting only slightly more than 2-to-1 on his money. This means that even with 10.5 outs (drawing potentially to two pair as well as a flush) he's 3.38-to-1 against making a hand. With a naked flush draw, he's 4.11-to-1 against making a hand. Again, my bet is mathematically and technically correct, but he calls anyway. To correctly call this bet, he would need in excess of 23 outs.
RIVER: (8s 2h Js 3h) (9s)
Hero bets $7.30
What am I doing?
Betting $7.30 to put my opponent all-in.
Why?
Frustration. This could have been my severe error in this hand. Was I a) trying to bluff that I made the flush and price out any weaker flushes? b) trying to push him off a hand? c) Just seeing if he'd lay down a busted heart draw?
Why that amount?
I felt that if he had to go all-in with a weak flush that he would let it go, or I was just pissed off, frustrated, or whatever. It was also a sense of a blocking bet, because if I had checked it, he would've pushed his last $7.30 in, and I would've been forced to call.
He called and showed down the Queen-high flush, sending my aces to the muck as the losing hand.
I'm not sure this hand would have or could have gone differently regardless of how I played it. The opponent had a VP$IP of 71%, a PFR% of 3%, and an Aggression Factor of 0.84, an extra-loose calling station. In hindsight, and being results-oriented, perhaps a stronger push on the flop would've forced him out. Maybe pushing all-in there, or pushing all-in on the turn may have helped, but again, we'll never know. The opponent made errors at almost every decision point and still won the hand. That's where the gambling part of poker comes in.
Let's analyze the opponent's play:
PRE-FLOP:
Error #1--He called a raise and re-raise cold with Q7s. Even speculatively, this is a decidedly -EV move. At this point, he made up his mind that if he flopped a flush draw, he would chase it to the river.
FLOP:
Error #2--He called a flop bet without sufficient odds to draw to a flush. He did have a two-gapped 3-to-a-straight draw as well, but even adding the 1.5 outs to that doesn't give him odds to profitably call the bet.
TURN:
Error #3--He called a pot-sized bet with nowhere near the odds needed to call. Even if you factor in the implied odds, he's calling $9 to win $30.85 more TOTAL(3.42-to-1) on his weak flush draw (4.11-to-1).
RIVER:
His first correct play of the hand. With a flush, you have to call this bet. Even if I had a higher flush, being that pot-committed, you have to call the last $7.30 off your stack to see if I bluffed it the whole way. My action prior says I don't have the flush. You have to call here, getting 4.75-to-1 on your money that I don't have a suited king in spades or a suited ace in spades.
Ok, this is some real second- and third-level thinking here. How about a chart based upon how much you need to bet, relative to pot-size, to price an opponent out of a draw to a hand that could potentially be better than yours? Much of this is read-dependent, obviously, but based upon what you know about an opponent's hand, maybe this can give you a guide.
That table essentially is all about how much you should bet to make sure that an opponent's call will be incorrect. Of course, it is just a guideline, and using the guidelines to the letter will pretty much ensure that you'll get sucked out on your share and more. Bet stronger than the guideline. Better to win small pots than lose a big one.
I hope to use some of this information to not only create more articles, but also to refine your (and my own) hand analysis skills. When looking at a hand you've played, one of the things I've learned is to review the hand from the opponent's perspective. That will likely be the focus of my next article. Good luck at the tables, and happy reading!
Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.
But here, I suggest the Theory of No-Limit Poker: In addition to the above, I submit this:
In No-Limit Poker, every action, every bet, every element of every bet--down to the amount of the bet--exists for a reason. Every decision has a desired consequence. If you cannot determine the appropriate rationale or consequence for completing a given action, the action does not have appropriate EV.
To apply this theory, we need to consider each action in the hand individually. Take for example (no, please--take it) this hand I played yesterday:
Seat 1: Donkey ($20.15)
Seat 2: Button ($23.30)
Seat 3: SB ($9.75)
Seat 4: BB ($17.80)
Seat 5: UTG ($22.15)
Seat 6: UTG+1 ($35.80)
Seat 7: MP1 ($10.20)
Seat 8: MP2 ($9.65)
Seat 9: Hero ($46.35)
*** HOLE CARDS ***
Dealt to Hero: (Ah Ac)
2 folds,MP1 raises to $0.50, 1 fold, Hero raises to $1.25, Donkey calls $1.25,3 folds, MP1 calls $0.75
*** FLOP *** (8s 2h Js) ($4.10)
MP1 checks, Hero bets $2.60, Donkey calls $2.60, MP1 folds
*** TURN *** (8s 2h Js) (3h) ($9.30)
Hero bets $9, Donkey calls $9
*** RIVER *** (8s 2h Js 3h) (9s) ($27.30)
Hero bets $7.30, Donkey calls $7.30, and is all in
*** SHOW DOWN ***
Hero shows (Ah Ac) (a pair of Aces)
Donkey shows (Qs 7s) (a flush, Queen high)
Donkey wins the pot ($39.85) with a flush, Queen high
I'm not using this as a bad beat post, but as a description of where I went wrong here:
PRE-FLOP: (Ah Ac)
Hero raises to $1.25
What am I doing?
Re-raising.
Why?
I want to tell the table that a) I have a strong hand. b) I want to make anyone with a weaker hand pay to see any flop that can beat me. c) I want to build a pot for me to win if/when people DO call.
Why that amount?
The original raise was a wimpy min-raise, so I raised to 5BB, 2.5x the original raise.
FLOP: (8s 2h Js)
Hero bets $2.60
What am I doing?
Betting $2.60.
Why?
To show strength and to eliminate any flush draw from calling.
Why that amount (about 2/3 pot)?
This is where I made a mistake. Part of me wants the call, therefore the sub-pot-sized bet. The other part wants to price out draws, but do I bet enough here? Anyone with a flush draw has 9 outs, not including any overcards or pairs they may have. We'll assign 10.5 outs, and assume that the player has (As 2s), the hand least likely to fold here. The opponent has about 3.5-to-1 odds to hit with 10.5 outs, or 4.2-to-1 odds to hit with a naked flush draw. My bet gives him only 2.57-to-1 on his money, which means he would need >18 outs to correctly call, so my bet was technically and mathematically correct, but the question is--would he have called given a full-pot bet? We'll never know.
TURN: (8s 2h Js) (3h)
Hero bets $9
What am I doing?
Betting a full-pot sized bet--$9.00
Why?
To build a potential pot, and to price out the now two flush draws that are out there on the board.
Why that amount (Full pot)?
Again, I'm trying to price out any potential drawing players. With two draws out there, I need to bet large. I need to protect my hand, which is quite vulnerable, not only to the flush draw, but also to any potential two pair hand. I bet $9 into a $9.30 pot, meaning that the caller is getting only slightly more than 2-to-1 on his money. This means that even with 10.5 outs (drawing potentially to two pair as well as a flush) he's 3.38-to-1 against making a hand. With a naked flush draw, he's 4.11-to-1 against making a hand. Again, my bet is mathematically and technically correct, but he calls anyway. To correctly call this bet, he would need in excess of 23 outs.
RIVER: (8s 2h Js 3h) (9s)
Hero bets $7.30
What am I doing?
Betting $7.30 to put my opponent all-in.
Why?
Frustration. This could have been my severe error in this hand. Was I a) trying to bluff that I made the flush and price out any weaker flushes? b) trying to push him off a hand? c) Just seeing if he'd lay down a busted heart draw?
Why that amount?
I felt that if he had to go all-in with a weak flush that he would let it go, or I was just pissed off, frustrated, or whatever. It was also a sense of a blocking bet, because if I had checked it, he would've pushed his last $7.30 in, and I would've been forced to call.
He called and showed down the Queen-high flush, sending my aces to the muck as the losing hand.
I'm not sure this hand would have or could have gone differently regardless of how I played it. The opponent had a VP$IP of 71%, a PFR% of 3%, and an Aggression Factor of 0.84, an extra-loose calling station. In hindsight, and being results-oriented, perhaps a stronger push on the flop would've forced him out. Maybe pushing all-in there, or pushing all-in on the turn may have helped, but again, we'll never know. The opponent made errors at almost every decision point and still won the hand. That's where the gambling part of poker comes in.
Let's analyze the opponent's play:
PRE-FLOP:
Error #1--He called a raise and re-raise cold with Q7s. Even speculatively, this is a decidedly -EV move. At this point, he made up his mind that if he flopped a flush draw, he would chase it to the river.
FLOP:
Error #2--He called a flop bet without sufficient odds to draw to a flush. He did have a two-gapped 3-to-a-straight draw as well, but even adding the 1.5 outs to that doesn't give him odds to profitably call the bet.
TURN:
Error #3--He called a pot-sized bet with nowhere near the odds needed to call. Even if you factor in the implied odds, he's calling $9 to win $30.85 more TOTAL(3.42-to-1) on his weak flush draw (4.11-to-1).
RIVER:
His first correct play of the hand. With a flush, you have to call this bet. Even if I had a higher flush, being that pot-committed, you have to call the last $7.30 off your stack to see if I bluffed it the whole way. My action prior says I don't have the flush. You have to call here, getting 4.75-to-1 on your money that I don't have a suited king in spades or a suited ace in spades.
Ok, this is some real second- and third-level thinking here. How about a chart based upon how much you need to bet, relative to pot-size, to price an opponent out of a draw to a hand that could potentially be better than yours? Much of this is read-dependent, obviously, but based upon what you know about an opponent's hand, maybe this can give you a guide.
| You Put Opponent On... | Opponent's Outs | Odds Flop to Turn | % of Pot to Bet | Odds Turn to River | % of Pot to Bet |
| Flush Draw | 9 | 4.22:1 | 35% | 4.11:1 | 35% |
| Flush Draw + 1 Overcard Flush Draw + GSSD | 12 | 2.92:1 | 53% | 2.83:1 | 55% |
| Flush Draw + 2 Overcard Flush Draw + OESD | 15 | 2.13:1 | 89% | 2.07:1 | 94% |
| OESD | 8 | 4.88:1 | 26% | 4.75:1 | 27% |
| OESD + 1 Overcard | 11 | 3.27:1 | 45% | 3.18:1 | 46% |
| OESD + 2 Overcards (high end) | 14 | 2.36:1 | 74% | 2.29:1 | 78% |
| GSSD | 4 | 10.8:1 | 11% | 10.5:1 | 12% |
| GSSD + 2 Overcards | 10 | 3.70:1 | 37% | 3.60:1 | 39% |
| 2 Overcards | 6 | 6.83:1 | 18% | 6.67:1 | 20% |
| Pair (using 1 hole card) | 5 | 8.40:1 | 14% | 8.20:1 | 15% |
| Pair + Flush Draw Pair + Flush Draw + GSD | 14 | 2.4:1 | 72% | 2.29:1 | 78% |
| Pair + OESD | 10 | 3.70:1 | 38% | 3.60:1 | 40% |
| Pair + GSSD | 6 | 6.83:1 | 18% | 6.67:1 | 20% |
| Pair + Flush Draw+ OESD | 17 | 1.76:1 | 1.33 X pot | 1.71:1 | 1.41 X pot |
That table essentially is all about how much you should bet to make sure that an opponent's call will be incorrect. Of course, it is just a guideline, and using the guidelines to the letter will pretty much ensure that you'll get sucked out on your share and more. Bet stronger than the guideline. Better to win small pots than lose a big one.
I hope to use some of this information to not only create more articles, but also to refine your (and my own) hand analysis skills. When looking at a hand you've played, one of the things I've learned is to review the hand from the opponent's perspective. That will likely be the focus of my next article. Good luck at the tables, and happy reading!
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