Fundamental Theory Question

I'm re-reading ToP for the umpteenth time, and had a situation last night that got me to thinking. I'll post the hand when I get home from work.

Here's my hypothetical scenario:

NL holdem and you've got AA on the button with one opponent. Flop was Ac8c9d. Opponent bets 1/3 pot, and lets say he's been known to bet his draws, so you're pretty sure he's on a flush or open ended straight draw(maybe both). Say there was 9XBB, and he bets 3XBB.

First question: How big do you raise?

With a this draw, I'm wanting to either drive him out, or make him pay big for his flush. I'd usually go with somewhere between 1/2 pot and pot size raise, depending on what I think he'll call. That would be a 6 to 12 X BB raise. I now think this is wrong according to Sklansky's Fundamental Theorem.

Basically, I want my opponents to make mistakes, ie act differently than they should if they could see my hand. If my opponent has at best 15 outs, he has about a 31% chance of hitting, or close to 2:1 odds (1/3 of the time he hits, 2/3 of the time he doesn't) of hitting on the next card. A half pot raise faces him with call 6XBB to win 18XBB, or right at 3:1. He's gotta make that call, and he's correct in doing so. The person making the mistake is me, because if I knew he had 15 outs, I should raise enough to make it wrong for him to call. In this case thats somewhere bigger than the pot.

Note this gets worse if he figures to stay for two cards, but lets not go there yet.

Second question: What is the correct action if his remaining stack is less than the pot? You basically can't make him make the mistake. If he calls, he's doing the right thing according to Sklansky, I think. So what is the correct action on your part? All "play the player" considerations aside (some people just wouldn't call, regardless of the math, if it was going to bust them), shouldn't you just call?

You can't fold, your odds of winning are 1:2(69%), and you're calling 3XBB to win 12XBB. This doesn't even consider the fact that the board could pair, making you unbeatable. Plus, that just sounds stupid.

If you raise, you're putting more money into a pot when it is correct for your opponent to call. So you're only choice is to call, right?*.

Third question: Now assume its you who can't cover the pot bet. Say your stack is only 6XBB, for a piddly raise of 3XBB. I don't think that changes very much, but it points out the importance of keeping as much money on the table as you can. Without enough money to make it incorrect for your opponent to call, you are allowing him to stay in the pot without making a mistake.


*Note, this I really think this is the wrong answer. You're basically making the bet that you will win the pot. Anymore money you put in the pot is a good bet. You're betting one for one with a 69% chance of winning at that point. You should take that bet everytime.

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Well I haven't read any books and have a limited knowledge of "theory" but I think that in this situation the right call would to be look at your own pot odds. Assuming he has less than the pot, and he has X chips, the expected win being Y, do (Y*.69)/X...the .69 being your stated chance of winning. If this is above 1, then the right move is putting him all-in, if not then the correct move is calling and waiting for the turn. If it is not his card, then I would THEN put him all-in regardless.

But this is just how I would look at the situation.

Originally Posted by Ripptyde

Push ALL IN no question

Yeah, I know the whole all-in viewpoint. I'm trying to explore why it works and if its really correct or not.

When you go all-in, you are likely to fold him. According to Sklansky's theory, that would be a correct play by him, which doesn't make you money. The way I read him, forcing your opponent into making the correct play is not the optimum strategy.

Getting him to make several mistakes is, again according the the Fundamental Theory viewpoint. Getting him to call a 1.5 or 2X pot size bet, then doing it again on the river, seems to be a better play-everything else being equal.

At the same time, giving him a free shot, or a raise that he can correctly call, isn't good either.

question 1.

i would bet at least the pot plus his 3rd pot bet. that would ruin his drawing pot odds. if i thought he'd call more, i bet as much (beyond the pot + 1/3rd pot) that i thought he would call.

question 2.

even if you can't ruin his pot odds, you're still the favorite. same answer as to #1.

questions 3.

odds in your favor and you have the best of it - all-in.

Great questions. Great scenarios.

This is one of thse situations where you can either win a little or lose a lot. You want to know how to make winning a lot an option.

According to your post, you should call his bet, and place the same bet (1/3 the pot) on the turn if he hasn't hit a club or a Q,T,7,5 (to complete his straight) Allow him to do the correct thing and you can play the odds and win the hand 70% of the time.

But I hate losing, even if it is only 30% of the time. I'll look at the pot size, and my stack size and raise accordingly. If I can afford to lose the money, you make a very good point on how to possibly maximize my profits. But in most situations, I will want to get him out and cut the hand off there. Because there will always be that 30% where he pulls out his flush and you start steeming and calling just to see it, or hoping that the board pairs. If you are a short stack and playing with about 6X BB. I'd say AA is an automatic all-in pre-flop.

I completely agree with Fishstick.

If you both have decent stacks, bet the pot size (counting his bet). The hands that have the best chance of outdrawing you are JT and 76 of clubs, both of which would give him the 15 outs (flush draw and straight draw) that you mentioned, and like you said, that's about a 31% chance of hitting on each card. Betting the pot size would make him go slightly against pot odds, even if he holds the best possible hand against yours.

But chances are he doesn't, and he'd have to go well against pot odds to call on a straight draw or flush draw or even a flush draw with a gutshot straight draw. And really, your odds are better than what's listed above, because even if he hit either draw on the turn, you have 10 outs (about a 20% chance) of beating him (3 board cards having 3 other cards each to pair the board, and the 4th ace). That's not even considering that the turn could pair the board and give a flush with the same card. So even if he has the open ended straight draw and a flush draw, a pot size bet is plenty to make him go against odds.

Trying to scare them out in the first scenario doesn't make sense to me at all. Make him go against odds if he wants to call, and hope that he does.

In the 2nd and 3rd scenario, either you or him have less in your stack than is already in the pot, meaning that in both cases he should be more likely to call an all in than if you were both big stacks. So you have the best of it, and he's likely to call. Here the correct play is to go all in, every time. Making the move on the turn instead of the flop would be a horrible decision, because either he hits his draw there and then has you beat, or he misses and then has a chance to fold with a much less chance of hitting (i.e. you just missed your chance to have his money in when you had the big advantage).

Because of the chance he might hit second best, I'm more inclined to push with AK or in an SnG.

1. Now you see the problem with blunt theoretical axioms. I really can't stand the way Sklansky puts "the secret to winning" (I mean, how esoteric can you get?) Put the damn thing in layman's terms: "You want your opponent calling lots of bets when his cards are crappier than yours."

3. If you are shortstacked, you're still the favorite to win. The only fundamental way you've changed the game is "defending the pot," or being able to bet him out later. Since you're something like 66% to take it down, you don't change your expectation from that set point, thus diminishing the skill involved (somewhat).

Which brings me to the next point...if you have somebody who will call every all in you make when they're 33% to win, the only fundamental difference in you having your small or big stack is "how much you're going to make over time." If you're in a game with too many limpers/callers, I don't really consider it a skill game: I call it a slaughter.

For the second and third questions i think its an easy answer: go all in. If you have him covered why not push all in. Yes he may have alot of outs by drawing to a flush and a straight. But on the other hand we dont know that. He could easily be drawing almost completely dead with top pair or two pair. This would also be a very possible situation for him coming out and betting that flop. Your assumption of the double draw is really a worst case scenario. Even if he just has one of these draws, wich is highly probable, you are still a huge favorite. Lets not forget you have flopped the nuts. You cant play scared and fear what cards may or may not come and if those cards may or may not help him. If you have him covered why let him draw cheaply for a raise when he might back out on 4th street. Why not put him all in right there when you have the nuts and he will either call with a draw (you are a big favorite) or with two pair (you are about 95% favorite) or will fold and you win the pot right there.

And if you are the one short stacked all-in is a no brainer. Once again you have the made hand already and even IF he is drawing and IF he hits his flush or straight you still have 12 outs to pair the board and win.

As scary as draws versus your all-in can be, we cant be affraid of what might come. It will only kill our winnings in the long run.


Great questions by the way!

Here's my take:

In a simplified scenario in which you were heads-up and knew your opponent has 15 outs and you had no redraw against him, it would be correct to just call. If calling puts you all-in, you should fold if considering this strictly from a chip EV point of view. It might be worth calling in a tournament, as you still have a pretty good chance to win without improving. (I think it's important to note that, in practice, it would be pretty unusual to give someone credit for an OESD + FD).

You should not reopen the betting because he actually has more pot equity than you and would be correct to push. In a way, you can think of it as if *you* are drawing for runner runner blanks on the turn and river as the odds are about 54% that one of the 15 outs will appear with two cards to come.

In this situation, you do not need to cause him to make a mistake. He already made his mistake by not pushing on the flop. It benefits you - not him - to see the turn.

On the turn, if a blank hits, you could then consider an appropriate bet size at that point, since his odds will drop to 29:15 (but only apparently 31:15 to him as he cannot see your hole cards. Remember that we assumed you *know* his hole cards). This is where you can get him to make a bad call and make a mistake.

Notice that even if you do not have enough to give him -EV pot odds, every dollar you force him to put in decreases his EV. You can both be +EV on the turn because of the overlay from the earlier betting rounds.

Your hypothetical situation is a little bit different, though, because one of his outs (8c) will complete your boat. Also, even if his flush or straight were to complete on the turn with one of the 14 remaining outs, you'd still have 9 outs on the river, so he technically wouldn't have the most pot equity on the flop.

In this case, he has only a 42.4% chance of making his straight or flush while avoiding your full house, so he cannot counter your raise by pushing with +EV. If you bet 83% or more of the pot, he'll have incorrect odds to call, ignoring implied odds.

This analysis ignores the idea of folding equity, but most knowledgeable opponents would be unlikely to fold a straight flush draw, even to an all-in, as they would consider themselves favorites.

There are 7 known cards on the flop, leaving 45*44 = 1980 possible combinations of cards to come. Of these, 14*35 + 25*14 = 840 will enable him to win without you completing your full house. 840/1980 = 0.424

Originally Posted by koolmoe

Here's my take:


You should not reopen the betting because he actually has more pot equity than you and would be correct to push. In a way, you can think of it as if *you* are drawing for blanks on the turn and river as the odds are about 54% that one of the 15 outs will appear with two cards to come.

Right on. In my first post I said I didn't want to go to the two card draw scenario at that time, but now you've brought it up.

With 15 outs, his odds are over 50%. The 8c was an oversight on my part, but even at 14 he's got better odds to win this hand than I do, at least I think that he does.

Thats where my theoretical knowledge runs slim. Knowing that he's got a 51% chance of hitting makes me a very slight underdog, even with the best hand at the time - but it doesn't take into account the idea that he might hit on the turn, and I could hit another any board pair to beat him with a full house. Thats 10 outs, counting the fourth ace that could fall.

So how do you figure that all in?

BTW, here's the hand that got me thinking about all of this:

PokerStars No-Limit Hold'em, $1 BB (7 handed)

SB ($136.85)
heatman ($109.70)
UTG ($160.65)
MP1 ($84.15)
MP2 ($120.30)
CO ($83)
Button ($128.50)

Preflop: heatman is BB with , .
UTG calls $2, MP1 folds, MP2 calls $2, CO folds, Button calls $2, SB completes, heatman checks.

Flop: ($11) , , (5 players)
[color:CC3333]SB bets $8[/color], [color:CC3333]heatman raises to $24[/color], UTG folds, MP2 calls $24, Button folds, SB folds.

Turn: ($67) (2 players)
[color:CC3333]heatman bets $83.7 (All-In), MP2 calls $83.70.

River: ($234.40) :Th: (2 players, 1 all-in)

Final Pot: $234.40

Results below: heatman shows (straight, ten high).
MP2 shows (high card, ten).
Outcome: heatman wins $234.40.

I didn't have the three Aces, but I flopped the nut straight. His straight outs wouldn't help him, but he thought they would so he was counting them. He went on and on about having 19 outs, etc. after that hand, which led me to wonder whether the all-in was theoretically correct or not.

This guy had been already played two flush draws, and I'd only been at the table a round or two, so I was sure he had at least that. Plus,
two hands earlier, we had had this little run-in:

PokerStars No-Limit Hold'em, $1 BB (7 handed)

UTG ($138.85)
heatman ($54.85)
MP2 ($156)
CO ($84.15)
Button ($177.15)
SB ($84)
BB ($131.50)

Preflop: heatman is MP1 with :Kh:, :Kd:.
UTG folds, heatman raises to $6, MP2 folds, CO folds, Button calls $6, SB folds, BB folds.

Flop: ($15) , :Js:, (2 players)
heatman bets $6,Button calls $6.

Turn: ($27) (2 players)
heatman bets $10, Button calls $10.

River: ($47) :As: (2 players)
heatman checks, Button bets $35, heatman calls $32.85 (All-In).

[b]Final Pot: $114.85

Results in white below:
heatman shows :Kh: :Kd: (two pair, kings and sevens).
Button shows :Th: :Qh: (one pair, sevens).
Outcome: heatman wins $112.70. Button wins $2.15.

Originally Posted by heatman

Thats where my theoretical knowledge runs slim. Knowing that he's got a 51% chance of hitting makes me a very slight underdog, even with the best hand at the time - but it doesn't take into account the idea that he might hit on the turn, and I could hit another any board pair to beat him with a full house. Thats 10 outs, counting the fourth ace that could fall.

So how do you figure that all in?

I addressed the full house at the bottom of my post. Factoring in the full house, he's a 57.6%:42.4% underdog, a reduction in his win percent of about 12% compared to the case when you just have top pair. That's why a set is so powerful against a flush draw. Even with the open-ended straight outs, he's still an underdog to you. This has powerful implications when your opponent doesn't have any straight outs against your set...

<edit> Just saw the 10 outs instead of 9, so I need to check my calcs.

OK, so using 7 outs on the turn and 10 on the river, the correct pot equity is 41% for the OESD + FD.

The calculation is as follows:

45*44 = 1980 possible turn and river combinations
14*34 = 476 ways to win on the turn without a boat or quads
24*14 = 336 ways to win on the river without a boat or quads

(476 + 336)/1980 = 41%

So his odds drop over 13% from the non-set case.

Thanks Moe,

I follow the 45!44! part.

Where does the 24*14 and 14*34 come from. Thats something I haven't seen before?

Two ways for him to win:

- hit one of his outs (14) on the turn and any card besides one of your ten outs on the river (44 - 10 = 34)
- miss on the turn but you don't get the boat (45 - 14 - 7 = 24) and hit one of his fourteen outs (14) on the river

Dang it. In the second scenario, there are only thirteen outs on the river, since another of the diamonds is dirtied by the blank that hits on the turn.

That makes the new percentage 39.8% for him to win. I hope that's correct.