Positive Expectation or no??? I need some help.

johnbeans · #1 03-04-2006, 04:52 AM

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PokerStars No-Limit Hold'em, $0.50 BB (8 handed) converter

UTG+1 ($16.20)
HERO ($73)
MP2 ($49.50)
CO ($121.50)
Button (VILLAIN) ($49.70)
SB ($5.45)
BB ($74.15)
UTG ($9.30)

Preflop: HERO is MP1 with A[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/heart.gif[/img]. UTG+1 posts a blind of $0.50.
UTG calls $0.50, UTG+1 (poster) checks, HERO raises to $3, 2 folds, Button (VILLAIN) calls $3, 2 folds, UTG folds, UTG+1 folds.

Pretty standard PF. I put him on a PP, most likely TT-QQ with the smooth call.

Flop: ($7.75) 2[img]/images/graemlins/club.gif[/img], 8[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/diamond.gif[/img] (2 players)
HERO checks, VILLAIN bets $6, HERO raises to $24, VILLAIN raises to $46.7, HERO calls
$22.70.

Here's where it gets fun. Villain knows I'll C-bet 2/3-full pot. Especially on a flop like this. So, I check instead with the intention of PS-raising to make it look like I'm trapping him (as I know he's going to be this flop). Through my betting on the flop and our history, I'm trying to represent AA/KK.

Well, he wasn't buying it. He pushes leaving me with slightly under 4-1 to call. I go into the take (tank*) for awhile. The only hands that he could have that would make me fold are AA/KK/88/77/22. Otherwise, I'm only a 3-1 dog against an underpair. I don't think he has any of those hands (although if he does 88/77 is most likely) so I call.

Turn: ($101.15) Q[img]/images/graemlins/heart.gif[/img] (2 players)

River: ($101.15) A[img]/images/graemlins/spade.gif[/img] (2 players)

Final Pot: $101.15

Was the flop raise good or should I have folded given my read of his hand? I was confident I could get him to fold. I talked to him afterwards about it. He said he smelled [censored] because I never check/raise. He thought that was fishy and put me on AK/AQ (good read, huh?).

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A buddy of mine posted this hand in the SSNL thread quite some time ago wondering if he had enough odds to call my all-in (I was the villain), and how his play was yada yada yada. A better question, that never got answered in the thread, would be what percent of the time do I need to not have a set to make his call good. I only had 33, but instantly knew once he check-raised me that my hand was good, as the Hero (whom I have a lot of hands on) doesn’t make that check-raise with a hand that beats me.

In The Theory of Poker Sklansky suggests that anytime you give your opponents the correct odds to call they gain and you lose. Well in the above situation there is no re-raise I can make with my stack that will not give him correct odds to call. In the moment I was thinking, “I have the best hand now, let’s get in all in right now.” Should I have instead been thinking, “His check-raise is a mistake already made, if I push right now I’m giving him a positive expectation to call. I should just call here and then either call his continuation push on turn or push myself if a blank falls, if an A, K, and maybe a Q comes I can then fold.”?

Basically I’m asking if my push on the flop is +EV for me if I know he has AK, AQ, or QKs, and will consequently be forced to call because he is getting good odds on his money. Or in other words can two people both have a positive expectation for a hand? And if my push on the flop is +EV then in a hypothetical situation where I have a made hand and my opponent has a draw but will not call any bet where he isn’t getting the right price, assuming he knows his implied odds/reverse implied odds perfectly, will betting the max the opponent will call on the flop or an unimproved turn ever yield a higher positive expectation than betting more than my opponent can call on the flop and just winning the pot right there? I would imagine the answer is no, and that would lead me to believe that my push on the flop was incorrect despite knowing I had the best hand. I should note that I have not read TOP, but am aware of the Fundamental Theorem of Poker, and if Sklansky answers this within the contents of TOP then I apologize.

JaredL · #2 03-04-2006, 06:18 AM

Welcome to the forums.

This type of thing comes up from time to time. Hopefully I can help clear it up. For the following I'm describing the situation in the FTOP sense, in other words the two players' cards are known to each other.

You asked if it's possible for multiple players to have positive expectation for a hand. I'm not sure that this is the question that you meant to ask. The answer is yes. If you and I are playing in a loose game and have strong hands that aren't dominated then we are possibly both gaining money from preflop action from players that are loose and putting their money in with inferior holdings. If, for example, I flop a big draw and you have some sort of made hand then it is entirely possible that both of us have only made +EV moves on every single street (assume that the loser of the hand folds the river). The reason for this is that we both gained a huge amount from the loose players at the table.

In a heads up situation it could be possible as well due to the blind money that is put in preflop. If the hands in question are relatively close and the odds of the weaker guy improving simply work out so that one player keeps betting and the other calling (I'm thinking limit here) with odds then both are making +EV moves on every street. In NL with deep enough stacks this isn't possible. As you say, one player should according to the FTOP force the other to either fold or call without proper odds. Hence, if you define +EV using the FTOP as a sort of metric it's not possible for both to be +EV for every possible action.

On the hand in question hero (your opponent) made a mistake in the early action. Later, when you made your all-in bet hero was able to make a +EV call. Unfortunately for the hero, the expected gain from the call is less than the expected loss from the raise. So basically with the call hero is getting back some of the lost EV from the earlier mistake. Overall hero's flop action yields a negative expected earn.

Let's move on to the side question - what should villain do here? The answer is most likely to bet as much as you can. If you are the favorite for a hand that is heads up then for every dollar put into the pot you gain. This is not in the FTOP sense, but ignoring the pot. If you are a 3:2 favorite then you are getting a 50% return on any money you put in. Obviously in such a scenario you would want to put in as much as you can. I wrote likely because it could in extreme cases depend on what your opponent would do on later streets. For example, if your opponent would call any bet and never bet on both the turn and river then you could wait until the river and push only if you are ahead. This would be pretty extreme realistically you should be happy to put as much money in as you have.

Jared

AaronBrown · #3 03-04-2006, 12:58 PM

I think you're making this more complicated than it has to be. First let's assume your read is correct, you have 33, he has AK, and he knows you don't have AA, KK or a set.

I think there's $37.75 in the pot, with $18 to you, when you go all-in. Based on your assumptions, if you had $54.95 and went all-in (that is, call $18 and raise $36.95), you don't care if he folds or calls. If he folds you pick up $37.75 for sure, if he calls you win $74.70 71.5% of the time and lose $54.95 28.5% of the time, which has an EV of $37.75.

You never want to raise less than that amount, although you might want to raise more if you think he would call it. But you have only $46.70, so that's not an issue. You have to go all in. He should call (his EV is $5.27) and you have an EV of $34.20.

Now you have to consider the possibility that your read is wrong. If he has a weaker hand, you don't really care. With 33, you don't want to keep him in the pot whatever he's holding, and you can't bet more than $42.70. If he has a stronger hand, you're probably going all in anyway. Your best bet to win is to get him to fold, and your best bet for that is to go all-in (although you don't have much chance of scaring him out with your stack given the amount already in the pot).

So it's an easy all-in for you.

johnbeans · #4 03-04-2006, 03:18 PM

But according to FTOP shouldn't I just call his check-raise on the flop and then if a blank falls give my opponent an opportunity to make a bigger mistake when he pushes on the turn or calls my push? If I can manage to get all the money in on a harmless turn instead of the flop he no longer has proper odds to call with overs and according to FTOP I am gaining an he is losing. Is this the better play?

AaronBrown · #5 03-04-2006, 09:33 PM

It's true that you want to bet enough that he either folds or gives you additional EV by calling. But you can't do that, you don't have the stack. So the next best thing is to bet all of your stack in this case.

It's true that if he doesn't hit on the turn, you can now force him out. But you're giving him a free chance to beat you.

If you knew for sure he had exactly AK, it might make some sense to check. But in a real game, you won't know for sure if he hit or not. So the turn card gives him a lot of information and you very little (unless it's one of the two threes, but it's three times as likely to be one of the six A's or K's).

johnbeans · #6 03-06-2006, 03:06 AM

In the December 2005 (issue #24) Card Player, Matt Mastros wrote an article, "The Free-Card Myth". Mr. Mastros outlines a hand where he has KK and just calls (in position) a tricky LAG's flop bet that he correctly put on a big draw. The turn was a blank that didn't hit the realistic straight draws and didn't help the flush draw. This is where he decided to re-raise all in with his KK. The villain’s draw ended up being so big that pushing on the flop would have been -$330 EV but waiting for a blank turn and then pushing resulted in a +$880 EV.

I’m relatively inept at calculating EV so bear with me. On the flop I determined I had an
EV of +$59.04 = (pot size, 101.15)(odds of winning, .7152)-(my bet, 46.7)(odds of losing, .2848).
$59.04 is pretty far off AaronBrown’s $34.20. I was unsure if the aforementioned formula is correct, so I tried this:
EV of +$25.64 = (pot size – my bet, 54.45)(odds of winning, .7152)-(my bet, 46.7)(odds of losing, .2848).
Perhaps both of these methods are incorrect however using the same formulas on the turn I have an
EV of +$84.26 = (pot size, 101.15)(odds of winning .8636)-(my bet, 22.7)(odds of losing, .1364) or an
EV of +$64.65 = (pot size – my bet, 78.45)(odds of wining, .8636)-(my bet, 22.7)(odds of losing, .1364)

Even if both of the above formulas are incorrect I have to think they are somewhat representative of my true EV, and in both formulas my EV improves on the turn. I felt very strongly that the hero in the hand or from my perspective the villain had AK. I know he doesn’t make a 6x’s BB raise from MP1 after 2 limpers with QKs and it’s very unlikely to be AQs, I’m not even sure why I initially listed those two hands in his range. On top of that he doesn’t semi bluff on the flop with AQ or QK. I feel like by just calling his check-raise on the flop I would have effectively given him only 1 card to hit his 6 outs as he no longer has proper odds to call on the turn if a blank falls. This also lets me save $22.7 if he does hit on the turn. I think this scenario is much different than a situation where my villain semi-bluffs me with a flush or straight draw and only leaves me with a meaningless amount left in my stack to re-raise with. In that situation obviously I push the rest in with a made hand, and obviously the villain is getting correct odds to call with his draw even if he is up against a set.

JaredL · #7 03-06-2006, 05:12 AM

OK, instead of using odds let's do some analysis looking at all the possible things that could come up and aggregate. This gives the same result but can be easier and more thorough.

Here's a quick summary:
Villain is shorter stack with $50 before the flop. Villain has 33 (I'm going to assume you have the three of diamonds, this will slightly change things if you don't), hero has A[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/heart.gif[/img] flop is 2[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/diamond.gif[/img]. You can either call the check-raise or reraise all in. If you call the check-raise the pot will be about $55 and you villain will have $23 left. If you push then the pot will be $101.

Let's play the hand with the cards face up and consider the call and wait for the turn play. There are 7 cards accounted for and 45 unknowns. So there are 45*44 = 1980 possible turn-river combos (order matters here so dont' divide by two). There are 5 types of turn cards - aces and kings, diamonds that aren't aces and kings, threes, 8 or 7, and blanks.

If an ace or a king come on the turn you will have to fold because you will be a huge dog to win on the river. There are 6 of these cards and the river card doesn't matter so this is 6*44 = 264 possible combinations. In this situation you win 0.

If a three comes you similarly take it down. There are 2*44 = 88 combinations. You win 55.

If a diamond comes that's not an ace or king it's slightly more tricky. He will need a diamond, ace or king to win. With 6 AK and 6 other diamonds (remember I assumed you have one) he will have 12 outs. Clearly you are a favorite and will go all in. The pot will offer 78:23 which is better than the 32:12 that he would need. So he will call here. There are 8*44 = 352 combinations. In 8*12 = 96 of them you lose 23. In 8*32 = 256 you win 78.

If an 8 or 7 come then he will have 9 outs - 3 aces, 3 kings, and 3 of whichever of the two didn't come on the turn. He will then need 35:9 odds from the flop which he will not be getting hence he would fold to your all-in bet. There are 6*44 = 264 possible ways to make it happen and you win 55 when it does.

Similarly, on a blank turn you force a fold. There are 2 deuces left and three each of 4-6 and 9-Q. That makes 23 cards that are blanks and 23*44 = possible combinations. In these you win 55.

Before going on let's do a preliminary check. Do the combinations add up to 1980? We have 264 AK, 88 treys, 352 diamonds, 264 8/7s, and 1012 blanks. Add them up and you get 1980, ¡Olé!

So if we play this hand out the representative 1980 times we would earn:
264*0 + 88*55 - 96*23 + 256*78 + 264*55 + 1012*55 = 92,780. Your EV is this divided by 1980 or $46.85.

Suppose you go all in. Keep in mind that in my calculations before I considered money put in on the call on the flop to be dead. Since a chop isn't possible here we are either going to be winning 78 or losing 23.

Now we must do a similar analysis of what situations could come up with the last two. Now order doesn't matter so there are 45*44/2 = 990 possible combinations.

You lose if:
- an A or K come and no 3.
- two diamonds come
- an 8 and a 7 come

There are 6*42 = 252 combinations for the first possibility, 8*7 = 56 for the second and 3*3 = 9 for the third.

So 252+56+9 = 321 times you will lose 23. That means that 990 - 321 = 669 times that you will win 78. In 990 representative times you will earn 78*669 - 23*321 = 44,799. Your EV is then 44,799/990 = 45.25.

So you are correct. Calling and pushing on the turn is correct, however it is close.

Note that I am doing this at 1 in the morning so some typos or arithmetic errors could be in there.

Jared

johnbeans · #8 03-08-2006, 05:17 AM

Getting all my money in on the turn if the board pairs or a diamond falls is still +EV for me. So is it really correct to lump those combinations with the combinations of an A or a K falling? I feel like something else needs to be included in calculating my flop EV to turn EV. Also, I know the formulas I used for determing my EV were not right, so.... help? Thanks for the all this feedback.