Maximizing EV

[bbqsquirrel]

I have had the experience when I went all-in against a nice, trailing but improvable 2nd-best hand on the flop. Now I got my money in as the favourite, but is there a way for me to maximize my EV by just calling, assuming that villain will be married to his hand no matter what?

Here are 2 examples, NL25.

Villain had ~60BB, I had him covered. I raised 4x preflop with KK, and my unimaginative donkey villain limp-called in EP, everyone else folded. The flop was KAA, giving me a vulnerable full house. I bet 5x into a 9x pot and was minimum check-raised by villain.

Now it's obvious that he's got an Ace, he really liked his trip Aces, and I was a 77% favourite. In actual play I 3-bet all-in, he called with A4s and paired his rag on the river.

Assuming that villain won't lay down his hand no matter what, would it be even more profitable for me to just call down flop and turn before shoving river unless he obviously improved to a full house (turn and river pairing) or quads? This would allow me to get away and save some money if I was OBVIOUSLY outdrawn (not here, coz I wouldn't recognize the 4 as his out, but I could get away from 4 cards -- the Ace and 3 other cards that would pair the turn -- on the river).

Another example:

I have 64s in BB and called a 3x raise by an LP. A tight-passive nit open limped in MP and called the raise as well.

Flop was 357 raimbow giving me a straight. I led out 6x into a 9x pot and MP raised me big (to 24x), original raisor folded. Since villain was tight passive in general he had to have a set here. I pushed my full stack, he called. He had 77 for top set, and he didn't improve.

As played I got all-in on the flop as a ~67% fav. But was 67% good enough? I knew I could probably get away if the board paired on turn. Is it better to call flop and c/r all-in a non-pairing turn?

[flyingPenguin]

If they are likely to get all-in when you are that far ahead, get it all-in (both those hands were played well). With better opponents you might have more difficulty getting them all-in, so you may have to try to get it in on a later street.

Getting it in with 67% to win? Them's good odds. The problems arise when you don't get it in and a scare card comes. If the board paired in that second hand he could have a full house, or he could just have a strong overpair. What do you do then?

[bbqsquirrel]

In retrospect I think hand 2 was played well. If scare cards like a 4 or a 6 hit I might not be able to extract more.

Hand 1 I think should be played more slowly. I am in position, and there are simply no scare cards that could slow down villain hence I think it's better to let him hang himself or get out myself if he managed to draw out on me..

[Warpe]

You're over analyzing hand 1. Getting all your money in the middle when you're ahead is the best play in the long run, end of story.

[dev]

I think in the first example, I might wait for the turn to move in, but that really only helps you when the case ace hits the turn. But at that point you might be inclined to call him down anyway.

This reminds me of a situation with a friend of mine... He kept overbetting the flop against players who liked to draw, and when he got outdrawn, he was livid. I told him that based on the players he was playing against, it would be safer to get all of his money in on the turn, when they've only got one card to save them. These particular opponents were calling down anything with their draws anyway, so it didn't matter when the money went in. So, he lowered his variance a bit because he could fold if the obvious draws hit.

[biondino]

I understand where you're coming from, and I'm impressed with your thinking, but I suspect this particular concept is a slight red herring.

Two main issues: 1) can you really dump a full house when, in all likelihood, most of your respective stacks is already in the middle? If the final ace came, sure, but if he had A4 and a 4 came on the river? Most donks think trip aces is the nuts anyway - you can be sure they'll be acting like they've got a lock.

and 2) by continuing in the hand, you take the risk of scare cards coming and drying up your milch cow. Obviously in the few, beautiful situations where the villain has a 2nd best monster this is probably irrelevant, but most of the time you'll have hands like straights, sets, even two pair and each of these is easily and obviously scared by certain cards.

Anyway, I like this thread a lot, but that's my tuppence'th.

[bbqsquirrel]

How about this hand? My most recent debacle:

http://www.pokerhand.org/?776622

If I could maintain my composure during the heat of the battle I could have saved myself $7.65. Now, $7.65 is nothing compared to the size of the pot, but hey, it's still money. And it's not only about the amount, it's also about the process, how things happened.

First let me go over the reasons why I chased the gutshot:
1) It was an obscure draw, and no one will give me credit for hitting it.
2) It was a nut draw on a rainbow board.
3) It's a raised pot. Stacks were deep (over 100 BBs), compared to the amount that I have to call, i.e. implied odds were there.
4) PF raiser was a loose caller. He might pay me off as well.

So I hit my miracle gutshot on the turn, I had the nuts, great! $$$$$$?. Bittensnake was a reasonable player -- certainly not out of line. A preflop-raise-coldcaller going apeshit postflop usually means a big hand i.e. set. If his $4 bet didn't scream set, his reraise certainly did.

My initial raise was probably too big. A set will certainly not fold on this benign-looking board no matter what I do, and any weaker hand prolly won't call that raise.

So Bittensnake came over the top for a substantial amount, but not all-in. Now it was a mistake for me to push. The board was still quite dry. Does he put me on 54? Certainly not. Will he fold his set for $7.65 if a 4 or 5 arrives on the river? Probably not, so why not slow down, see the river card, make sure I'm winning 100% before committing?

So in conclusion, if I made a smaller raise on the turn and just called his 3-bet, I could save myself possibly >$10 -- that's almost half a buy-in -- if he boated up, while I could still destack him if my hand held up on river.

[bigslikk]

Poker is about the decisons, not the results- you know this.

If you bet a dollar against another guy's dollar, your odds of winning the two-dollar pot determine your probable profit or loss. (probable gain is synonymous with eventual "expected" gain over time; over time probability asserts itself more n more.) Flip a coin twice, you might get 100% tails, nowhere near the probable / expected outcome of 50%. Flip a coin 10,000 times, you're going to get much closer to 50%. Flip it a billion gazillion ++ etc. times heads will seem to come up exactly 50% of the time.

So if you have 60% chance to win a one dollar v. one dollar bet (2:1 odds), probability says you will win ( (.60 * $1) - (.40 * $1)) = $.20 or twenty cents. Sometimes you will lose a dollar on that bet. Other times you will win one. Probability says that you'll win just enough more that basically you're "earning" 20 cents on that bet.

Basically, whenever you're ahead and you bet, you "earn" money. (+EV). When you're priced right for a draw and you call, you earn money. Basically, right moves = +EV = $$$$$.
Yes this shlt is redundant to a great many players on this board, and doesn't even cover the half of it. However, its a basic explanation.

When you have the nuts, and you know the villain is willing to die with his hand, then betting more, or the most (allin) increases / maximizes how much you earn. I think that it may be +EV if you can wait to see if the draw hits or not (minimize loses) only if they will still call allin if it does not (which you are saying). However, you'd have to be pretty damn sure the guy would die with his hand, even after the next card (if his draw doesn't hit, or a scare card comes and he gives up)- also, you'd have to be disciplined enough to fold when his card comes (fold your straight to a **possible** boat).

IMHO, you'd hafta have a helluva read and incredible foresight to squeeze out the extra +EV on this hand. I think most times it'd be better to push with the nuts if villain will call surely.

[Miffed22001]

in the latest hand you posted you got all the money in when your opponent had less than a 30% to win the hand. Thats called maximising ev.
kthx.

[Halv]

in the latest hand you posted you got all the money in when your opponent had less than a 30% to win the hand. Thats called maximising ev.
kthx.

I didn't read all the posts (the OP was a bit too long by itself), but I'm gonna go ahead and disagree on a theoretical level. Maximising EV would be to get all the chips in when he's drawing dead. If we have that awesome read that the villain will never fold his hand, plus we know what his hand is, then we can just c/c to the river and shove if he didn't improve. Even without knowing his excact holding, like in hero's example, we can get more EV by c/c down and shove a non-A river (thus having protected ourselves against him outdrawing to quads). There is an example in NLTAP about this I believe.

The bottom line in real life is of course that we will never have that excact read, but if we did we would be foolish not to act upon it. +EV does not equal max EV.

[pokerroomace]

I think both hands are played well. Get your money in when you are ahead. Also, you aren't 100% sure what his cards are. You might think you're sure but you're never 100% sure.

If you could see his cards. Then maybe waiting for a later street is better. Mike Matros wrote an article about this on Cardplayer.com. I think it's under poker math. It's to do with giving your opponents "free cards". His example is AA with a flush draw. It turns out that waiting till the turn to push is more +$EV than pushing the flop. Even though you know he has a flush draw and could outdraw you on the turn.

[bbqsquirrel]

in the latest hand you posted you got all the money in when your opponent had less than a 30% to win the hand. Thats called maximising ev.
kthx.

I didn't read all the posts (the OP was a bit too long by itself), but I'm gonna go ahead and disagree on a theoretical level. Maximising EV would be to get all the chips in when he's drawing dead. If we have that awesome read that the villain will never fold his hand, plus we know what his hand is, then we can just c/c to the river and shove if he didn't improve. Even without knowing his excact holding, like in hero's example, we can get more EV by c/c down and shove a non-A river (thus having protected ourselves against him outdrawing to quads). There is an example in NLTAP about this I believe.

The bottom line in real life is of course that we will never have that excact read, but if we did we would be foolish not to act upon it. +EV does not equal max EV.

This is exactly my point -- +EV <> max EV. If your opponent has nothing but a flush draw it could be the best play for you to overbet shove turn if you know he'll call any. Opponent won't call anything after the river is dealt and his draw missed. But in cases where opponent has a legitimate hand himself and will still pay you off without improving, waiting until river to shove might be the higher EV play.

In hands 1 and 3 where my reads were impeccable, I should definitely maintain my cool, call down and wait till the river before I shove. The difference between 77% and ~90% EV in hand 1, or 80% EV and 100% EV in hand 3, might just be what separates the great players from the slightly above average ones.

By the way, what is NLTAP?

[zenbitz]

In order for you to save that $8 by folding a river (getting 8.5:1!) that pairs the board, he has to have a set 90% of the time, and never fold. Your reads are not that good. He could have J7 or AA here, or even 3 bet bluff. It happens. (most recent hand)

For the other hands, the equations change if there is lots of money behind (and of course you are very sure of your read). But in general, you can never assume your read is 100% accurate (maybe if you were playing a bot your brother wrote)

[zook]

By the way, what is NLTAP?

No Limit Hold 'Em Theory and Practice, a book by Sklansky & Miller. [plug]Being discussed in our Book Club forum right now.[/plug]

[bbqsquirrel]

Do I ever learn? Apparently not. Not yet anyways. My latest debacle:

http://www.pokerhand.org/?795623

AA probably would flat call so I put opponent on top-pair only. But then I was too excited about suckout time and failed to make the best play according to my read. With the board drier than Sahara desert and only 2 remotely scary turn cards (tens) available, my best line would be call flop and checck-shove turn.

[bigslikk]

I don't understand what you are saying. He called an all-in while behind. What more could you ask for? You want to check-shove the turn... He'd still call- he called a push on the flop with only A's and a King kicker. I don't get it...

Are you saying that it would be better to wait for the turn, so that his odds of sucking out decrease ever so slightly? That makes no sense... yes you've got greater pot odds if he'd push a blank on the turn... but you forget the chance that that free card might be an ace or (gulp) a king (lots of reverse implied odds there). No I don't think this hand relates to the "if he'll always call a push, wait to see if he sucks out" rule. B/C a king / jack / queen (or ten as a scare card) might screw you on the turn, and then u'd be in trouble. No, no waiting on this very vulnerable, yet clearly ahead at this point, hand.

[bbqsquirrel]

Why is shoving turn be a better play? I decided to perform some detailed calculation to illustrate my point.

Assume 1) villain was not folding his TP (AK, AQ or AJ) on the turn, which was a reasonable assumption coz there would be 12.50 in the pot and villain would have 12.75 behind (and that this was micro NL25). 2) Also assume that villain and I had equal stacks ($17.25 each) and 3) assume that we were heads-up already preflop (makes the maths easier).

My hand (T2) is a 72.9% favorite if we got all-in on flop. Hence my PE would be 35.5 * 0.729 = 25.89.

If I just call flop 5 things can happen on 45 possible turns:
28 times a blank (3 to 9) appears on turn, we improve to a 82% favourite. On average we end up collecting $ 35.5 * 36 / 44 = 29.04
4 times we boat up, villain will be drawing to 2 outs, PE = 33.89
2 times villain hit trip Aces. we fold, and we would have $17.25 - 5.25 = $12 remaining in our stack.
3 times villain hit 2-pairs, we fail to get away so we're drawing to 4 outs. PE = 35.5 * 4 / 44 = $3.23
8 times one of the other 2 broadway ranks appear on turn, giving villain 12 outs (2 pair or trips (5) + gutshot (4) + board pair (3)). My PE = 35.5 * 32 / 44 = 25.82

Now, (28 * 29.04) + (4 * 33.89) + (2 * 12) + (3 * 3.23) + (8 * 25.82) all divided by 45 = 26.42 (74.4% EV) which is slightly higher than 25.89 (72.9% EV) that we have if we shoved flop.

In conclusion, the key to this play is my ability to get away from opponent's trip aces. (the 2 * 12 term in my equation). It doesn't make a whole lot of difference in the final PE (just 1.5%), but as I stated before, attention to details like this is probably what turns a winning player into a bigger winner.

[bigspenda73]

I tried to buy groceries this weekend with my Sklansky bucks and the girl at the register just stared at me.

[pokerroomace]

Why is shoving turn be a better play? I decided to perform some detailed calculation to illustrate my point.

Assume 1) villain was not folding his TP (AK, AQ or AJ) on the turn, which was a reasonable assumption coz there would be 12.50 in the pot and villain would have 12.75 behind (and that this was micro NL25). 2) Also assume that villain and I had equal stacks ($17.25 each) and 3) assume that we were heads-up already preflop (makes the maths easier).

My hand (T2) is a 72.9% favorite if we got all-in on flop. Hence my PE would be 35.5 * 0.729 = 25.89.

If I just call flop 5 things can happen on 45 possible turns:
28 times a blank (3 to 9) appears on turn, we improve to a 82% favourite. On average we end up collecting $ 35.5 * 36 / 44 = 29.04
4 times we boat up, villain will be drawing to 2 outs, PE = 33.89
2 times villain hit trip Aces. we fold, and we would have $17.25 - 5.25 = $12 remaining in our stack.
3 times villain hit 2-pairs, we fail to get away so we're drawing to 4 outs. PE = 35.5 * 4 / 44 = $3.23
8 times one of the other 2 broadway ranks appear on turn, giving villain 12 outs (2 pair or trips (5) + gutshot (4) + board pair (3)). My PE = 35.5 * 32 / 44 = 25.82

Now, (28 * 29.04) + (4 * 33.89) + (2 * 12) + (3 * 3.23) + (8 * 25.82) all divided by 45 = 26.42 (74.4% EV) which is slightly higher than 25.89 (72.9% EV) that we have if we shoved flop.

In conclusion, the key to this play is my ability to get away from opponent's trip aces. (the 2 * 12 term in my equation). It doesn't make a whole lot of difference in the final PE (just 1.5%), but as I stated before, attention to details like this is probably what turns a winning player into a bigger winner.

the problem is you have made too many assumptions. you cannot have a 100% correct read on your opponent no matter how good you think you are. you might be right 9 out of 10 times. but that last 1 in 10 you'll be wrong. and that's if you have an incredible read on your opponent.

the percentage error in your calculation is more than 1.5% (due to the assumptions you have made). therefore you're calculation has no meaning and does not show that you should call and push turn.

[Sci Fi]

Seems to me in that last hand the problem isn't getting it all in but calling with 10 2. Don't think this is +ev.