The size of the btn 3bet makes it looks like he wants to get it in with UTG, without risking much of his stack in the blinds. I’m punishing this 3bet with AK and 99, but folding AQ. 4bet/call a shove.

Since we have no information on opponents image, or our own image either, only 2 things govern this play: getting the right price vs. hand ranges, and the reality that either of these 2 could be holding some of our outs.

If we are liberal with the UTG range, we will put him on 66+, AJs/o+. If we are liberal with the button range, we will put him on 66+, AJs/o+ as well. If all 3 of us get it in, we are a 28% favorite to win against both opponent ranges. This does not work, because we are absolutely getting a horrible price, as 1 player is severely short stacked, and we can only get 3:1 on just the top end of our stack.

So if we are going to play this, we need to isolate it down to 1 player, to where we become almost a perfect coin flip against those ranges. With the dead money added to the pot by the third player who has folded, we should be able to get at least 2:1 on our money if we get it all in right here. 1) If we shove and SB folds and BTN calls, we are getting 2.12:1. 2) If SB calls all in, and BTN folds, we are getting 2.49:1. 3) If all 3 shove, we are only getting 2.51:1, which is absolutely not the right price for our 28% hand.

Thus, this is either fold or all-in. We are gonna need to see all 5 cards to maximize AK, it will negate our awful position, and apply max pressure to get at least 1 fold.

Strictly considering ONLY the math: I’m shoving here. We are +EV against these ranges, and it is exceptionally likely we are going to get at least 1 fold, and most common scenario we are either in a perfect coin flip against pockets or dominating Ax or Kx, all for better than 2:1 on our money. Let’s shove and put the pressure on them if they want to race.

As for AQ or 99? Fold. Forget it. We are significant dogs against those ranges for the price we are getting if we shove. Those hands are 37% and 44% respectively heads up against the ranges we considered.

T Reply:
July 19th, 2010 at 6:43 am

I chose fold but I think you make a great point.
Thanks for crunching the numbers.

Do you agree that it is most likely we are getting just the button to fold if we shove?
I was pondering whether you might be a bit generous estimating the ranges.
I do take UTG raises seriously in general. Of course he is SS in this case but not desperate at all.
But the button doesn’t need that good a hand to get it heads up and profit from his position.

general johnson jameson Reply:
July 19th, 2010 at 12:50 pm

You kinda answered your own question there about the button: 3 betting from a button position is so common now a days that it was totally ok for me to be liberal with his range. In fact, I would almost skew it down to including JT. So when you say he doesn’t need a good hand because he is profiting from his position, you’re answering your question of if its likely that we will get the button to fold, and that answer would have to be yes, since button 3 bets are generally more light than we might think. My opinion is that he is probably not holding a $48,000 hand.

As for the UTG range: Yes I agree, raises from this spot are usually more serious than a dime a dozen button 3 bet. However, with no reads on UTG or on ourselves, we have to just take the average. I was a little more liberal than I originally wanted to be. If I could edit it I would probably change his range to 99+, AQs+. Because really, if you get 99 or TT in that spot are you folding? Absolutely not you almost always have the best hand right now. The average player would for sure play these, so we must include them in the range. But really, if we get it all in against only him, his cards don’t matter unless they are AA or KK.

Remember that if he has QQ, they’re no better than 22. The only advantage to him having QQ over 22 is that it pretty much removes our ability to form a straight. Other than that, don’t get scared over the inherent power QQ or JJ has, when with our 2 coin flip over cards they may as well be playing with 22.

M Reply:
July 19th, 2010 at 12:58 pm

Very good point. But while there is no difference between QQ and 22, opening up his range to include more hands gives him more possible combinations to get ahead in equity. So it messes with the pot odds that we need to justify a call.

Think we need to shove here. The button’s $8000 gives us the odds that we need to make a call here profitable against almost any hand. Assuming I shove, UTG calls, and button folds, we’re risking 19k to win 32k (the 13k pot plus the 19k UTG stack). With this I’m getting pot odds of about 1.7 to 1, so I only need to win this hand 37% of the time to break even. As long as UTG doesn’t have AA or KK, I’m somewhere around a 44% underdog to any pocket pair and anywhere from 60-72% favorite against unpaired whole cards. This puts my equity way over the necessary 37%.

Using the numbers from general johnson jameson’s post, we have 28% equity against both players using a liberal range. This is no good. We lose a lot of money in expectation with two callers. We would be risking 48k to win 80k (13k from pot, 19k from UTG, and 48k from button), getting 1.7 to 1.

Good news is that in no way do I see both players calling. I see it much more likely that UTG calls our all in, and I don’t see how button could call without the top 1% of hands. If UTG folds and button calls, we risk 48k to win about 60k, giving us 1.3 to 1. We need to win about 43% of the time to break even. So even if UTG folds and button calls we still make money here, as our weighted equity is probably around 50% against button as long as he doesn’t hold AA or KK.

IMO, without anything else to go on, the numbers crunch and we need to be willing to shove here.

I fold AQ in my sleep. Once again, using general johnson jameson’s numbers, if we are 44% underdog with 99, then we should fold, but it is close. We could make a case because the most likely scenario is that UTG calls and button folds, so we only need to win 37% of the time. The problem is that his range is a bit liberal, so it may approach 37% if we tighten it up.

Shove.

general johnson jameson Reply:
July 19th, 2010 at 1:32 pm

Just a note: Remember that when we are betting, our pot prices look a little worse than they actually are, and this is because we are first in to the pot. When we are calling it is easy to look at when we are getting a good price, but when we are making the initial bet, don’t forget to include the amount of the potential caller. So when we are betting X to win Y, the ratio shouldn’t always be just X+Y/X=R, it should be X+Y+X/X=R. The 2nd X here is the call of the villain. It should always be included because if he folds, we didn’t risk anything to win anything, we win 100% of the time. Math crunching only matters when we are contested with a caller. Good discussions!

M Reply:
July 19th, 2010 at 2:00 pm

I’m actually a little confused. I don’t doubt that your comment is accurate, I just need a little clarification.

When I calculated the pot odds of hero being the first to enter the pot, I did include the villain’s call. For instance, take my first paragraph. If I shove and only the UTG calls, then the total pot is the 13k already in there plus the 19k that v puts in there. So its 13 + 19 = 32. So my reward is 32 and my risk is my 19 that I have to put up, giving us 1.7 to 1. We shouldn’t be adding our own bet into the pot, though. The same way as if we were calling a $10 bet into a $100 pot. We would say we have 100/10, or 10 to 1. We wouldn’t add our 10 in and say we have 110 to 10. Apologies if I really messed up what you were saying.

general johnson jameson Reply:
July 19th, 2010 at 4:22 pm

Haha, whoa you’re right I better explain a few things.
1) First of all, we may be interpreting the graph differently: When it says player A has 19k stack, and has put in 3k already, I’m concluding this means he came into the hand with 22k. Because if we went to the flop, the pot would be even, but it would still list him as having 19k, which is clearly confusing and incorrect because we don’t know who put in what and how much with all of these raises, re-raises, and folds going on. Their stack number has to decrease after the 3k, because the 3k is no longer theirs that is the pots. So I think we should conclude his stack was 22k before this hand, so for us to go all in against him, we will be risking 22k, not 19k.
2) Next, totally ignore the pot odds numbers in my first post, I wrote that at like 430am and I wasn’t even close. I just re-read it all and cringed. The 2.5 etc numbers are clearly wrong, we aren’t getting more than double our money per investment. However, the conclusions of being good on our money are still right, my math was just wrong. Your numbers are correct. Don’t look at mine haha.
3) !WARNING! BS THEORY AHEAD: I should have clarified in the comment before this one: What I meant was that in situations where we are NOT concluding betting, (such as just regular bets that are not all-in) we should include our bet when being first in because always assume you will be called.
Example: pot is 100. you bet 50, and I decide to call. I am getting 3:1 on this investment because I know you’ve already committed your 50, and I cannot win just by committing these chips, so it’s a true 3:1 pot odds. But so are you getting 3:1 ONLY if I call. in practice, you were risking 50(X) to win 100(Y). but in theory, if I fold, the X doesn’t matter, whether it was risking 1 chip or 10,000 chips. Pot odds and equity only matter in a contested pot. Explain further:
Say you flop a flush draw, and I flop top pair top kick. Typical scenario right? We’re 65/35. pot is 150 chips. If you bet your draw, you will have to bet 1/3 pot. Because you know if I call, you’re still +EV, since now you’re getting 4:1. So you bet 50, and I called, so now you’ve risked 50 to win 200 giving you 4:1 on your money for your 3:1 hand, for +EV. Your bet size here is chosen based on the assumption that I am calling. In practice, you bet 50 into 150, giving you a completely break even ratio, which makes this bet completely pointless. However, being first in means that I could fold, and if I do, your risk here was non-existent, there is no more contest. 50 into 150 is not +EV for you, but that doesn’t matter, you chose a size that when called, gives you +EV pot odds for your hand.
Still with me? Now say I go first. I want to bet my top pair and protect it from the flush, so I bet 100 into 150. I’m not concerned about pot odds and equity now because I already have the winning hand, and since I know the exact percentage of you winning, whether you call or not does not matter. If you fold, fine my best hand won. If you call, that’s fine too, you chasing pot odd mistakes are my win in the long term too. So when I make any bet over half the pot with the best hand, I win no matter what, whether you call or not. But, when you bet on a flush draw, It’s kind of the same theory, but just in reverse for whichever side of the hand you are on. you cannot go higher than the odds give you for your investment. So in theory, betting your flush draw is pointless, because 50 into 150 is breaking even. However, you’re choosing 50 exactly because when you get called, you haven’t committed an error, but actually +EV yourself. Now, say you bet 50 into 150, and I shove over the top for 900. You have to fold now, and your bet was actually -EV! Your bet being +EV is conditional if and ONLY IF I flat call. If I fold though, what you risked didn’t matter, because you won 100% of the time, made hand or not. But the bet size with call in mind is most important here, because you couldn’t bet 900 into 150, cuz if I call you are -EV. If I fold, the bet size didn’t matter because nothing was risked. Does this all make sense? What I was trying to say was when you bet draws, you always have to size accordingly to getting calls because you don’t have the winning hand, so that is why you have to use X+Y+X/X=R. When you bet a draw, you’re not betting to get a fold, you’re betting to give yourself +EV. The 50 into 150 wasn’t chosen to induce a fold. it was chosen to induce a +EV call. If they fold that is just simply a bonus. When we are all-in though, or if we are betting the river, or any situation where betting has concluded, this theory obviously doesn’t apply. Hope this makes sense even though I’m really windy.

I hate calling here. If we miss the flop, which we will 66% of the time, we are out of position and will face a c-bet from the button pretty much all of the time. There’s of course the very imminent possibility that the short stack will shove behind us pre flop if we call, which will in turn give the button another action, wasting the fold equity we have.

A raise here to around 25k does the trick I think. It shows we mean business and could well force the button off hands like 77-JJ that we are currently behind. Shoving is also a decent option for pretty much the same reasons.

i think shoving is the right play, even though i hate doing it deep in tourneys with a nice stack going. the thing is the shorty will probably call with a range were beating, and the button will have to be scared of the action unless he’s got qq+. only kk/aa hurts us.

the problem is calling basically invites the shorty to shove, and the button to shove over him to try to force us out. folding ak against a shortstack and button isolation raiser is weak. and if youre going to raise, you need to apply max pressure.

M Reply:
July 19th, 2010 at 12:54 pm

I definitely agree. Calling is the worst of the options here. If we miss the flop and check we are almost certainly getting the c bet all in anyway. Why not get the chips in the middle now when we are the likely favorite. Even if we’re the underdog, as long as both players don’t call, we are getting the right price from the pot to justify being about a 44% underdog.

Even though calling is the worst option, I tend to think that folding is close behind. We’ve got to be willing to make plays that have a positive expected value. The best part being that not only are we getting the right pot odds, but the most likely scenario has UTG calling and button folding. So even if we lose this pot, we still sit around 28k, or 23BB.

M Reply:
July 19th, 2010 at 12:57 pm

Just a clarification: by “likely favorite” what I really meant was getting the correct pot odds. There is a good chance we are up against pockets, so in that case we are an underdog.

General Johnson Jameson: for some reason I couldn’t hit reply so I had to post at the bottom of the thread. I haven’t read your entire post yet, I will, but probably not until later tonight or early tomorrow. I just wanted to comment on the first thing you said, though.

My apologies, I forgot to take into account the fact that we only put in the BB and not the 3k that V bet out. Forget for a second the presence of the button, we put in 1,200 so we need to call an additional 1,800 and then the 19k. So it isn’t quite 22k because we have already committed our 1,200. This is now part of the pot we are vying for and is considered part of our reward, not our risk. So if we forget the button altogether, even though V had 22k to start out with, we are technically getting slightly better odds because we started with 1,200 committed to the pot. I know it’s really a small point, but worth noting. Assuming we push V all in given this same scenario, our pot odds expecting a call would be V’s 22k + our 1,200 / 20,800. So in short, because we have committed the BB, we aren’t technically risking the full 22k.