I found myself in a really unique spot this past weekend and from more of a theory standpoint, thought it would be interesting to discuss if this play could ever be considered +EV.

2/5NL

UTG+1 Very Active player raises to $25, standard sizing.
MP Pretty Loose player who is often FOS/splashes around a lot 3! to $75
BTN, Straight forward pre flop although has gotten aggro post-flop 4! to $180

Hero has a tight image, playing TAG and folding almost all hands recently, hasn't 3! any hand but KK this session, looks down in the small blind at A3o with $450 behind. Covered by all other players.

So we know BTNs range here is exclusively AA/KK. However, with an A blocker, we know his range is 6 combos of KK and only 3 combos of AA.

Is this ever a spot where we can/should actually cold 5! bluff all-in, and have it be +EV? It is almost impossible for any thinking player to range a cold 5! as anything but AA at LLSNL, and should fold every hand but AA.

Assuming Villain folds 100% of his KK, and 0% of his AA the EV should be:

66.67% he folds KK and we win $287
2.08% he calls with AA and we win $557
30.79% he calls with AA and we lose $450

For +EV of $64.36

If we have A3s in this spot it is even better:

66.67% we win $287
3.95% he calls and we win $557
28.95% he calls and we lose $450

for a +EV of $83.09


I would also love some checking done on my math, and there is some other math that I'm struggling with calculating:

-I know I excluded any chance that the original raiser or the original 3! have AA (or will call with KK/QQ/AK ect), but am not sure how to include it in my EV calculation

-I'm also struggling finding the break-even % of time the BTN needs to fold his KK for this to be +0 EV



In game I folded (sorry for anyone looking for a sick story). But I honestly did tank for 5 seconds thinking it would be a really sick spot to 5! bluff. I just didn't have enough faith in the BTN (or most LLSNL players in general) to fold KK even if he had it, and figured it would be a really thin line at best.

Curious to think what other people think about the spot and figured it could be a cool discussion.

I think your analysis at the end is right. You can't count on them folding KK unless you've seen them do it. Plus, you have to count on the other guys to fold whatever they have too which may not be the case. There's only 3 combos of AA, but there's 3 villains who could have them.

Firstly, you should not assume anyone is folding kings for 100bb. Secondly, you did not take into account the times utg+1 or mp have a hand they will call with. Thirdly, the button is super unlikely to fold his hand, he only has to put in 270 into a pot that will be like 950$.

If this play has any chance at all of working, you need to have some serious fold equity. At this stack depth and with the assigned 4bet range of KK+, good luck.

Your stack size doesn't make this profitable ever. Also you don't have enough money behind to even make calling difficult. This is terrible and an excellent way to light 100bb on fire.

Props for even entertaining the thought, but good luck getting someone to fold KK for 100 BB's. And that still doesn't account for the OR or 3! which may call it off with their own AA, KK, AK or QQ.

I agree under most circumstances no one is folding KK for 100BB, I just thought this was a really unique situation where someone pretty easily could: aka I am representing a range of 100% AA and nothing else based on pre-flop action and my image, and also have a blocker to reduce the probability any of the other players have AA and can call. We should have just about as much fold-equity as possible in this spot.

For the times he does call with KK, we also still have 32% equity with A3s, which is why I was also curious about how to calculate the break-even point that he needs to fold KK

I also agreed and said above that the other 2 players in the hand definitely decrease the chances of the bluff getting through, I just wasn't sure how to include that into my EV calculations either.


Edit: would you all call off with KK in the BTNs spot if you were cold 5! from one of the tightest players at the table and it folded back to you?

Yes. Unless I know the player extremely well, there is just too much possibility he is over-valuing AK and lower pocket pairs.

Yes

There's really no need to be thinking about your cold 5-bet bluff ranges in a 2/5 game!

Just for theory's sake, here is how you would calculate your needed fold equity.

Let's say we have the hand we actually have, A3o.

Let's also assume that no one else calls your shove--which, as others have mentioned, is actually a big drag on your EV. But let's start with the easy part.

Let X be the probability he folds KK to your shove. There are 2 ways to compute your EV; I'll use this one--we're going to compute the size of the pot when called, compute your equity in it, and then subtract $450 (the amount you put into it) to get your overall EV.

The size of the pot if you shove $450 and only the button calls you will be 450+450+75+25+5+2 = 1007; let's actually call it 1000 because there's probably rake (and tip, etc.).

Now, when he has AA, you will building a pot of $1000 in which your equity is 7.22%. That's $72.20 in pot equity, minus your 450, is -377.80. This will happen one-third of the time; we'll get back to this later.

When he has KK, he folds with probability X and calls with probability (1-X). When he calls, you're building a $1000 pot with 29.05% equity, for $290.50 in pot equity, minus your 450, is -159.50. When he folds, you win the existing 287.

So your EV in this spot is:

(1/3)(-377.80) + (2/3)(1-X)(-159.50) + (2/3)(X)(287)

which approximately equals

-232.27 + 297.67X

If you want to find your break-even point, set this expression equal to 0 and solve for X. You get

X ~ (232.27)/(297.67) ~ .7803

This shows that V could fold KK as much as 78% of the time and shoving is STILL bad. Turning that around, V could call with KK only 25% of the time and shoving is still unprofitable for you.

Remember that we also have not considered the probability that you get called by someone else! This looks like a terrible bluff.

EDIT: Also, as a sanity check on your math, if you set X=1, meaning he always folds KK, you get that your EV is 65.40, very close to what you calculated (yours probably isn't exactly right because your percentages don't add up to 100%).

Thank you so much!!!

Actually, if I had a tight image and you had a tight image at the time (but it would take seeing a couple complete hands at showdown and looking at the lines you took for me to really label you as that tight), then I would probably fold kings. Again, I would have to somehow know you're capable of folding QQ/JJ here.

Thanks! This is what I was looking for - So I basically need to know for sure that both of the first two players are folding and the BTN is basically always folding KK here to even consider the play, which seems super thin & similar to what I thought in the moment and decided to just fold.

So I think in order to think about this play being profitable in this spot, Villains ranges' definitely have to be wider & effective stacks definitely need to be deeper where I can 5! fold, with A2s-A5s being pretty much the best hands to be holding.

I actually looked last night and found a really similar spot in a HS cash game where making the move actually makes a lot more sense & worked: https://www.youtube.com/watch?v=3UflcW_YCxI - thought it was funny he had basically my exact hand.

I'm 100% folding QQ/JJ possibly even KK here...cold 4!s are just never anything but KK/AA from this type of player at 1/2-2/5

I think three conditions need to be in place for this move to be feasible:

1. You need to have hours and hours of experience playing with the button, so he can be very confident you would never go wild with AK or similar.
2. The table would need to be very deep stacked, so that your bet could be around 100 BBs and still leave the implicit threat of an additional 200-400 Bbs that would be presumably going in on the flop. Importantly none of the other villains can be short stacked, or they might just shove and hope to get lucky.
3. You need to have actually seen the button make a big lay down at some point in the past. Some people are generally ok players but will just never lay down KK preflop as a rule. You need to make sure he isn't one.

PM'D you my address so the next time you contemplate lighting a stack on fire, you can send it to me instead.

KK never folds there, so good fold by you. Self-inflicted bullet dodged. Whew!

It's not the same because their range is way w4eaker then a 2/5 and they are much deeper.

Lol @ expecting someone to put in $180 with KK with all the dead money aside and folding for $270 more.

But very interesting thought process, it's what makes you better.

The more interesting question would be if you could 4bet here instead of 5bet if you knew BTN was a light 3bettor.

this is nowhere near the same. they still have huge stacks behind them, it's not pot committing by any means.

plus he has A3s, a hand that flops way way stronger than A3o. if he has A3o, i think he mucks this.


i would just stick to not attempting to get LLSNL players to fold good hands. KK pre is a good hand.