Hero just move to the table able so no history whatsoever.

Fold to Hero.
Hero (1000) is in MP + 2 with AJo. Hero raised 25.
Villian (covers hero) HJ called
Small blind also called

Flop (80) A 3 Q rainbow.

Hero bet 50. Hero thinks he can get call from worst Ax and this is a standard spot to bet.

Villian called without thinking too much.

Turn (200) 3 no flush draw.

Hero bet 150. Hero kicker now doesn't play. Hero bet with the intention of bluffing the river as his range is pretty strong.

Villian called without thinking too much again. I think this call eliminate AQ and a random 3 in his range. Hero shows strengh and in a vacuum Villian should raise.

River (500) 9

Hero goes all in trying to push Villian off a chop.

Overbet seems a be ridiculous. I think betting 300-350 looks stronger and probably gets a similar percentage of the time.

Reads on villain? In general I dont think this is necessary. You will get snapped off by AK/AQ a lot.

I like it, nh

I'm reminded of a podcast with Bart Hanson and Ed Miller, where Ed mentioned a mathematical graph where villain range is capped the most +EV play is to bet as much as possible. In fact, EV is positively correlated with how much you bet.

There is a hand in poker after dark with Dwan and the realtor guy. Realtor guy hold AQ on Q high board but I think he checks river which capped his range and Dwan over bet all in.

What do we think about this? If I am holding AA QQ 33 or 99 I am making the same play.

I think if he holds AK or AQ we hears from him PF, OTF, or OTT.

I'm pretty sure that the villain can have 2 pair and a set in this situation since he was calling. This isn't a capped range at all. In addition, with you pounding at the pot the villain doesn't need to raise the turn. He can let you do all the heavy lifting while remaining in position.

I'm sorry I was typing the OP on my phone. On the turn, there was a flush draw not no flush draw. I also think that with 2p+, villain thinks more and exhibit more "live" emotion e.g. shaking or whatever. I saw a hand right when I came to the table where Villain turned or rivered the nut straight and he was definitely shaking.

More reason to check the river.

You think villain called flop with SC on A Q board. Call turn when the board pair with a flushdraw?

No, but qx with bdfd is certainly possible.

ok.

River (500) 9o

Hero checks
Villain bets 300.

Hero????? Should he calls for a most likely chop?

Why should villain ever raise you in this spot if V has AK, AQ, QQ, 33, A3, or 3x???

There is no draw on the board. Hero has shown tremendous aggression with near pot sized bets. Villain has position on Hero. Hero is barreling into Villain.

Also remember that majority of LLSNL villains make mistakes. The two biggest mistakes imo are they overcall when weak and they like to play passive passive trappy trappy when they are near nutted.

If V is an unknown and he is bad enough to call a preflop with a Reverse Implied Odds hand like A3s then this same villain would be bad enough to just be passive passive trappy trappy with AQ or A3. So we shouldn't assume V isn't slowplaying something sick.

It would be absolutely sick if V did peel off a ******ed 53s hand and call the flop hoping to bink or improve to a backdoor draw...

So what is V's range here? Based on the turn bet V's range has got to be exclusively QQ, A2 - AK, 43s - 63s.

So, out of this range, we are beat by approximately:
6 combos of QQ
9 combos of AQ
12 combos of AK
4 combos of 43s
4 combos of 53s
4 combos of 63s

Beat by 39 combos

What range of hands do we tie with:
A2 - AT = 2 available aces x 4 available cards x 8 cards = 64 combos
AJ = 4 combos

68 combos of hands we tie with.

so, approximately 64% of the time we chop, and 36% of the time we lose.

Now the real question mathematically is, how often does villain fold a lessor hand if we shove this river. And how often do we NEED villain to fold a lessor hand in order for our flop shove to be profitable? We assume V NEVER folds any of the 39 combo of hands that beat Hero. So folds only apply to the 68 combos of chop hands.

Pot is $500, Hero has $750 behind and V covers
P = $500
f = % that V folds, if V folds 50% of the time, f = 0.5.
EV1 = Scenario where V folds one of the 68 combos of hands
EV2 = Scenario where V has one of the 39 combos of hands that beat us
EVT = 64% EV1 + 34% EV2


In EV1 we can just say that we will chop the pot as a function of how often V folds to our bet.

EV1 = P x (1 + f)/2

In EV2 we can just say that hero loses -$750

So putting the two equations together and setting for 0

EVT = 64% x EV1 + 34% x EV2
0 = 64% x (P x (1 + f) / 2 )+ 34% x -$750
0 = 64% x (P x (1 + f) / 2 ) - 255
255 = 64% x P x (1 + f) / 2)
255 x (2/64%) = P x (1 + f)
797 = P x (1 + f) = 500 x (1 + f)
797 / 500 = 1 + f
1.6 = 1 + f
1.6 - 1 = f
0.6 = f

So basically, we need villain to fold 60% of the time for this shove to break even.

Assuming that V actually folds 100% of the time, then our total EV works out to about $62

So, we are shoving $750 with the best case long term scenario being a $62 profit .

Now, the pot is $500. We bet big on flop and turn right? So lets assume that instead of shoving $750 that betting $350 into that $500 pot accomplishes the same thing. How would that change our EV?

Well, the $750 turns into $350 and guess what, if villains DOESN'T fold our $350 is profitable long term. Think about it. 34% x $350 = $119. However, on the other side of the equation, if we chop we chop a $500 pot meaning we win back $250. $250 > $119.

This is why sizing is so important and how you will often hear pros talk about how certain bets are the same (or similar) in terms of producing the desired effect.

Here are some EV values of the above equation just so you can do an apples to apples comparison in terms of bet sizing. Remember, fold equity in the below table ONLY applies to Ax hands that we chop with and we assume that V calls with AK, AQ, QQ, and 3x hands that are in his range.



So based on everything, hope you can see how this isn't the optimal play.

Bet the least you think it would take for V to fold Ax hands.

or put another way, lets say if you bet $350 V folds 60% of the time, but if you jam $750 V folds 70% of the time, you can see how that extra 10% of fold equity via increasing our bet by another $400 isn't optimal

NOTE: opps, I just saw a slight error, the 34% should be 36%, but I'm too lazy to go back through all this to correct for that 2%, so meh, close enough for government work

Note #2: We are being EXTREMELY generous with the amount of Ax combos we are putting in villains range. If anything, we could easily cut those combos in half making our river shove even less profitable. If I have time later I may come back and do the same calculations but with a much less generous range of Ax combos for villain. I mean, is V really calling our preflop raise with A4o or A6o

Dgi, you never dissapoint. Great post.