Hero overbet/pushes pre - what's villain's play?

[DrStrange]

Playing 1-2 live, eight handed. It is about three hours into the game. Crazy has just joined the game in the last 30-minutes and has totally changed the dynamic. Its like a school of Piranha when a cow tries to cross the river . . . .

This is intended to be an easy hand, but it should be a good example for the basic thought process - give a range, calculate your equity and compare it to the pot. No implied odds, no multi way decisions, no future streets to consider.

Cast of character:

Hero sits with $135. He is still nursing his original $60 buy-in even though the rest of the table is averaging $400. Hero is tighter than the rest of the table, generally predictable - plays ABC poker. (But then there are occational times Hero gets out of line.) We have all seen this play from Hero before - push into a good sized pot preflop after lots of folks wade in. Hero mostly shows down a reasonable hand.

The hand:

Hero sits in the big blind, crazy straddles $4. UTG+1 makes it $17, folds to Button who calls. Villain sits in the SB and calls. Hero pushes for $135 total. All fold to villain in the small blind.

Villain has 7 7. Does he fold or call? The pot is $190 ($4 +$17 + $17 + $17 + $135). villain owes $118 to call.

To make the math easy at the table - a couple of useful facts:
77 is almost a 55-45 favorite vs two over cards (not quite though, so if its really close err on the cautious side.)
77 is an 20-80 dog vs an over pair.
77 is a 70-30 favorite vs one over card (if anyone puts such a hand into Hero's range)

Bonus question - what are we to think about Hero's short stack (especially with Crazy joining the game)? We know money isn't the issue. We know Hero often plays very deep, though he rarely buys-in for more than $300 no matter how deep the rest of the table is.

DrStrange

[bentax1978]

Interesting, despite it's apparent simplicity. In the end the decision to call or fold is going to be based on Villain's read of the Hero in this particular situation. I know that at my game there are a couple of players who I would insta-fold to in this situation, but from the majority of players I'd have to consider quite a few factors before deciding.

Given what you've described, I'm putting the Hero's range on approximately 65% over pair (88- AA), 15% two over-cards (AK-A8 ), 15% under pair (22-66) and 5% one over card (A7-A2). So running the number, given that the Villain is getting 1.6:1 on his money to call, I would estimate (based on my estimated range) that my expected value of calling is about a $8 loss. Obviously had I assigned slightly different values to the overpair (say 60% instead of 65%), the EV would be almost zero. So I would view the situation as being pretty much a coin flip (~0 EV) based on the range I put the Hero on.

So perhaps it's now best to focus on your "bonus" question, what do we think of the Hero's decision to play short stacked. Without knowing more about Hero (or playing with him), his decision to play short stacked is interesting given that he often plays deep and the fact that crazy is sitting at the table. For whatever reason he has decided to play short stacked and the fact that he has nursed the stack for a while could be due to a number of reasons. This could sway my decision (as the Villain) either way as I could convince myself that after being conservative all night Hero isn't going to shove with anything other than two big cards or an over-pair to my 77. As the same time, you always wonder if Hero has had enough playing short stacked and is ready to double up or rebuy. Again, not knowing Hero nor playing with him probably would have me cancel out these two possibilities. At that point I'm right back to a fairly neutral EV based on the range I put him on.

So in the end I would just decide if I was in the mood to gamble (which might end up being a function of how my night is going).

[JM]

Need more info on Villain. How much is he sitting on and how much is he up/down at this point?

[bentax1978]

Originally Posted by JM

Need more info on Villain. How much is he sitting on and how much is he up/down at this point?

I guess I was answering the question more from the "if I was the Villain" perspective, not the "what is this particular Villain going to do" perspective.

As I said in the last line of my post, after running through the math and realizing there isn't a compelling mathematical case to fold or call (IMO), a lot would come down to how I was running that night and what my stack size was (the latter being less important at my particular home game as we have no cap on buy-ins).

[JM]

yeah I think its basically a coin flip and do you feel lucky if you're villain.

[DrStrange]

Villain has just under $500 and is bought in for $500. He loves to gamble, and would see a slighly bad call to see Hero's cards to be worth the lost EV.

DrStrange

[bentax1978]

Originally Posted by DrStrange

Villain has just under $500 and is bought in for $500. He loves to gamble, and would see a slighly bad call to see Hero's cards to be worth the lost EV.

DrStrange

Well, then I guess I'd expect the Villain to call if he both likes to gamble and doesn't mind a potentially slightly negative EV in order to see what Hero went all-in with.

[jldecarlo]

The math is coming up with a range and calculating the EV of a call (or our pot equity).

We know that hero is "tighter than the rest of the table" but spazzes occasionally (my words).

If we say he only does this with AK or a premium pair (JJ or better) then there are 16 ways to have AK and 24 ways to have JJ-AA so we own 55% of the pot 40% of the time (vs AK) and 20% of the pot 60% of the time (vs overpair). That's 22% of the pot and 12% of the pot respectively for a total of 34% of the pot. This means we call when the pot is laying us 2:1, which it is not.

However, likely Hero has a wider range than this. Adding AQ, AJ or non premium pairs changes things a lot. So now let's say we put him on any AK-AJ or any pocket pair. That's 48 overcards, 42 overpairs, 1 same pair, and 30 underpairs. I refuse to do the math in my head, but that looks like a clear call to me.

Overall, I think the math favors a call based upon my guess of how hero would behave. In this situation, I think he's playing a short stack hoping to get it all in, so I put him on a wider range.

L

PS please feel free to point out any math errors I mad as I'm typing this off the top of my head while flying home from Las Vegas.

[DrStrange]

Let me toss in that Hero expects to get a call most of the time.

The table knows that one or more people commonly call Hero's push, especially "short" stacked. Often callers don't have top 2% or even top 10% hands.

They should know that Hero knows this and expects it, but somehow I doubt that everyone sees it that way.

jldecarlo - your math looks reasonable given the ranges assigned.

DrStrange

[Meddler]

You guys are really good at breaking down hands. Thanks for sharing.