Live 1/3 @ PARX

Utg ($100) raises to $20. He's kind of an angry dude who apparently show d up with the intention of torching $1k $200 at a time. He's raised every hand with ATC.

Folds around and I 3b to $60 on the button with 99.

BB jams for $160 and UTG calls.

I need to call $100 to win $280.

How often do I have to be correct to make this call (about 35%?) and mathematically how often are we up against a bigger pair?

This angle of poker math is a big leak for me. Any resources you all could provide would be appreciated.

Isn't the pot $380 when it comes back to you? $160 x 2 plus your first $60. In which case you're pretty much getting 4:1 and if you win 20% of the time you break even.
Odds of a bigger pair is undeterminable without some really good reads on your opponents. Obviously could be some big Aces or suited broadways as well as pairs.
I would likely fold given you might have to fade 4 overs as well as the chance there is TT+ out there.

$20+$60+$160+$80=$320

I was off but not by that much. Also isn't there a percentage that you'll run into a higher pair with only 2 opponents to act? I swear I've seen it somewhere before but maybe not. Like knowing the odds of running KK into AA blind vs blind.

Also considering that I'm playing for a small side pot ($60+$60) could factor into the math. Also if we put villains on over cards, can we think in terms of them potentially blocking each other thus strengthening my 99?

UTG only has $100, so the pot is smaller than $380. It's UTG's $100, BB's $160, and hero's $60. Hero needs to call $100 to win $320, 3.2 to 1 odds. Hero needs to have 24% equity to profit here.

It's hard to say how often you are going to run into a bigger pair here without knowing more about BB and what his range looks like. Is he a loose gambling type? Is he a tight OMC type? 99 figures to be way ahead of UTG though, and you are getting a good price. Calling can't be too big of a mistake.

This is a helpful guide for learning pot odds: https://upswingpoker.com/pot-odds-step-by-step/

To follow-up, if we assign UTG a very wide range of decent hands (33+, all suited broadways and suited aces, some offsuit broadways) and BB a solid range of TT+ AQs and AK, 99 has 26% equity, so this would be a +EV call.

You're focused on the wrong player. You need some reads on the BB, not the UTG. Readless, you're way behind a 1/3 player's range who cold shoves against a 3bet. I doubt he's doing this with worse than 99 or AQ. I'd have no qualms about mucking 99.

The guy shoving in the BB can play AA and 77 the same in this spot. If he's a nit then he only has QQ, KK, and AA here. Me personally because these guys are short stacked and I need to call 100 to win like 340 (once I put my chips in) I'm calling all day. Time to put a bad beat on the nits. I think the formula for pot odds is risk / (risk + reward).

You can compute the odds for opponents that have not acted yet and have two random cards. Once BB jams and UTG calls they don't have random cards any more, they have hands in the ranges they felt good enough to play in this situation. For BB this is a much stronger range of hands but how much stronger varies from opponent to opponent. UTG's could still be nearly anything but his range probably is weighted towards the good end.

This is one of the few times I gamble vs bad players. $100 to win $420. 24% to be +EV

I gave v1 a range of 77% of hands.
V2 a range of 6% of hands. 77+. Ajs+. Aq+ kqs

We have $105 of equity on the first $300 and $54 equity on the last $120 side pot. +$60ev to call

V2 5% range with 99+and AQ+ is $43 equity in side pot and $87 in the main pot - 74% range V1. +$30ev to call

We're being asked to call $100 to win $320, so we require equity of about 100 / (320 + 100) = 24% to break even.

If the BB is only doing this with a pretty tight range of TT+/AK, our equity in a HU pot against him is 31%. The third player's ATC probably changes things a little bit, but we still look to be getting a pretty good price to make a call there.

The other thing to factor in is (a) $160 is a pretty small stack in 1/3 NL that can be gotten in reasonably easy by a lot of players and (b) we're in a weird dynamic where the first guy is raising ATC very short so our 3bet on the button could be seen as quite wide.

So if I've mathed ~reasonably ballparky (sidepots always screw me up), I think I'd need pretty nittish reads on the BB to fold here.

ETA: If you take the worst case scenario against BB of being up against just TT+, we're at 19% (ok, so we're not quite getting that). Add in AK, we're way above at 31%. Add in AQ, we're lol'ing at 37%. Add in just one underpair of 88, we're killing it at 41%. I mean, yeah, there's the other guy's ATC that is factoring in too so it isn't quite that gravy. But still, looks like a call to me against all but the nittiest of nits.

GcluelessNLnoobG

Not that it is relevant to this situation at all, but I think you're thinking of the Phil Gordon Pair Principle, which states that the chances of running into a bigger pair than yours is (N * R) / 2, where N is the number of players behind you left to act and R is the number of ranks higher than yours.

It isn't helpful in this case though.

GcluelessNLnoobG