$1/2 NL

You have 6 7

flop 5 6 q
turn 4

villain pushes all-in on the turn for 2x pot.
I need 3:2 to call, which is 40%.

open ended straight flush draw: 15 outs
a 6: 2 outs
a 7: 3 outs

20 outs x 2% = 40% assuming all my outs are good. (ie: he has a non-club tptk)

I guess him have naked tptk or worse is the only scenario where I have the odds to call?

You have 45% against AhQh.

Hold'em Simulation ?
44 trials (Exhaustive)
board: 5c4c6dqs
Hand Equity Wins Ties
6c7c 45.45% 20 0
AhQh 54.55% 24 0


Against 55, it's not so pretty.


board: 5c4c6dqs
Hand Equity Wins Ties
6c7c 31.82% 42 0
55 68.18% 90 0

Well it depends. This is more of a range analysis question. If your opponent is capable of shipping it in like this on the turn w/ a weaker hand (like his own draw), you probably should call. Remember, when determining pot equity, sometimes you have to remember that you may have the best hand.

This is not an exact probability problem but it can become a reasonably good approximate one if you provide data like how we got to that 2x all in, in as much detail as possible and any prior history or recent tilt/duels etc.

You see 2x pot is more like a bold move that happens due to tilt or because he has the image to get paid by opponent's suspected tilt (lol) or because he has a big draw himself that dosnt mind getting called but he will be glad if you folded too (or he doesnt have a big draw but the draw he has can still win it and he has sensed you are not strong). Or he may think you are weak and fold over 50% and he can get away even with a small draw or a top pair and some flush blocker etc (basically legitimate , to manipulative, to game theory ideas). But it can be also a bad player or some guy that is afraid to let it continue with a good but vulnerable hand (still debatable if its the best choice for him).

Basically give us positions, preflop action, flop, bets if any at turn from you ie what happened at turn to get him to do that and how fast it happened. Some people once they see a board start looking problematic they may represent the made hand to scare opponent (still debatable if good idea). Here he may be posing for 78 and instead have 56 that is afraid to continue. But he can also have a ton of other hands that would play this way and this is why we need the data asked. I mean imagine from the non top hands he can even have AcQc or Ac3c or 8c9c or Q7s or Q3s (some of which are junk if prior action doesnt make sense to have them here). Basically ton more hands pending your data.


But think in terms of some math here in general to see why;

Lets say he imagines you fold some fraction f and if you call he is bad but has still some equity e. How does this connect e and f for his move to be plus EV (but not necessarily better than other alternatives)?

If you fold he picks up x and goes to 2x+x=3x. If you call he has a fraction e on 5x pot. He has 2x left so for this to make sense he must have 2x<3x*f+(1-f)*e*5x or e>1/5*(2-3f)/(1-f) (still of course not playing that way and checking or betting little may be a better option than this)

So if he thinks you fold 50% of the time he must have e>20% (very small requirement in equity actually all draws semi bluffs have it vs top hands and more). If he thinks you fold more that 66.7% of the time he doesnt even care what equity he has, he can have a total nothing hand or the stupidest draw (ie top pair draw lol) or blockers to enhance the chance you cant call. If he thinks you fold only 30% he needs to have e>31.4%. That is till small equity requirement for such frequent 70% calling.

See, from his perspective all he needs is to know you fold some 50% or better and he can get away with small draws too.

From your perspective you need to have equity e such that 2x<e*5x or e>40% vs his pushing range. You may have that here if he is game theoretically wide likely but only barely it seems.


We can now try to solve this game theoretically and see what hands he must have to push and what is your response.

That might be a good chance to make it more mathematically interesting project that may apply to other poker spots too and worthy of a probability thread.


Now that i think about it, that may be a very exploitative of other weaker players push that sees them fold too often here with a ton of hands that have some equity or blockers of other big hands to make the folding more likely. If the guy knows opponent folds often due to prior history and behavior in the hand, the game theoretically pushing range here can get pretty wide i think to force significant profits if the other guy is not responding also with game theoretically balanced range and folds a lot, giving credit where he shouldn't.


Start by asking yourself also what hands do you call with without overthinking it and what with a bit of debate (and see how often they are in your range for his push to start making sense to be real wide here even). If you havent shown a lot of strength before this may be a significant fold probability for him here to get away wide. If draws and mid pairs fold here and your preflop range is not very strong in his eyes i can see a good player wanting to push you around here with unmade hands. I know a lot of people that might even see a fold with many QX here vs opponents they dont have a reason to think are loose enough.