Implied odds spot quiz

We have 10 outs on the river - about 4:1 odds needed to call. By my math, effective stack at this point is 76BB. If villain bets 35bb we need to win 140. Pot would be 88.8 and villain had 41 left for a total of 129.8 - not enough. For 30 the numbers are 120 needed and 129.8 possible, so we might justify calling 30 if we’re pretty sure villain calls a river shove. Pot at this point is 53.8 so 30 is 55.7% of the pot. Since you give 50 and 75 as choices I am going with 50

I think that's a decent crack at it stremba. I don't know the answer. We probably have to start letting it go b60+ is my guess.

V bet 53% or thereabouts and i called, which made me realise I know basically fa about implied odds. Brilliant donk

If SB always has a flush and always pays you off when you hit a FH, the breakeven turn call is around 40BB before considering rake, so that would let you call ~75% on the turn.

You can look at it like you're calling X amount to win the pot+ the effective stack, which is 132BB.

Agree with the second part. But when we add v's remaining stack to the final pot/pot odds formula (54+76=130), I get these figures:

v b50 = 25/130 = 19% pot odds req
v b75 = 37.6/130 = 29% pot odds req

Vs a pure flush range 4h4s has ~22.5%

So correct answer is somewhere between b50-b60?

No.

When You call a bet of 1 into a pot of 1, you need to win 33% and not 50% because your call becomes part of the pot, and you need to win that back to break even.

yeah but 1 x 1 = 2

Am I missing something? The hand history says SB has a 102.4BB stack. That is the effective stack; I’m not sure how you got 132bb.

There are a number of ways you can solve this. I'll do it in a way that is easier to visualize. We'll start with our knowns and stated assumptions

1. Hero has 44 on Ac3s4cTc

2. Pot is 53.8bb

3. Villain has 76.0bb behind

4. Rake is ~0

5. Villain always has a flush, but never has a flush containing a 3c

6. Villain will get it in on *every* river no matter what

Hero wants to know what bet size he can profitably call on the turn under the assumptions listed above.

We'll say villain has exactly two clubs and never the 3c. This means hero has exactly 10 outs to improve on the river and there are 8 known cards... so 10/44 of the time he will win.

When we call the following things can happen:

1. We call and lose our call amount, X, at a 34/44 frequency

2. We call and win 53.8+76.0 (10/44)% --> we don't include the amount we're calling here

EV =(10/44)*(53.8+76.0) - X*(34/44) = 0

X = 38.176 chips

38.176/53.8 means you can call up to about a 70% psb under the assumptions listed above.

not folding a set to any bet in this spot, but prefer check otf

Re-read the post. The pot + eff stack is around 130.

This may be correct in the realistic situation since we donÂ’t know villain has the flush. In reality he could have 33, KcX, A3s, A4s, AT, or maybe even some other Ax if heÂ’s aggressive. That plus the implied odds when we are behind would probably make calling ok regardless of size. But hero canÂ’t check turn; SB bets X - either call or fold, no check.

OPs question though wasn’t about the realistic decision but rather the hypothetical “assume SB had a flush, how large of a bet can we call?” Calling any size bet is not the correct answer to that one. If we played it 1000 times in an ideal, zero-variance world, we would win 227 times and lose 773 times. From the decision point forward, we would lose X BB when we don’t hit the boat, and we would win 53.8 bb (current pot) plus 78.4 (SBs remaining stack 104.4 to start minus 26 bet PF and otf), for a total of 132.2 bb for each win. Total win is 227 x 132.2 = 30009.4 BB. To break even our losses must equal this. We lose X * 773 total, where X is SB bet ott. X = 30009.4/773 = 38.82 BB. Anything bigger and we must fold. Anything smaller and MAYBE we can call. If villain will always stack off with his flush we can call right up to this size. If villain is good enough to find some folds (especially since we were to assume he had a flush, but not necessarily the nut flush), we must have a smaller sizing to call. 38.82/53.8 = 72.2%, so we certainly cannot call a 75% pot bet. We can probably go a bit larger than 50%, but given the poll choices 50% is the best answer.

EDIT - I missed the “almost always” rather than “always” have a flush. With the “almost always” 75% pot is probably ok. With a realistic range, a larger size probably could be called. I voted 50% in the poll, but I would not argue with anyone saying 75 given the almost always phrasing of the question.

Thanks. I misread that post

I just think this exercise is silly because you have to make a bunch of assumptions that aren't really condusive to playing good poker.

It's not silly at all. It helps one understand the math behind it and get a better understanding of implied odds.

You’ve never taken a science class, have you? To get a good understanding of basic concepts it often is necessary to make simplifying assumptions. To study laws of motion (and end up with the correct ones) for instance we assume frictionless surfaces. Failure to make this simplifying assumption was what led to the mistaken idea that motion in space is inherently different from motion on earth. We look at the planets moving, the sun and moon moving through the sky and they seem to go on forever without slowing down. Nothing on earth behaves this way, so it’s understandable why we thought these different inherently.

In like manner, it would be possible to give villain a realistic range here, give him some shove calling range when we hit our boat and make some calculations as to what sizing we can profitably call. This is needlessly complex though to get at the big picture - how do we go about calculating whether a call is profitable when implied odds are a consideration.

The actual answer here is relatively insignificant. We are not likely to ever have this exact hand, have a villain with this exact range, have exactly the same action on previous streets and have exactly the same effective stack size. What is interesting is the problem solving strategy. That can help us understand how variations in these factors will affect the decision in other spots.

maybe this is just my point of view on poker, but ultimately I don't think poker is a science or an academic discipline. it's about making decisions with varying degrees of belief/probability and you will never be able to "calculate" the right play in any spot. which is why I hate posts like this where we are trying to autistically calculate the exact bet size we can call and the fact that it is a quiz implies that there is a "right" answer.

there is no right answer to any complex spot, only opinions and assumptions.

I wouldn't take my quizzes too seriously mate, or anything i say for that matter

That said.. I didn't know how to figure this out ,and I do now.

I agree to an extent. There is a right answer to a complex spot. You are never going to be able to calculate that right answer while at the table. What you can do is approximate the right answer, and that is undoubtedly beneficial. Like I said above, getting the right answer to this particular spot is completely unimportant. The odds of ever being in an equivalent spot are astronomical. Yet, the odds of facing a similar (but not identical) spot are pretty good. How does changing your hand just a bit, changing your opponent’s range just a bit, varying the bet size just a bit, or changing the stack sizes just a bit affect the decision making? That’s the real value with something like this. And there certainly is value to making some simplifications to make a problem solvable and therefore studyable.

Think about physics as an example. In reality, you cannot EVER use Newtonian gravity to generate an exact solution to a problem. That is because once you add a third body to a situation, the equations are no longer solvable for an exact solution. Therefore we should give up on using Newtonian gravity? Of course not. We used it to predict planetary orbits, launch spacecraft into orbits where we wanted them, send astronauts to the moon, and send probes to other planets. The analogy is the same; it’s too complex to generate exact answers, but exact answers aren’t always needed. Good approximations will often suffice, especially when we have a decent understanding of how those approximations are likely to deviate from the exact answer.

Funnily enough similarish spot positions reversed occurred the very next day:

BTN: 198.4 BB
SB: 102.8 BB
Hero (BB): 159.8 BB
UTG: 65.4 BB
MP: 167.4 BB
CO: 100 BB

SB posts SB 0.4 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has 6♠ 6♦

fold, MP raises to 2.4 BB, fold, fold, fold, Hero calls 1.4 BB

Flop: (5.2 BB, 2 players) 6♣ 8♠ K♣
Hero checks, MP bets 2.8 BB, Hero raises to 9 BB, MP calls 6.2 BB

Turn: (23.2 BB, 2 players) Q♣
Hero checks, MP bets 16 BB, Hero calls 16 BB

River: (55.2 BB, 2 players) 3♥
Hero checks, MP bets 41.4 BB, fold

MP wins 53 BB

(not 100% about river fold, suspect close but ok @ micros)

Anyway point being, in that spot I felt better prepared. Poker is literally the study of deception and yet sometimes people seem wound up when you post fake hands or confected polls/whatever because, well, i guess it's never a nice feeling if you think you've been gotcha'd or manipulated.

But ultimately: spot is a spot, however you get at it. [And if you aren't throwing in the occassional possum hero call into the vast, vast ocean of common fold spots that constitute 8/10 strat posts - you're definitely losing advice EV imo. You want things to remain fresh, advice challenged, and objective. Which can be tough when you're asking for help in such a by-nature prosaic environment.]