Hi all. So I am a live 1-2 player who has logged about 3000 hours. While my win rate is 7 BB/hour I am embarrassed to have never really mastered some of the basic math so I am trying to fix that now. Below are three hands that I analyzed the math on but I'm worried I could have made mistakes... Does anything seem glaring? Are there better methods than mine? Thanks so much!

HAND 1: I flop a set and get drawn out on but mostly just want to confirm my pf play was alright.
UTG player raises to 10. Two players call. I call with pocket 7s from hijack . CO goes all in for 37, button folds, 2 others call and I call the additional 27 to close out action pre flop. Now there is 160 in the middle and 3 of us in a dry side pot and I flop my set on a 672 rainboard. PFR (a LAG) bets $30. I call. Amd 4th player folds. Now we're heads up in the $60 side pot. Turn comes 9 and he checks.. I bet $60 with 85 behind. Board is not at all scary except for that the 9 could complete a T8 straight draw. On river he bets all in and I call and he has made a runner runner flush with T9. What are you gonna do?
Maybe I could've 3bet pre? Probably I should've raised that flop bet smallish to get things going? In this particular case he would've folded his gutshot but with any other piece or with better overcards he couldve called a smallish raise.
My equity pf was 27/(10+27+37+37+37+10)=17%
Because odds of flopping a set is 12% I almost have direct odds already and even if my implied odds were low I almost always have some so this pf call is easy all day. Plus I close action.
My first pf call (for $10) had odds of 10/(10+10+10+1+2)=30% equity which seems decent when factoring implied odds and since my stack was 215 I had 20x raise size (following the rule of 20) so even if I thought this would play heads up I still had odds to call.
Does that reasoning all make sense?

HAND 2: I call off with K5 clubs on Tc5h3c flop against strangely played AA and want to make sure I had the odds to call.
Maniac raises to 12 from EP. Tight calls from MP. I call from MP. Loose calls from LP. Maniac leads flop for 30. Tight calls. I jack to 115. Loose folds. Maniac calls. Tight player jams for 390. I tank
and call. Maniac had about 125 behind which made the call feel easier. (because he would surely call off with his good odds (even though he actually ended up folding)).
Why did tightplayer not pop preflop? I tend to 3 bet a lot but his trap was pretty bold given that he was likely to face multiple opponents. Why didn't he pop the first flop bet? His play was so confusing he confused himself and had to tank before jamming which made me think he could have ace high flush draw but mostly I just had to put him on set. How was my call against AA? How was my
call against (theoretical) set? How much difference made if maniac calls?
I'm 30% against sets, 50% against 2 pairs or single pairs 6 and up or any ace high flush draw, 75% against open ender and 90% against any pair worse than my 5.
My odds were 275/(275+390+115+30+50)=32%. Does this mean that I could (almost) call even if I knew for a fact that he had a set? And because there's any chance that he might not have a set I absolutely have to call?

Hand 3: Theoretical flush draw.
Say I flop a four flush in a $100 pot and am heads up and my opponent jams (and also for the sake of argument that I don't have pair outs but that all my fd outs are clean (opponent can't fill up or overflush me). How much can I call? I have 35% equity here right? Can I then make an equation of x/(x+x+100)=0.35 where x is the most that I can call? In this case it would be $116. Any simpler ways to do this math in the moment than with this formula? Also when I do the same math for the turn (when my equity drops to 19%) this equation it shows that I can only call $32 which seems a little crazy compared to the amount I could call on the flop. Does this drop from 116 to 32 make sense?
And I guess the equation that I'm using as I understand it is (price of call)/(price of call + all the winnable money that's already in). Decimal numbers seem messy for mental math but perhaps most just think in ratios instead? And what would that look like?

Thanks all! My first post here so don't tear me up too much pls.

On hand 1 you've barely got a pot sized bet left so jam over the bet, it'd be unusual for him to bluff at a dry side pot so get it in

2 is spew at every stage

3 you can call about a pot bet

I'd probably raise the flop in hand 1. I don't mind just calling with a set on a dry board but not when villain bets such a tiny amount relative to the size of the pot.

fold pre in a hand 2.

Hand #1 ... A very typical spot for a 1/2 table. Really no right or wrong here, but nothing you do is fully 'right' either.

1) You have the set odds correct at 8 to 1 (12%) ... so why did you call $26 to win $136? Typically with set mining you want anywhere from 10-16x 'potential' since you do lose occasionally when you Flop a set. So you 'technically' needed to get almost an additional $100 into the pot 'to break even' on the call. Were you confident that was going to happen? Typically the lower the pair, the higher 'potential' winnings you need to justify the call. Also, most Players don't want to put in 13.5bb to set mine, even if they have the right implied odds, so lets keep that to about 5-8bb where our opponents don't have to go all-in to justify our investment.

2) Did you feel comfortable against the all-in range (and the 'calling' ranges of the other 2 opponents)? If so, then you can 4-bet or shove PF to try and isolate. If the other 2 opponents fold then there's plenty of dead chips in there to justify a low risk (13.5bb) flip ... which you are a slight favorite to win in most cases. You are actually slightly +EV against AA here (26/160 is 16%) if the other 2 Players fold.

3) You Flop a set, YES! But the Board is funky connected and a guy tries to blocker bet you. I'm all for getting that side pot going in order to 'recover' my investment in the main if I lose to the all-in. So I might just call here, but I'm making sure that a steeper price is paid on the Turn if I don't 'raise for value' on the Flop. Sure, you bet 'pot' ... side pot that is ... but you gave your opponent 4.67 to 1 (60 to win 280) to win it all on any drawing hand, which he did. Your not going to get that additional $85 from most opponents on a blank River, so you're better off trying to get it into the pot quicker, especially against 'a maniac'. Maniacs generally aren't stupid in that they aren't going to just donate to you on a River blank ... but they will take your donation when they hit!

So shoving FP is probably the better play here, where you are roughly 19-52% to win in most cases and maybe crushing 22-66! Variance got you in the side pot, but you made it too easy to continue as well. GL

Hand #2 .. This will 'always' be considered a spew on this site. Posters here will heavily lean towards keeping you out of jail rather than tell what to do while your in jail or how to get out of jail!! Let's take a look at it anyway ...

KxXx, even when suited, is a hand you need to be ready to fold. And even when you Flop well you are wide open to getting out drawn on Turn and River. So the idea of playing a hand 'full speed' for 200bb with this holding is pretty scary unless your bankroll is plenty deep!!

1) You flat PF .. whatever .. 1/2 Players are going to do it.
2) You Flop pretty damn well but it's really just bottom pair and a nutty draw.

3) Bet, call, decision time. The safer route is the obvious call here. You're getting almost 4 to 1 to draw to the flush and if you hit 2 pair against Mr. Tight's AK over-call you might win a decent pot. But will you get paid when the flush hits? And why not get rid of Mr. Tight in lieu of keeping Mr. Maniac? But you also have position on both of them .. Ugh, what to do?

4) I think your semi-bluff raise sizing is pretty close but could've been slightly higher. Your actual raise is 85 into 140, giving 2.67 to 1 to a caller. That's not crazy, but if Mr. Maniac calls he now gives Mr. Tight even better odds to stick around. IMO Mr. Maniac generally will call any size bet if he's going to stick around, so let's put a little more juice into our raise and not give Mr. Tight as good of odds to call. It's pretty hard to fold at this point in time so let's set our price a little higher to generate more folds than calls.

5) After Mr. M calls Mr. T sees he will only have a 60% pot bet behind if he calls, so he shoves ... presumably with the best hand ... and we are now faced with a decision. A decision we should've already thought about before we raised here. We need to call $275 to win $1005 (27%) and Mr. M might add more chips if he calls as well. This is a pretty easy call at this point in time as we are roughly 50% against AA-JJ and 30% against sets with our 2 pair/trips and flush draws.

So again, 'as played' on the Flop with your semi-bluff and all-in call I'm not really going to say 'bad play' based on the spot in front of you. But the issue is being in that spot to begin with and what are you really gaining long term if you continue to press these types of spots.

Let's look at the simple math ... You were either 50% or 30% to win, so that averages to 40% and you got your chips in at 27%, so an EV of +13%. So you are risking $400 to gain $52 in the long run!! How deep does your bankroll need to be to chase that gain in that scenario? That's where the 'spew' label comes from. GL

PS ... If the flush hits the Turn and they both (or all three) fold to your bet, you win $96-126 and only invested $42 to do it ... which spot looks better?


PSS .. Hand #3 .. Yes, you can call a pot-sized bet and 'break even' but are you looking to break even? No, so you might want to limit your calls to 2/3-3/4 pots or less so you can see a 'real' gain in the long run in these spots.

A couple of things. You seem to be using 'odds' and 'equity' interchangeably. While they are related concepts, they are not the same. Odds are the ratio of negative events to positive events. Equity is positive events divided by total events.

Second, when asking someone to check your math, it helps quite a bit to first describe what your calculations are trying to show or what you are trying to do, and then second, break out your calculations into separate lines, with annotation. Trying to reconstruct the action and figure out what each value means to check the statement "My odds were 275/(275+390+115+30+50)=32%" is more effort than most people are willing to do.

Now, regarding your math. Let's take your calculations in hand 1

"My equity pf was 27/(10+27+37+37+37+10)=17%"

So, this statement represents a misunderstanding of what equity is. Equity is the percentage of the pot that you 'own' based on your likelihood of winning. What you have calculated in the above line is not equity. You have calculated the equity required for your action to be EV neutral over the long run. (I am assuming that the denominator represents the total amount of the pot, including your action, that you would win. I am too lazy right now to figure out what 10+27+37+37+37+10 represents). Equity is determined by the cards in play, not by the betting action.

Not sure what you're doing here but this is wrong. You work out your equity by firstly assigning your opponent a range of hands, and working out how we fair.

If we think villain UTG has AQs+, TT+ for example, we would have 31% vs his range here with 77. This spot is a bit trickier with added opponents but we then look at the pot odds we're getting and work out if we think the call is profitable. There are added factors of course, but that is a basic explanation for you to work with.