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 and 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.

Pot odds are off in hand 2. It should be:

Assuming maniac folds:
275 over 390 (your net contribution assuming you call) + 390 (main Villain's net contribution) + 115 (maniac's assumed net contribution) + 50 (initial pot size).

Assuming maniac calls.
275 over 390 (your net contribution assuming you call) + 390 (main Villain's net contribution) + 240 (maniac's assumed net contribution) + 50 (initial pot size).

You have the gist of it in hand 1, but it is actually more complicated. On the flop, you only have 32% odds to hit your hand assuming that you get to see both turn and river. This may not be the case if Villain makes another big bet on the turn. I don't have a good answer as to how to make a more accurate version of this calculation.

Disclaimer: i failed brutally at math in high school. To be fair I drink less now than i did back then and have stopped smoking weed alltogether, so give me a chance anyway...


H1: math looks good, enough implied odds to setmine both times. Only thing i want to add is that if CO is so short and likely to shove, you might not get to see a flop that often since the original raiser can still raise to isolate.

No idea why you don't shove turn tho. 145 left i think, with 220 in the middle...

H2: Not sure what is the worse decision preflop, you calling with K5s or MP flatting AA, lol.
Postflop looks good, we are clearly priced in after MP shoves. We want/need some fold equity with these hands tho, since our equity diminishes so much when we brick on the turn (see also H3). So raising flop is muy bueno.

As Aisrael mentioned, you forgot the 115 the maniac put in. Also, we have closer to 28% vs sets, not the 32% we need, but whatever, he apparently has more than enough random pairs to make up for that.

H3: Yes, our $EV drops hard on the turn vs on the flop. Typically we need some implied odds to call turns without a made hand.
I don't particularly like these theoretical hands, since villain is always gonna have a draw or redraw himself some non-zero % of the time, so all these percentages are gonna be off a bit. Also, stacksizes matter a bunch. If villain bets flop with only $32 left behind, we just gii on the flop, obviously. If he has more, we usually gain implied odds on the river and can mostly call $32 on the turn.


Random rant: as a european, I've never understood why americans put there odds in X:Y ratio's. Putting them in percentages feels so much easier to me. Specially when it seems easy to remember a PSB =33%, 1/2 PSB=25%, and (with the rule 4 and 2) 9 outs twice=36%, 9 outs once=18%, etc.
I guess it depends on what your used to.

Thanks! I see my H2 math error. I added maniacs 30 call not his 115 call so:
My odds were 275/(275+390+115+115+50)=29%.
Really I was more math concerned with this post but the strategy advice is super helpful too. Consensus seems to be that K5s is trash and I get that but I'll stand by my semibluff flop raise since it looks like a good spot for fold equity's sake... Probably noone else agrees though and i should've just flatted the 30 instead of bloating things?

Grunch. OP, please put some spaces in your walls of text. It will make them easier to read. I added some.

Hand one: You're using the word equity wrong. Equity is what you have based on your chance of winning the hand. You are actually figuring pot odds, though describing them in percentage, which is fine. It's what I do as it's easier to compare to equity.

You are being asked to pay $27 into a pot of (total, including your call) $131. 27/131=20.6%. You figured it in the correct method, your call divided by total pot, but I think you inflated the pot. Not sure where you are getting $160. It looks like you put the $10 into the pot from the players who called at first and then putting $37 in for when they call the shorty's shove. Just like you, they are only putting in $27 more.

Obviously, you aren't going to flop a set 20% of the time, but I still think it's fine to call given likely IOs. You could also try to isolate with a big raise, as the 2 callers ranges are capped pretty low here and the OR should have re-raised if he had a premium too.

Your first call you forgot to put your money into the pot when you did this. I usually don't include the blinds in my calcs, as they will basically cancel out the rake and it makes things simpler, so your 10 should be divided by a total pot of 40 (OR's 10, 2xcallers 10's, and your 10). Your call represents 25% of the pot.

As you mentioned, the IOs are more important here than the direct odds though. This is a call to set mine all day long.

Hand two: Fold pre AINEC. K5s in MP is hot garbage. AP, never folding OTF but raise is iffy depending on whether Vs actually have fold buttons.

AP with the jam, you are being asked to pay 275 into a pot of 943 (48 pre, Maniac's 115, Tight's 390, your 390), or 29.2% of the pot. If maniac calls, pot will include another 125, so you will need less equity (but also have less, as he'll have some). In that case, you would be paying 25.75%. Again, you have the method right, but seem to be adding money to the pot twice. If maniac called your raise to 115, he put in 115 total, not 115 plus the 30 he originally bet. His call only cost him 85 more.

Against AA, you're laughing. You have 47% equity, way more than you need. Against a range of all the possible sets you have 29.2% equity, exactly the price you need, though it actually depends what set. If he showed you TT, you should theoretically fold and if he showed you 33 you should call.

Realistically, of course, his range is made up of a bunch of things. Let's say Tight's range is Ac9c-AcQc, JcQc, all sets, and 6 combos of overpairs. He's tight, so he shouldn't ever have 2-pair or an open-ender here. Against that range you have 43.9% equity, which is obviously plenty.

If maniac calls, he has the all the draws and a bunch of two pair, but probably no overpairs or sets, as he would have re-raised you himself. Let's start his NFDs at Ac2c and also give him Qc9c+ and 8c9c, give him all the suited two-pair combos and OESD combos. Against those two ranges together, you drop down to 26.8% equity, which is still more than the 25.75% you're paying, though obviously maniac folding a NFD-heavy range is good for you.

I'll do your theoretical on in a separate post, as this is already getting really long.

Hand 3 is approximately correct. Real equities vary a bit depending on holdings and board, but 35% and 19% are about right, and your formula is fine.

What I do at the table is use the rule of 2 and 4, which means that our chance of hitting any given out on any given community card is approximately 2%, so if we are looking for outs with one card to come, multiply number of outs by 2 to get our estimated chance of hitting, and by 4 if we are all in on the flop, as we'll see two cards. So for a bare FD, we have 9 outs, which means that we have about 32% equity in a flop shove situation and 18% in a turn shove, or chance to hit on the turn in a flop call that is not a shove.

These numbers are slightly off, but they work for all numbers of outs, so you can do the same thing with 8 outs for a straight draw, etc. The minor underestimation is fine, IMO, as it somewhat makes up for the times we hit our hand and still lose.

So if I'm at the table with a bare FD facing a shove, I know that I can pay up to about 1/3 of the total pot, which means that if his shove is less than a PSB, I can likely call. Obviously this is a bit more complex in multi-way pots, but it is still math you can do at the table.