Basically, I'm really working hard to improve my "in-game" math skills, and to be able to mathematically explain why a certain call is correct, etc...

I've recently started reading "Poker Math That Matters" by Owen Gaines.

Hand:
1/3
$250 effective stack

V limps MP.
Hero raises to $15 with KQ
V calls.

($31) Flop 853

V checks.
Hero bets $18.
V calls.

($65) 9

V bets $35. FWIW, I put V on 2pr+ at this point.

Just from experience, I know I have IO to make this call, but now I'm motivated to be able to prove it mathematically...

So referencing charts in "Poker Math That Matters," (page 68 for those who have it and copied below for those who don't) to figure out how much more I'd need to win to make this a profitable call, I did the following rough math at the table:

Figure out my equity: 9 outs = ~18% equity

Our Equity / Multiply his bet by:
35% 2x
25% 3x
20% 4x
15% 6x
10% 9x

Multiplied his bet by 4 = $140

$140 - $100 (current size of pot) = $40 ~ the least amount of money I'd need to make on the river for the call on the turn to show a profit.

Does this look right to everyone? Does anyone else have an easier way to do it?

Also, this is someone of a guess, but how much larger would V's bet have to be on the turn before people consider folding?

I just go 9 outs x 2 + change is 4:1 hand odds (It's actually slightly higher than 18% I think).

Then (I keep track of pot size as the hand develops) say okay its 100:35 direct pot odds, that's a little worse than 3:1 but not much.

Then I go 'I need 4:1 at least to make this call, 4*35 is 140 which is 40 more than the current pot.

So basically my steps are - 1. Calculate hand odds quickly, 2. Calculate pot odds quickly, 3. Calculate how much more I need to shore up the pot odds to make it break even.

Finally I look at their stack to see about how much they have left and think would they part with what I need OTR. To decide that I usually think of absolute bet sizes because people at these stakes think of the dollar amount not the relative amount of the bet to the pot. He just bet 35 so 40 doesn't seem too unlikely a call for him. I call.

With his stack being what it is he'd have to make it 60$ or more before I'd tank.

The first thing is to figure out how many outs you actually have. It's not always 9--in fact, it's usually not 9. Sometimes it's more and sometimes it's less. If you forget about this, you could get yourself into trouble.

When it's more: when your opponent has one pair, at least one of your overcards is live. You'll have 12 or 15 outs--unless he is also killing some of your spades.

When it's less: when your opponent has a set, you have 7 outs. You'll still lose on board-pairing spades. Also if your opponent has a hand like 98, the 9 is not an out, so you'll have 8 outs. When your opponent has a nut flush draw, you have 6 outs--your overcards only.

It's exactly 9 basically when your opponent has a straight, AA or KK, or 85.

So, knowing the math that you wanted your OP to be about is important, but if you get your outs wrong, you'll come to wrong conclusions.

here figure on 8 or 8 1/2 outs. as he can fill up on one of your flush cards.

so much easier to say, he bet 35 and i am a 4 to one(which you are more than) dog so i must make 4 times his bet to call.

but it gets complicated when he makes a full and you make a flush as to how much more you will lose if he bets or raises you. so you have to add some for that, which few do.

then take away cards that can come where you can bluff him off, like straight cards. they may become more outs for you if you think he will fold his two pair to a big bet.

sorry for ruining your simple calculations.

As already stated, some of your outs will pair the board. This is a segue to the concept of "reverse implied odds."

Easy math: You'll receive a flush card 1/5 of the time. With an OESD, you'll get a str8 card 1/6. So with a gutshot it's 1/12.

So with 2 cards to come, you'll get your flush 2/5, your OES 2/6, and your GSS 2/12.

To continue CMV's point, IO isn't just about the math. IO is about figuring how much the villain will call when you hit. For some villains and situations, they won't call if the FD comes in. You can bet anything and he'll just c/f. In that case, you don't have any IO.

So you put V on 2 pair. Maybe he has 98 & saw potential to call the flop with his backdoor flush & str8 draw & 5 outs to 2 pair or better vs. your overpair.

However, he coulda' also turned a str8. In that case, he may have a spade.

Let's assume we have 8 outs to the flush, as he has 98 & he either holds the 9 or, if not, it gives him a boat.

There are 46 unseen cards going into the River, but you "know" he has 98, so there are 44/8 = 5.5. [It can't be hard to immediately see that 8*5 = 40] One of those times you'll make your hand, so you're a 4.5:1 dog.

Also note: If you put 98 into PokerCruncher as V's hand vs. yours, it shows you as a 4.5:1 dog going into the river.

Multiplying your outs by 2 for one street & *4 [-1 for every out over 8] for 2 streets when going all-in, is an approximation that I don't use.

Even if you don't assume what the V has & go with 8 outs into 46 unseen cards, that's 5.75 & one of those times you'll make your hand, so you're a 4.75:1 dog. [I've done this type math for so long that I now know automatically that 8 clean outs going into the river is 4.75:1]

I would need to believe I can make a minimum of 5* [you want to make a profit long term, no?] whatever I have to call in this case, since my 'read' puts him on at least 2 pair, if not a str8.

Now the question, as stated above by others, is will he pay you otr. The answer would be 'yes' [maybe] if he's seen you semi-bluff in this type situation otr with nothing but an overpair when a spade came.

I do not understand what you stated below:

You can't have 9 outs vs. 2 pair unless you put V on 85. Then, and only then are you a 3.89:1 dog & can justify a call making 4x what you put in the pot ott.

9 outs is 19.56% equity not 18%. That makes you a 4.11:1 dog when you don't know what your opponent holds. 3.89:1 is when V has 85 because we now know he doesn't hold a spade and there are 2 more 'seen' cards.

However, at least by using the chart, you're still requiring yourself to make at least 4x what you have to call, which is a slight overlay on your money, IF, V holds 85, or a str8 w/o a & nothing else. That's a good thing.

Why not do it this way:
46/9 = 5.1 & one of those times you'll make your hand.

How hard is it to see [over the table] that 9*5 = 45, leaving 1, so it's 5.1111111111111111111 or 4.11:1 dog [because 1 of those times you'll make your hand]?

Question: If you have 12 outs going into the river, how do you know how much equity you have [off the top of your head at the table] so that you can match that up with your chart above?

You don't have 12*2 =24%

You have 12/46 = 26.08% equity. I wouldn't wanna' have to divide 46 into 12 over the table to figure out my equity.

So, are you going to use the 4x rule [for 20%+ equity] or 3x rule [for 25%+equity] off of his chart?

This would be the case if your V had K8. You would have 12 outs going into the river.

Why not just divide 12 into 46? That's 3 leaving 10. Add a zero & we all know from grade school that 12 goes into 100 8 times, giving us 3.8xx, so we're a 2.8:1 dog.

Multiply what we have to call by 3 so that we make a little money long term & we get 35*3 = $105.

That's a helluva' lot easier, for me anyways, than dividing 46 into 12 to figure out my equity so that I can use your chart above.

Or, I guess you could use the 2*12 rule & add 2% to get the right answer and then use the chart.

However, when does adding 2% still give you the wrong answer?
If you have 13 outs *2 = 26, but your actual equity is 28.26%. So that's still pretty close when adding 2%.

Maybe my way is so easy for me because I've been doing it for so long. Like long b4 no-limit was the game & long b4 you could open a library with all the poker books that have been written.

By the way, if you want to memorize a few numbers that may be helpful in the future: you are a 1.86:1 dog otf to make your flush by the river, and your considering calling a bet that would put you all-in otf. That's if your outs are clean. That doesn't compensate for redraws for your V.

You're a 2.18 dog otf to make your str8 by the river under the same circumstances.

Just think of it as the bet you're facing ($35) needs to be 18% of the money you win (pot after you call + what you get from villain on river). $35 is 18% of $194.44. You need to win $59.44 (135 + 59.44 = 194.44) on the river to break even.

Obv you can round to more even numbers to do it quickly in-game.

from a practical perspective it pays to round things off and then make a decision. and i usually tend to go for it as long as its close for two reasons.

one is that it makes me a caller and they will tend to not try to run me off as much and makes me harder to read.

two is all to often your read is wrong or they are goofy and you have much more the best of it. for instance here say he had tens or jacks and decided it was better to lead with a smaller bet than he would have to call. now you have more outs.
or he had a smaller flush draw and hit the nine or decided to bet with just the draw. you know that people do those things.

Basically just chiming in with others.

1) Estimate your outs. As others have said, estimating on the downside of 8 (instead of 9) is probably a good idea here.

2) Know the odds you need to chase x outers. A 9-outer is about 4:1, a 8-outer is about 5:1 (more-or-less, we don't have to be exact).

3) Figure out what odds you are currently getting to know how much you'll have to make up on the river to breakeven. We're currently getting ~about 3:1 (again, doesn't have to be exact), so if we think we're on an ~8 outer, we'll need to make up ~2 bets to breakeven (i.e. another 2 * $35 = $70).

4) Consider whether you'll make up the rest you need. If you call, the pot will be $135 and we think we need to make up $70 (just a 1/2 PSB, which isn't very large). If we put Villain on a large hand (such as two pair / set / straight) and he's shown that he can payoff bets before (like most low-stakes players do) then he'll probably have a hard time folding to a 3/4 PSB bet of $100 or so. Course we might also have to factor in whether we can fold to a fullhouse if he bets large when our flush comes in.

GcluelessNLnoobG

If you call ott with your 9 out draw an all-in bet HU where the pot gives you 4:1 on your money, you will lose long-term because you are a 4.11:1 dog.

However, if you have no doubt that your V has a set [with a card on board that is the suit of your flush draw] or, has top 2 pair, with the top 2 on the board being of your suit, then you can eliminate the chances of your V having one of your suit in his hand & you're a
44/9 = 4.89 which is 3.89:1 dog.

So, to be safe, I would look to be making money either way & require at 4.25:1 on my money. Even then, if it's a helluva' lotta' money you have to call, do you really want to chase that slim money edge? Probably so, if you have the bankroll to handle the variance and/or you have already put a helluva' lotta' money in the pot.

in gambling every edge you give up adds up over your lifetime and becomes a monster number. you need a real good reason to forgo an edge.