Hi (again)

Sadly this hand was played on a mobile so I don't have the exact hand history but it's my reasoning that I'd like checked more than anything else.

1c/2c cash full ring.

Situation is that I've been dealt 99 which I've open raised pre-flop. Got one villain in the pot with me and I'm in position. The flop comes down with a 9 making my set. Happy days I think, villain checks and I bet which Villain calls. Then we get the turn card. Now this card puts the third diamond onto the board and villan wakes up and bets. I have no reason to think that he has not just hit the flush.

At this point I'm not sure what to do. Any flush beats my set (obviously) but I believe that I still have a few outs. I have the last 9 in the deck but I also have 3 board cards that could pair to give me a full house. Two of the board cards are diamonds so if villain has a flush that means each card has 3 outs I can hit. The third board card might be missing the diamond as villain may have it so only giving myself 2 outs on that one. So total of 1+3+3+2=9 outs.

a single shot at 9 outs on the river is 9/46 or roughly 20% chance to hit.
(I think that is right anyway)

If I have a 1 in 5 chance to hit then I need pot odds of 4:1
(again I think this is right)

I can't remember the exact pot odds (curse the lack of mobile hand histories!!!) but for now lets assume it was only 3:1

I decided to call reasoning that if he has made a good flush already there is a good chance (especially at the micro level) that he will bet it again after the river even if the board pairs.

At this point in the hand was that a reasonable line to take? My main concerns are the maths and the assumption.

If my maths is wrong then I better know that sooner rather than later!

Is it 'good play' to assume your opponent will play 'bad'? I've assumed that he will not be looking out for the house on the river and that even when it hits he will bet his flush hard instead of just checking it down or folding to my bet. Should I be giving villain more respect?

I'm not concerned with what actually happened in the hand I'm concerned with my decision making at this point.

It's tough to say without certain details like (a) your preflop position, (b) your preflop raise size, (c) your flop bet size, (d) how long it took the opponent to call the flop, (e) how long it took the opponent to bet the turn, (f) your opponent's turn bet sizing, (g) how big the stacks are, (h) any and all reads on your opponent.

However, I can make a few generalizations:

If your opponent would check raise a flush, as many would, then you have the best hand a large fraction of the time on the turn.

If your opponent would donk bet a flush, you're drawing a large fraction of the time.

If your opponent would make large overbets on the river, as is becoming more and more common vs turn checks, then checking the turn becomes more profitable.

Any deeper analysis would require some more information.

ps, when you have a naked set on the turn, there are 10 cards that help you improve to a full house or better.

Some observations

1. Looking at the way you recount a hand, it is clear that you aren't seeing the whole game(by no means am i trying to be insulting, as we were all beginners once, just trying to help point out blind spots.) Any hand description should include stack sizes, reads and table image, position, and board texture. From your description, for example, we can't evaluate how likely it is that he is betting a missed draw with.

2. I don't follow your logic on why you took an out away from yourself.

3. The concept you are trying to describe is called implied odds. It is the amount of money that you think you can win in the next round of betting should you hit your draw. Some hands have better implied odds than others (flushes, for example, have poor implied odds, as everyone tightens up when the third flush card hits. Sets have great implied odds, as it is hard to read a player as having a set with a redraw to the full house)

4. Leading out on the turn may or may not mean a flush. He may be bluffing a scare card. He may have put you on a c-bet on the previous round. Or he might be leading out to find out where he is with and to protect a small flush. Leading out against a previous aggressor is not always considered strong. (This is called a donk bet)

5. Your math is correct but you are confusing yourself. Either think in terms of odds (the ratio of unfaroable outcomes to favorable outcomes) or in terms of equity (the % of time you win the hand). If you keep going back and forth, you will confuse yourself. In this case, using your number of 9 outs, there are 37 negative outcomes to 9 positive, or roughly 4 to 1. You need to be able to win (including what you estimate he will call on the river) 4 units for every 1 unit of your call.

You're on the right track.

If villain has a flush on the turn, you have ten outs to a boat or quads.

Usually you should call when in position on the turn, partly because villain will often give up on the river and you can showdown a hand that often wins, and partly because you'll suck out and stack villain's flushes.

When villain bets the turn he sometimes has the flush and sometimes he's betting because he does not think you have the flush. He may have a broadway card of that suit, which reduces the possibility that your range contains 2 of that suit since you raised preflop.

No way you fold a set OTT in your example.

If he has the flush, you have 10 outs to beat villain, not 9 (don't forget that the last 9 in the deck helps your hand, too).

Thanks everyone for the responses.

I'll try and address some of the points raised.

I would love to give you all the proper hand history however this hand was played on a mobile phone which does not record them. It was in the middle of my 'lunchtime session' so whilst I remember some of the details I don't want to invent the ones I don't remember for fear of confusing things.

I have no real reads on villain. Without any sort of HUD on the mobile I have nothing but what I saw to go on which was not enough to draw any meaningful conclusions.

These cards will not be correct, for reasons stated above, but I'm sure there wasn't a straight he could have. So after the river we have something like this:

My holding 99
Board: 95102

My reasoning for outs was:
The 9
The 5
The 10
The 2
I discount the 5 reasoning that if he holds 2 cards there is a reasonable chance he already has it and I can't draw it. Of course he might not but I figured reducing the outs was being cautious. This may be a mistake as we never worry about folded cards in the calculations.

Again don't take the cards I've quoted as what was actually there because there is no way I've got it totally correct from memory.

In the absence of other information I've found that in these micro stakes 1c/2c people on the whole tend to love flushes and when they bet them they almost always have them. Again it's not very scientific just based on me losing a lot of hands thinking 'you don't have it...... oh, you do'. Again I was being cautious reasoning that I wanted to figure out how good a position I was in to beat a nut flush and not how good a position I was in beating a flush or a better set, 2 pair, top pair or a bluff.

I'm going to see if I can get at the proper hand history later when I get back to a pc.

One of the things I'm finding hardest to do as a beginner is to try and collect and process all of the information that you guys pick up in the limited time you get to act. I guess it's like anything else. At first it's all too much to do but as you get better it becomes second nature.

I do appreciate the responses though.

You still count the 5d as an out.

There are times to discount "total outs" to likely "good outs", but this isn't one of them.

You would not be making a mistake if you always figure you have at least 20% equity in these sposts, and it's likely you have way more than that.

The best is when the 5d actually lands on the river and Villain thinks he hit gin with his naked Ad.

So I have to ask if I've got this right (despite it being a bit of a derail).

I should have counted the full 10 outs in the example above.

You only discount an out when it's obvious that it would not help you. Best example I can think of now would be:

Holding 99
Board 258K

In this case the 9 doesn't really help us because although it makes our set it puts a flush on the board. (ignoring for now the fact that we could end up splitting the pot if villain holds no themselves)

Is that what you mean?

(actually that's a really rubbish example because if villain holds a diamond we have no outs at all anyway)

Yes. No logical reason to eliminate it. It could possibly be in his hand, but not that likely.

His action could very well indicate a hand like K Jx, and now he has picked up the OESD + FD and he's semi-bluffing to get you off a better hand than his like AK or AJ with no

If only for simplicity, you should just count every card that makes you a hand that beats a flush. If you are in a situation where you know that one of your cards is dead (exposed hand for example) you adjust the numbers.

Also, more information is always appreciated and makes for a better analysis, but in your example the answer is almost always to call the turn and reevaluate on the river.

Estimating odds is not an exact science (especially when you are also estimating implied odds and % of bluffs in villains range). While the 5d may be in some of the combos of made hands, it isn't in enough of them to discount it. So you make the best approximation, which would be to included the 5d as one of your outs.

A situation that comes to mind is that somehow you find yourself with 95 on 987 board and are encountering action. Even though a 6 makes a straight for you, you may not want to count that as an out because it makes a better straight for anyone with a T, or that you are encountering resistance because someone has a 6 for an OESD.

Another case is similar to the example you presented but you have the OESD and there are two to the flush on board. Say you have 8h7h on Kd, 9d, 6c board. In such a case you may not have 8 clean outs. Td and 5d could give someone a flush. Any T could give someone a higher straight. while you don't know exactly what helps or not, you could proceed with the idea you have about 6 or 7 outs.

Ed Miller's book "Small Stakes Hold'em, Winning Big with Expert Play" had a good chapter on discounting total outs to quality outs, if I recall properly.

If you believe he has a flush you should count more than 10 outs. If there are 9 diamonds left that is 36 combinations of which 25% contain the 5d. But that also means that you have 42 cards unknown instead of 44.

So instead of 10/44 or even 9/44, you have (9/42 + 3*10/42)/4 which equates to about 10.2/44. Knowing he has a flush increases your equity, not diminishes.

But that aside, you can't be folding sets too often. I would need bet and stack sizes to know whether river is a good fold here. If it's quite short you could have just shoved the turn and gotten value out of AdTx or QdJx or weirdly played T9 that doesn't want a fourth diamond to come off etc.

Well it appears I have to apologise to you all. I've got hold of the hand history and it's not what I said in my post. My initial question was genuine and I thanks you all for your answers.

Seems I need to get my memory checked!

Here is the real hand which plays out totally differently....

MP3 ($1.60)
CO ($1.81)
Button ($1)
SB ($2.27)
BB ($1.89)
UTG ($2)
UTG+1 ($2.09)
MP1 ($1.24)
Hero (MP2) ($2.26)

Preflop: Hero is MP2 with 9, 9
2 folds, MP1 calls $0.02, Hero raises $0.04, MP3 (poster) calls $0.02, 3 folds, BB calls $0.02, MP1 calls $0.02

Flop: ($0.17) J, 4, 3 (4 players)
BB checks, MP1 checks, Hero checks, MP3 checks

Turn: ($0.17) 9 (4 players)
BB bets $0.08, 1 fold, Hero calls $0.08, MP3 raises $0.16, 1 fold, Hero calls $0.08

River: ($0.57) K (2 players)
Hero checks, MP3 bets $0.38, Hero folds

Total pot: $0.57

Raise bigger pre-flop. Minraising achieves nothing, as it fails to isolate the limper.

Post-flop looks fine/standard. Villain almost always has a flush when he raises the turn, but there's plenty of stack depth to get paid off on the river if the board pairs.