So mathematically, I should never raise without the nuts?

[glass_onion]

I’ve sat down and calcuted a simple table for pot odds so I could reference it while playing online. What the numbers seem to be saying to me is that I should never be betting on a draw hand, even if it is the nuts. The logical extension of this is that anyone betting the flop should have flopped the nuts or they are playing incorrectly (I understand bluffing, semi bluffing, and I am fairly experienced holdem player, but I’m speaking mathematically today, and its not like bluffing the flop in low limit omaha8 would ever work anyway).

Take the Ace high flush draw (4 cards, need 1 more). 9 outs of 45, or a 1:5 shot on the flop. If there is any chance that the low hand will materialize, than you effectively can call it a 1:10, since you will only win 50% of the pot 1 out of every 5 times. So betting this, you'd have to have 11 callers to make it profitable, which is obviously impossible. Moreover, if you don't hit a flush on the turn, and someone holding 3 of a kind is more likely to draw to a full house (10/44) than you are hitting your flush (9/44).

So the only hand I can see to raise on a draw is the uncounterfeitable nut low hand. You have A234, flop is 28. Wonderful. You have 4 outs to the nut low, uncounterfeitable and fairly unlikely to be quartered. So 16 outs divided by 45 is 1:2.81. Unfortunatedly, you are only likely to win the low, so really the math is 1:5.63.
Is my math right first off?

How about my conclusions, comments or suggestions?

[thrillhouse]

Where do you play and what is your screen name??

Seriously, your math is wrong if you think it is only "mathematically correct" to raise with the nuts and never play draws. If you play this way you are playing VERY weak, and you will lose all of your money. Drawing hands can be the most profitable hands you can have if played correctly, which often means raising.
-Thrill

[glass_onion]

I'm not saying I don't play draws, obviously calling with nut flush draws is profitable from a pot odds point of view, but according my my math presented above, it doesn't make sense to raise a nut flush DRAW. Correct me if I'm missing something.

Ok, first we need to aknowledge the difference between raising and calling and its effect on your bottom line - at least as I understand it:

You've got a A-high flush draw on the turn. $100 in the pot, 3-6 game, 3 low cards already on the board. 9outs for the flush divided by 44 cards is a 1:5 chance of filling up, or 20%. So if you bet, you need 5 people to call to break even ON THAT BET. This doesn't even include the fact that you will only win the high, or 50% of the pot, so you should multiply those odds by 2x, so it becomes a 1:10.

Calling someone else's bet, on the other hand, makes absoulutely good sense. A 6, or even $12 bet into you is still paying off, because 5 times 12 equals $60 (again, 1:5 probability), and if you get a few callers the pot will be that big when you hit even with the high/low split.

Correct me if I'm wrong, that's why I posted this math on this board. But don't just flame, back up your assertions with some math.

[Buzz]

glass_onion - The considerations for raising are not the same as the considerations for calling.

To have favorable odds to call a bet when you are drawing, you want the implied pot odds to be greater than the odds against making a winning hand on the draw. (There may already be enough money in the pot to give you favorable odds for calling with a draw).

To have favorable odds to initiate fresh money into the pot when you are on a draw, you need enough opponents who will call your bet or raise on the current betting round. The idea is to have the number of opponents who will call your bet or raise greater than the odds against making your draw.

But there are other reasons for raising besides having favorable odds. For example, if you think your opponents will all fold to your raise, thus conceding you the whole pot, then you might raise for that reason.

When the board is paired, quads is the nuts. When the board has three cards to a straight flush and you don't have a blocking card, a straight flush is the nuts. But these hands are rare enough (although you do see them from time to time) that you probably do better, in general, to largely disregard them. For example, if there is a pair of nines and an ace on the board, and if you hold a pair of aces, quad nines is the nuts - but you're leaving a lot of money on the table if you don't bet your aces full. (If you get raised, the player who is raising is more likely to have a poorer full house than to have quad nines). Similarly when the board is unpaired with the six, eight, and ten of clubs and you hold the ace of clubs plus a small club, you leave a lot of money on the table if, fearing an opponent might be playing a hand with the seven and nine of clubs, you don't bet your ace high flush. (It's much more likely an opponent will pay you off with a non-nut flush than you'll have to pay off an opponent with a straight flush).

I've given a couple of examples of "monster under the bed" hands - but there are other situations where you might bet or raise without the nuts, depending on your read of your opponents. But you do need sensitivity to your opponents to raise without the nuts, in my humble opinion.

You have to keep in mind that flopped nuts are often only temporarly in Omaha. Most notorious in this regard are flopped straights with middle cards. But any straight will often be beaten on the river when the board flushes, and flushes on the turn are often beaten when the board pairs on the river.

On the low end, if you hold A-2-K-K and the flop is 3-4-8, there are six cards that can ruin (counterfeit) your low on the turn, and then if you escape disaster on the turn, the same six cards can counterfeit your nut-low on the river. There's about a 25% chance your flopped nut low, when you hold A-2-K-K and the flop is 3-4-8, will not be the nuts on the river. Here's the math:
1-(39/45)*(38/44) = ~0.25

But I'm not suggesting you should not bet your A-2-K-K when the flop is 3-4-8. On the contrary, I think you bet and raise with that hand/flop combination. Your object is to cow your opponents into folding before the showdown, thus conceding the whole pot to you.

(I'll concede there are some dangers here. In addition, obviously you don't try a tactic that simply won't work on the opponents at the particular table at which you are seated).

[ QUOTE ]
anyone betting the flop should have flopped the nuts or they are playing incorrectly

[/ QUOTE ]

Wrong, in my humble opinion.

[ QUOTE ]
but I’m speaking mathematically today

[/ QUOTE ]

Me too.

[ QUOTE ]
If there is any chance that the low hand will materialize, than you effectively can call it a 1:10, since you will only win 50% of the pot 1 out of every 5 times.

[/ QUOTE ]

Seems, at first, as though the math should work that simply, but I don't think it quite does.

[ QUOTE ]
So betting this, you'd have to have 11 callers to make it profitable, which is obviously impossible.

[/ QUOTE ]

There are some other considerations. Usually when you flop the nut flush draw, if you're selective about your starting hands, you'll also have some shot at low. Also, you might bet the flush draw on the flop to make it a little bit less obvious you have made the flush when the flush is enabled on the turn or river. There's a lot more here too.

[ QUOTE ]
Moreover, if you don't hit a flush on the turn, and someone holding 3 of a kind is more likely to draw to a full house (10/44) than you are hitting your flush (9/44).

[/ QUOTE ]

Good point! In fact, two of your flush outs will also pair the board here, so that you only have a 7/44 chance of hitting your flush without the board pairing too. And therefore, you might not want to bet or raise after the turn with only a nut flush draw. But in a limit game, there probably will be enough money already in the pot, and that, plus what you can expect to get from your opponents if you make the winning hand, probably makes the odds favorable for calling a bet and drawing for the flush. (I wrote "probably," but you really need to consider these calls with a drawing hand on a case by case basis. It's possible, even likely, especially in a very tight game where you end up heads-up against one opponent, that you wouldn't have favoarable odds to draw).

I agree with you that you should not generally raise on the third betting round with only a flush draw.

[ QUOTE ]
So the only hand I can see to raise on a draw is the uncounterfeitable nut low hand.

[/ QUOTE ]

I strongly disagree.

[ QUOTE ]
You have A234, flop is 28. Wonderful. You have 4 outs to the nut low, uncounterfeitable and fairly unlikely to be quartered.

[/ QUOTE ]

Well....no. Sorry to be blunt, but you're pretty much entirely wrong here.

[ QUOTE ]
So 16 outs divided by 45 is 1:2.81. Unfortunatedly, you are only likely to win the low, so really the math is 1:5.63. Is my math right

[/ QUOTE ]

No. But it's a common mistake.

When you're drawing, an out for half the pot is worth less than half of a scoop out. May not intuitively seem to you like it should be that way, but it is. Fairly easy to demonstrate to you.

Put seven white chips into the pot to represent what you can win if you scoop. Now add one red chip to represent your investment on the current betting round. You get your own investment back and you win seven chips when you scoop.

Now divide the pot in half and award yourself the half with the red chip. After you subtract your own investment, how much do you actually win?

Do you <font color="white">_</font>win half as much with a one-way hand in a split pot as you win when you scoop?

Buzz

[Buzz]

glass_onion - Seems like you have a good handle on things. I wrote my first reply before reading your response to Thrillhouse.

[ QUOTE ]
according my my math presented above, it doesn't make sense to raise a nut flush DRAW. Correct me if I'm missing something.

[/ QUOTE ]

Maybe you're missing a couple of things. First, there isn't necessarily someone out there with three of a kind. Second, you probably have something else going for the hand besides just the flush draw. Third, you disguise your play a bit by betting before the flush gets there. Opponents may suspect you have the nut flush draw, but they can't tell for sure whether you have top set or a flush draw (or something else) when you bet a flop with two cards in your flush suit. Then when your flush comes in on the turn or river, your opponents aren't quite as sure you actually have the flush. It's also a way of disguising top set on a flop with two flush cards. If you only bet with top set here, your astute opponents can more easily put you on cards.

Of course if you don't have any opponents who try to put you on cards, then maybe it's a moot point.

The free card ploy doesn't work nearly as well in Omaha-8 as it does in Texas hold 'em, but it does work sometimes. If you bet the flush draw on the flop, your opponents may check to you on the turn when the bet limits have doubled. Thus you may save a big bet on the turn by betting or raising on the flop. (This ploy is very dependent on the particular opponents seated at your table).

[ QUOTE ]
So if you bet, you need 5 people to call to break even ON THAT BET.

[/ QUOTE ]

Yep.

Note there are also some other considerations that may be involved in betting or raising.

[ QUOTE ]
This doesn't even include the fact that you will only win the high, or 50% of the pot, so you should multiply those odds by 2x, so it becomes a 1:10.

[/ QUOTE ]

Here we disagree.

[ QUOTE ]
Calling someone else's bet, on the other hand, makes absoulutely good sense. A 6, or even $12 bet into you is still paying off, because 5 times 12 equals $60 (again, 1:5 probability), and if you get a few callers the pot will be that big when you hit even with the high/low split.

[/ QUOTE ]

Yep. Calling is a different deal than betting or raising.

Buzz

[glass_onion]

Hey Buzz,

I appreciate the thoughful response to my post. There are a lot of facts that I have to mull over from your replies, which might take me some time, but I do plan to address them both before sunday is out. You've given me a lot to think about. Appreciate it.

[glass_onion]

Basically, you post comes down to the difference between implied odds and pot odds, which is what I was describing as a difference between profitably betting and profitably calling. Same thing, different terms. Also, I’d like to scope of our discussion be on low limit O8 games, $1-$2 or under, with 60% of players seeing the flop or more, as those are the games I target.

In a nutshell you expanded the raise criteria to:

1). Getting a free card on the turn where betting is more expensive
1a). (an offshoot of 1) adding illusion to your flush if you hit it, upping profitiability
2)forcing folds.

My discussion/comments to each of these are as follows, using an example of AsKs3c4c and a flop of Ah4sQs. Your low is dead. You are drawing to the (current) nut a-high flush. With 5 people in the hand, aside from you, the decision is whether to bet or call. Obviously position matters, since calling the bet will be undoubtably the right decision in a pot odds perspective. However, mathematically, your implied odds (40% chance, 2:5, for likely half the pot) aren’t there.

Raise Criteria 1a): I don’t see too often in low limit O8 that this would work. I’m trying to think of what hands would likely call this bet. Say three of five players call on the low, someone likely has 23 or 24, with one person drawing dead on the low or looking for one out. If 2, 3, 5, or 6 hits I would expect the lows to raise the pot (correctly). Even a 7 or 8 would likely elicit betting. I won’t even go into what the high’s might hold.

Raise Criteria 1b). Similarly, I don’t see this as being too profitable. Low limit O8, you have 3 of the same suit on the board, 90% of the time someone has it. The fact that person one bet the flop and then bets the turn doesn’t mean anything to me. If he has nut low draw, 23, that’s the right move. Also, a person could easily have 3 kind as well as a low flush, or something along those lines.

2). As far as forcing folds, I think this is a good point. A person with a decent low that got counterfeited might fold, as someone with two pairs that didn’t hit, or A high flush draw that didn’t pan out on the river. You can’t give them free cards, understandably, and if they wanted to call and draw dead or on few outs that’s their business.


Also, just so I can understand. In your first post, you disagreed with calling an ace high flush draw a 1:10 shot drawing to the river. I figured, 9/44=20%=1:5, and you are probably only winning half the pot, so 1:10 is more the odds you should be looking at for implied odds for betting. Probably more mathematically speaking, in our example above (board: As4hQh, say Kd turn) 6 cards, maybe even 7, will give someone a low. So just under 50% of the cards will split the pot for you, and you have a 1:5 shot. So maybe 1:7.5 would be closer to the implied odds.

Again, it seems to me, that betting this nut flush draw wouldn’t be the wise choice ever on the turn, but calling it down nearly every time is the path to statistical advantage. I can appreciate your three points about raising above, and in a cardroom or casino where you can read players more effectively than online, and perhaps at $5-$10 limits or up where play tightens a bit, these methods should be employed more often. I will need more convincing that they can be employed effectively at lower limits and especially online, where nuts talk.

-Glass Onion

[Buzz]

[ QUOTE ]
Basically, you post comes down to the difference between implied odds and pot odds, which is what I was describing as a difference between profitably betting and profitably calling. Same thing, different terms.

[/ QUOTE ]

Glass Onion - Have you heard the term “fresh money odds”? That’s the concept I was using for raising in my first post. It’s also the concept you seemed to be using for raising in your 2nd post.

[ QUOTE ]
In a nutshell you expanded the raise criteria to:

1). Getting a free card on the turn where betting is more expensive
1a). (an offshoot of 1) adding illusion to your flush if you hit it, upping profitiability
2)forcing folds.

[/ QUOTE ]

There’s a whole chapter regarding reasons to raise in David Sklansky’s Theory of Poker. I did not intend my suggestion of possible reasons to raise to be limiting. I just tried to come up with a couple of examples of possible reasons to raise. I would imagine there are others.

[ QUOTE ]
My discussion/comments to each of these are as follows, using an example of AsKs3c4c and a flop of Ah4sQs.

[/ QUOTE ]

I’ll respond directly to your example of a hand and a flop. This can’t be exactly what you hoped for, and yet it has possibilities.

I’d like to see a spade or a four on the turn. Of the remaining cards, some are more favorable than others. For example, a king adds some more outs for the river - and they’re all scoop outs.

(An ace on the turn would be good too, although your aces full of fours might lose to an opponent with aces full of queens. But since you seem to be fixated on the nuts, I’m going to leave aces out of my consideration - though normally I might include the three missing aces as outs).

Some of the spade outs are worth more than others. For example the jack, ten, or nine of spades do not enable low, whereas the other spades do. A nice two card combination for you here would be the ten of spades followed by the nine of hearts. That’s better for you than the ten of spades followed by the eight of hearts. There are lots of possibilities here, but to keep it as simple as possible, we think in terms of your primary outs, the three high spades and the three missing fours fall into one category you might call “scoop” outs. The remaining seven spades enable low and therefore are not worth as much as the scoop outs. 45-13 = 32 cards are not particularly helpful.

My method of figuring whether I have odds to call or not involves some approximations and usually works well for me. I’d count the seven low spades as worth three scoop equivalent outs. I’d add these 3 scoop equivalents to the 6 scoop outs and figure roughly 32 to 9 as the scoop equivalent odds against making my hand on the turn. Since there’s also a chance of low on the river even if you catch a “scoop” out on the turn, I’d compute that as a bit more unfavorable, maybe 32 to 8 or 4 to 1 against me.

At this point I’d be counting the whole pot as mine, because I would have already (reasonably) accounted for the possibility of ending up with a split pot by using 32/8, rather than 32/13.

Bottom line: I’d want be reasonably certain that there would be four times as much in the pot at the showdown if the board spaded or paired with fours, as it would cost me to stay for this betting round.

Now let’s see what you have to say about your example hand/flop.

[ QUOTE ]
Your low is dead. You are drawing to the (current) nut a-high flush. With 5 people in the hand, aside from you, the decision is whether to bet or call.

[/ QUOTE ]

Not quite. If someone has already bet, your decision is whether to raise, call, or fold. If nobody has bet, your decision is whether to bet or check.

I’d probably bet if no one had bet yet, and unless seated on the button, I’d probably call if somebody had already bet. Seated on the button, if the first player to act had already bet, I might well raise - or maybe I wouldn’t. Whatever, I wouldn’t do the same thing each time.

[ QUOTE ]
Obviously position matters, since calling the bet will be undoubtably the right decision in a pot odds perspective. However, mathematically, your implied odds (40% chance, 2:5, for likely half the pot) aren’t there.

[/ QUOTE ]

Where did the 40% come from?

Likely half the pot? That’s true, but there are a goodly number of two-card combinations amongst the 990 possible on the turn and river that don’t enable low. There’s about a 23.3% chance of no low, without consideration of whether you win or lose. Here’s the math: (22*21/2)/990 = 0.233.

Likely half the pot, yes, but roughly one showdown out of four the high won’t have to split with the low.

[ QUOTE ]
Raise Criteria 1a): I don’t see too often in low limit O8 that this would work.

[/ QUOTE ]

What you’re calling “Raise Criteria 1a” seems to be what I’m thinking of as disguising your play, part of making yourself more unreadable to opponents.

Gee, I’m always trying to put my opponents on cards and figure out what they’re thinking. And I’m quite certain that some of my opponents are doing the same for me. Looking for patterns in play is part of that.

In my humble opinion, figuring out how your opponents are playing is a very important aspect of poker.

[ QUOTE ]
I’m trying to think of what hands would likely call this bet.

[/ QUOTE ]

Keep in mind that your opponents don’t all think the same as you. And some are looser than others. After a flop of Ah4sQs, hard to say what I’d play. 235X, AAXX, AsXsXnXn for sure - maybe AQQX and KJTX - maybe some others. It would kind of depend. I’m not recommending AQQX and KJTX for play after this flop - but I might play them, depending.

[ QUOTE ]
Say three of five players call on the low, someone likely has 23 or 24, with one person drawing dead on the low or looking for one out.

[/ QUOTE ]

Are we talking about the same flop?

[ QUOTE ]
If 2, 3, 5, or 6 hits I would expect the lows to raise the pot (correctly).

[/ QUOTE ]

I wonder why you write “correctly.” (Don’t tell me. You must think that would be the correct play. But my thinking is it would depend).

[ QUOTE ]
Raise Criteria 1b). Similarly, I don’t see this as being too profitable. Low limit O8, you have 3 of the same suit on the board, 90% of the time someone has it.

[/ QUOTE ]

What is “Raise Criteria 1b”? (The above is the first time I see “Raise Criteria 1b” mentioned).

How did you come up with the 90%?

[ QUOTE ]
The fact that person one bet the flop and then bets the turn doesn’t mean anything to me.

[/ QUOTE ]

It doesn’t mean the same thing for everybody at the table to me.

[ QUOTE ]
Also, a person could easily have 3 kind as well as a low flush, or something along those lines.

[/ QUOTE ]

Agreed. Lots of stuff is possible.

[ QUOTE ]
2). As far as forcing folds, I think this is a good point.

[/ QUOTE ]

Thanks. However, to be honest, I’m not sure it would work very well at $1-$2.

[ QUOTE ]
Also, just so I can understand. In your first post, you disagreed with calling an ace high flush draw a 1:10 shot drawing to the river. I figured, 9/44=20%=1:5, and you are probably only winning half the pot, so 1:10 is more the odds you should be looking at for implied odds for betting.

[/ QUOTE ]

I’m not sure how to respond, other than to write I don’t believe that is the correct way to proceed.

[ QUOTE ]
Again, it seems to me, that betting this nut flush draw wouldn’t be the wise choice ever on the turn,

[/ QUOTE ]

“ever”?

With only a flush draw, I probably would usually be happy to see the river as cheaply as possible. But I can’t say betting the nut flush draw would always be an unwise choice.

Have you heard of the term “semi-bluff”? Betting a flush draw on the turn would be a “semi-bluff.”

I don’t believe in fancy plays, but semi-bluffs don’t seem like fancy plays to me and can be very effective if used sensibly.

[ QUOTE ]
I can appreciate your three points about raising above ..... I will need more convincing that they can be employed effectively at lower limits and especially online, where nuts talk.

[/ QUOTE ]

I’m not trying to convince you of anything. I am just responding honestly to your posts, with the goal of seeking the truth. In the search for the truth, I appreciate different points of view. Thank you for yours.

Buzz

[Beavis68]

One concept that seems to be missing - sorry, I havent taken the time to read everything - is the concept of pot equity. Pot equity is really much simpler in non-split games, but say you are drawing to a nut flush, you are not sure if your Ace will win the pot - you have a 35% chance of hitting your hand by the river, so your pot equity is 35%, if you are against two opponents, it is +EV to raise on the flop as much a possible if they will both call.

[Buzz]

[ QUOTE ]
One concept that seems to be missing - sorry, I havent taken the time to read everything - is the concept of pot equity.

[/ QUOTE ]

Beavis - What you're calling "pot equity" is what I am calling "odds against making your hand" or, for short, "hand odds."

I don't think "hand odds" is my term, but I'm not sure where I got it. A cursory look through the various poker books I have here does not reveal any mention of the term, (but I have some of my books loaned out - maybe there is a mention of "hand odds" in one of them).

[ QUOTE ]
Pot equity is really much simpler in non-split games

[/ QUOTE ]

Yes it is. Much simpler.

How to figure and deal with pot equity, when you combine it with implied pot odds (for calling) or fresh money odds (for raising) for the more complicated split pot situations was the gist of part of the discussion.

But instead of using the term "pot equity," I used the synonym "hand odds."

In the future I'll use both terms.

Buzz