Omaha Hi: Playing unpaired starting hands

[Buzz]

TV Dad - Let me try again.

I responded in terms of you catching a pair on the board that matched the rank of one of the four cards in your hand.

But you're really interested in someone else drawing out on you when you have made a straight. You're really interested in an opponent who would be calling your bet on the third betting round and needing the board to pair to beat you.

Let's make up a sample hand for you, make up a sample board, and then consider the possibilities.

You can probably immediately see there will be some variability in terms of overlap of cards in your own hand with the board, and also in terms of exactly what an opponent might hold. (At this point someone could have a set, two pairs, three pairs, or four pairs).

Suppose you hold Ad-Kc-Qc-Jd and the board is Td-9h-8c-4s. The only way someone could beat you here would be for the board to pair. Further suppose that your one opponent has a set of tens, having started with something like As-Ah-Ts-Th.

If the board pairs, then you lose. If not, you win.

There are three missing fours, three missing eights, three missing nines, and one missing ten - any one of which would pair the board. Looks like your one opponent has ten outs. On the other hand, there are 30 missing cards that do not pair the board.

Thus the hand odds are 30 to 10 or 3 to 1 in your favor. Notice that if your one opponent has two pairs, three pairs, or four pairs, the odds are even more in your favor. Notice also that if you have more that one opponent drawing for a board pair on the river, the odds are even more in your favor. Notice also that if you have any cards the same rank as cards on the board, the odds are even more in your favor.

The board will have exactly one pair roughly 42% the time (not quite 50%), from the standpoint of someone standing on the rail who cannot see anybody's individual hand. (1098240/2598960). However, that isn't helpful here because it doesn't take into account the cards in your or your opponent's hands.

O.K. Now I've got it (I think). What you really want to know is how often the board will pair on the river when you already have a straight and someone is hoping for a pair so as to make a full house or quads.

If that's it, I think you're at least a three to one favorite.

Bet the straight and take it with a grain of salt the one time out of four when the board pairs.

Just my opinion.

Buzz

[ThinkQuick]

Buzz helped me see my mistakes: ie. subtraction and ignoring some basic card probability theory.
however, searching back I found Bozeman give the number 49.2% with no explanation here

Is one of you in error? Or do those numbers represent different things?

[Buzz]

ThinkQuick - They represent two different things. If you have no knowledge of the cards in any individual hand, there are 1281072 ways for the board to have:
one pair (1098240),
two pairs (123552),
three of a kind (54912),
a full house (3744), or
four of a kind (624).

The total of these is 1281072, which is 49.2% of 2598960.

Maybe I'm wrong, but I don't think that's quite what TV Dad was asking for here.

Buzz

[Ed Miller]

...for a question that said to ignore it if a pair doesn't hit the board half the time.

I'm too lazy to do the math, but a pair hits the board more like 20% of the time than 50%.

EDIT: Nevermind. I'm obnoxious and wrong. A pair FLOPS like 20% of the time. There will be a pair by the river much more often.

[tvdad]

Buzz, thanks for the calculations. You answered many of my questions, and a few I hadn't even asked yet.

The 42% figure is probably closer to what I'm looking for (ie. one pair hitting the board.) If two pairs or a set (that don't match me) hit the board, then my four unpaired hole cards are probably in big trouble and I can get out cheaply. And quads and boats appear on the board so infrequently that they can be ignored for all practical purposes here.

But the replies I have received so far seem to be assuming that I have already seen the flop. What I really want to know is, if there are 5-6 people playing every hand, as is the case in most of the low limit games I play, then how strong is a non-paired starting hand (ie. AKQJ)?

If I hit the straight on the flop, I can practically be sure that at least one of the other players has two pair or a set. It just makes sense that people playing any sort of reasonable starting hands will have some high cards and/or pairs. So if the flop comes QJT or JT9, I'm almost positive at least one player has TT, 99, QJ, or an overpair. If there's also a flush draw on the board (that I don't have) then I'm in even bigger trouble. I don't like my chances in any of these cases. My only chance is to dodge the flush and the board pairing.

If I flop the nut flush, I'm probably not going to get any callers unless the flop contains cards giving an opponent a set or two pair. Since I've got two high suited cards already, that would mean an opponent who flopped a set would have to have either a smaller pair or the 2 case high cards pair, or he could have two pairs. Example: If I've got AsQsKdJh, and the board comes 9s6s4s, then an opponent would have to have 99, 66, 44, or the more unlikely 96, 94 or 64. A flop like JsKs4h would be worse, since the odds are better that someone has a set of jacks or kings based on people calling preflop with higher cards (of course it also gives me the groovy 1-out Royal draw.) So with so many preflop callers very likely having flopped sets or 2-pair, am I happy with my nut flush? If the odds are 3:1 against the board pairing on either the turn or river, then I guess I should be quite happy, but they seem to be hitting at a much higher frequency than that. Of course, it could also be selective memory on my part. I just know that I lose an awful lot of flushes in this case.

This is the sort of thing I'm thinking about when I've got four high unpaired hole cards and I know 5-6 people are going to see the flop. So my question again: Is it worth it to play hands like AKQJ in this situation when I know the board will end up paired 42% of the time?

Thanks for sticking with me while I try to get my point across here. [img]/images/graemlins/smile.gif[/img]

T

[tvdad]

It's true that I don't need a pair in my hand to make a boat or quads, but what are the odds that I'll catch a perfect board like that? And if I do catch one, haven't I crippled the deck to the point where nobody will call me?

But of course a small win is better than a big loss so I'd take it.

T

[chaos]

If you flop the nut flush I think you will get some action from the second nut flush since this is a low limit game you are playing in. Also people tend to give you action with straight flush draws.

If you've got AsQsKdJh, and the board comes 9s6s4s, someone with the Ks and another spade, 8s7s, 7s5s, or 5s3s are likely to give you action as well as the two pair and set type hands. Depending on the quality of players you may even get action from the third nut or lesser flushes.

[Buzz]

"So my question again: Is it worth it to play hands like AKQJ in this situation when I know the board will end up paired 42% of the time?"

TV Dad - A paired board is not necessarily a bad thing for AKQJ. Some of the time when the board ends up paired, it will be with cards that make a full house for you. For example, AKQJ is the nuts when the board is KKJ75 or KJJ75.

I think suitedness is important in answering your question - but you have omitted it.

AcKdQdJc is clearly a stronger starting hand than AcKdQhJs - and there are various gradations between these two extremes.

Looks to me like there are an even fifteen different AKQJ hands when you consider suitedness. At least I can find fifteen that are different from each other, as shown below:

1. AcKcQcJc
2. AcKcQcJs
3. AcKcQsJc
4. AcKsQcJc
5. AsKcQcJc
6. AcKsQsJc
7. AcKsQcJs
8. AcKcQsJs
9. AcKsQhJc
10. AcKsQcJh
11. AcKcQsJh
12. AsKcQhJc
13. AsKcQcJh
14. AsKhQcJc
15. AcKsQhJd

You ask if AKQJ is playable. Which AKQJ?

• #6, #7, and #8, the double suited ones, are definitely playable.
• #9, #10, and #11, all single suited to the ace with only one card, are definitely playable.
• #2, #3, and #4, all single suited to the ace with two cards, though they make a flush approximately 28% less than #9, #10, and #11, are still definitely playable.
• #1 is single suited to the ace with three cards. You’ll make a flush with it approximately 45.1% less than when the acer is only suited to one card. (67284/122562)

----All ten hand types above are suited to the ace----The hand types below are suited to the king, suited to the queen, or non-suited. Being suited to the king still adds value to a hand, but not as much as being suited to the ace. Being suited to the queen also adds value, but less than being suited to the king. If you can get a read on your opponents, you might be able to tell when you are up against a suited ace, but it’s almost impossible to determine when you are up against a suited king.

• #12 and #13, both single suited to the king with only one card, still seem playable, though they are clearly not as good as #9, #10, and #11. The danger is making a king flush but being up against an ace flush.
• #5, single suited to the king with two cards, makes a flush approximately 24.5% less than #12 and #13, but also has less chance of being up against an ace flush. I think it’s playable.
(92592/122562)

• #14, single suited to the queen with one card, is better than non-suited, but not by much. You don’t want to be drawing to a queen flush after a flop with two cards in your queen flush suit, but if you’re drawing to a straight and then make the straight on the turn, and also pick up a flush draw on the turn, having a suited queen gives you a bit of protection against anyone who would make a baby flush on the river to negate your staight. (For example, you hold AsKhQcJc, the flop is JdTh6c and the turn is 9c - you’d rather have the suited queen here than not).

• #15 is non-suited (rainbow). Non suited hands are simply not as good as suited hands.

As to whether or not #15 is playable for you, I don’t know the answer. I think it may depend how you compare to your opponents, and maybe also on some other factors such as position.

Buzz

[tvdad]

Thanks again for the detailed reply, Buzz. This has all been very helpful to me. I always hear people talking about how any four face cards are a great starting hand in Omaha Hi, but I think my suspicions about being careful with hands like that at lower limit tables are proving correct. I would really prefer the A to be suited, and better yet I'd like to have a pair among the high cards.

I play pretty tight already, but I think I might tighten up even more. Now I know why it's been said that winning at Omaha can be extremely boring. [img]/images/graemlins/smile.gif[/img]

T

[Phat Mack]

Forgive me if that sounds impertinent, but I don't believe you are thinking about Omaha hi correctly. Omaha, like hold 'em-but even more so, is a flop game. The hand you play will be made of nine cards; four in your hand and five on the board. The first betting round is after you've seen four cards, or 44% of the total; the second betting round after you see 7/9, or 78%; third round after you see 8/9 or 89%; and the final round after you see 9/9 or 100%.

As you can see, the greatest increase in information comes on the flop. For this reason, I think the flop is where a lot of crucial decisions should be made. You're asking how many complete boards have pairs, I think with the intent of deciding whether to play four big unranked cards before the flop. But if the flop contains a pair that doesn't give you trips, in lo limit no foldem omaha, it's a no-brainer: you can toss the hand. So you should be asking if you can play them after an unpaired flop.

If you hit a straight or a flush, you want to know the probability of a pair coming on 4th or 5th street, so you'll know the odds of getting sucked out on. Once you know this, you can gage the profitability of continuing with the hand.

So the question you should be asking is, "If the board comes three different ranks, what is the probability that the board will pair on 4th or 5th street?" The answer depends on what you have in your hand, and what you assume your opponents have in theirs.

Another fun question to ask would be, "If I have four unpaired cards ten or higher, and I flop two pair, what are the odds I'll have the best hand at the end?"